{"id":7235,"date":"2024-06-19T18:16:25","date_gmt":"2024-06-19T09:16:25","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=7235"},"modified":"2025-10-31T09:29:06","modified_gmt":"2025-10-31T00:29:06","slug":"%e3%82%b7%e3%83%9f%e3%83%a5%e3%83%ac%e3%83%bc%e3%83%86%e3%83%83%e3%83%89%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8%e3%83%99%e3%82%a4%e3%82%ba%e7%b7%9a%e5%bd%a2%e5%9b%9e%e5%b8%b0","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa","title":{"rendered":"\u30b7\u30df\u30e5\u30ec\u30fc\u30c6\u30c3\u30c9\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3068\u30d9\u30a4\u30ba\u7dda\u5f62\u56de\u5e30\u306b\u3088\u308b\u30d9\u30a4\u30ba\u6700\u9069\u5316"},"content":{"rendered":"<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=6aaf69ec-7ab1-48b4-b1e1-e2f65dce7c24\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" 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href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E7%92%B0%E5%A2%83%E8%A8%AD%E5%AE%9A\" >\u74b0\u5883\u8a2d\u5b9a<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E3%83%A9%E3%82%A4%E3%83%96%E3%83%A9%E3%83%AA%E3%81%AE%E3%82%A4%E3%83%B3%E3%82%B9%E3%83%88%E3%83%BC%E3%83%AB\" >\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E3%83%A9%E3%82%A4%E3%83%96%E3%83%A9%E3%83%AA%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%9D%E3%83%BC%E3%83%88\" >\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30a4\u30f3\u30dd\u30fc\u30c8<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E3%83%A2%E3%83%87%E3%83%AB%E3%83%99%E3%83%BC%E3%82%B9%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%A8%E3%81%AF\" >\u30e2\u30c7\u30eb\u30d9\u30fc\u30b9\u6700\u9069\u5316\u3068\u306f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E4%BB%A3%E7%90%86%E3%83%A2%E3%83%87%E3%83%AB\" >\u4ee3\u7406\u30e2\u30c7\u30eb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#Thompson%E6%8A%BD%E5%87%BA\" >Thompson\u62bd\u51fa<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E3%83%99%E3%82%A4%E3%82%BA%E7%B7%9A%E5%BD%A2%E5%9B%9E%E5%B8%B0\" >\u30d9\u30a4\u30ba\u7dda\u5f62\u56de\u5e30<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E9%A6%AC%E8%B9%84%E5%88%86%E5%B8%83%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\" >\u99ac\u8e44\u5206\u5e03\u306e\u5b9a\u5f0f\u5316<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#Gibbs%E3%82%B5%E3%83%B3%E3%83%97%E3%83%AA%E3%83%B3%E3%82%B0%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\" >Gibbs\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u5b9a\u5f0f\u5316<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E5%A4%9A%E5%A4%89%E9%87%8F%E6%AD%A3%E8%A6%8F%E5%88%86%E5%B8%83%E3%81%8B%E3%82%89%E3%81%AE%E5%8A%B9%E7%8E%87%E7%9A%84%E3%81%AA%E3%82%B5%E3%83%B3%E3%83%97%E3%83%AA%E3%83%B3%E3%82%B0\" >\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03\u304b\u3089\u306e\u52b9\u7387\u7684\u306a\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E7%8D%B2%E5%BE%97%E9%96%A2%E6%95%B0%E3%81%AE%E6%9C%80%E9%81%A9%E5%8C%96\" >\u7372\u5f97\u95a2\u6570\u306e\u6700\u9069\u5316<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E5%AE%9F%E9%A8%93\" >\u5b9f\u9a13<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#RandomQUBO\" >RandomQUBO<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#RandomHUBO\" >RandomHUBO<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#RandomMLP\" >RandomMLP<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E8%A3%9C%E8%B6%B3_%E7%B8%AE%E5%B0%8F%E4%BF%82%E6%95%B0%E3%82%92%E8%80%83%E6%85%AE%E3%81%97%E3%81%9F%E4%BA%8B%E5%89%8D%E5%88%86%E5%B8%83%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6\" >\u88dc\u8db3: \u7e2e\u5c0f\u4fc2\u6570\u3092\u8003\u616e\u3057\u305f\u4e8b\u524d\u5206\u5e03\u306b\u3064\u3044\u3066<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E3%82%B9%E3%83%91%E3%83%BC%E3%82%B9%E6%80%A7%E3%81%AE%E4%BB%AE%E5%AE%9A\" >\u30b9\u30d1\u30fc\u30b9\u6027\u306e\u4eee\u5b9a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E7%B8%AE%E5%B0%8F%E4%BF%82%E6%95%B0\" >\u7e2e\u5c0f\u4fc2\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E9%A6%AC%E8%B9%84%E5%88%86%E5%B8%83\" >\u99ac\u8e44\u5206\u5e03<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\" >\u53c2\u8003\u6587\u732e<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/bocs-sa\/#%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\" >\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><\/span>\u6587\u732e\u60c5\u5831<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a57fca70-4830-42d1-9b8a-341d0f4565e7\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<ul>\n<li>\u30bf\u30a4\u30c8\u30eb: Bayesian Optimization of Combinatorial Structures<\/li>\n<li>\u8457\u8005: R. Baptista and M. Poloczek<\/li>\n<li>\u66f8\u8a8c\u60c5\u5831: <a href=\"https:\/\/proceedings.mlr.press\/v80\/baptista18a.html\">https:\/\/proceedings.mlr.press\/v80\/baptista18a.html<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=22fc0d64-bfc8-46c8-bc0e-fb0571ac00b1\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=fc627d3c-abaa-41ac-84de-a128e92163d0\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001\u76ee\u7684\u95a2\u6570 $f: \\mathcal X \\to \\mathbb R$ \u3092\u6700\u5c0f\u5316\u3059\u308b\u5165\u529b $x^\\ast \\in \\mathcal X$ \u3092\u898b\u3064\u3051\u308b\u554f\u984c\u306e\u3046\u3061\u3001\u76ee\u7684\u95a2\u6570\u306e\u5185\u90e8\u69cb\u9020\u304c\u4e0d\u660e\u3067\u3001\u76ee\u7684\u95a2\u6570\u306e\u5024\u306e\u8a08\u7b97\u306b\u6642\u9593\u304c\u751f\u3058\u308b\u3088\u3046\u306a\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u3092\u60f3\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=5afa127b-9cfe-4895-b355-963684d9a133\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n&amp; \\mathop{\\rm minimize}\\limits_{x \\in \\mathcal X} &amp;&amp; f(x) \\\\<br \/>\n&amp; \\mathop{\\rm where}<br \/>\n&amp;&amp; \\text{$f$ \u306e\u5185\u90e8\u69cb\u9020\u306f\u4e0d\u660e,} \\\\<br \/>\n&amp;&amp;&amp; \\text{$f(x)$ \u306e\u8a55\u4fa1\u306b\u6642\u9593\u304c\u304b\u304b\u308b}<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=0f762663-2bf7-4f35-ad90-bed8390727ba\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7279\u306b\u3001$\\mathcal X$ \u304c\u9ad8\u6b21\u51432\u5024\u7a7a\u9593 $\\{0, 1\\}^d$ \u3067\u3042\u308b\u3001\u3064\u307e\u308a $x \\in \\{0, 1\\}^d$ \u3067\u3042\u308b\u554f\u984c\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n&amp; \\mathop{\\rm minimize}\\limits_{x \\in \\{0, 1\\}^d} &amp;&amp; f(x) \\\\<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<p>\u4e0a\u8a18\u306e\u3088\u3046\u306a\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u3001\u672c\u8a18\u4e8b\u3067\u306f\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u306b\u5bfe\u3059\u308b <strong>\u30e2\u30c7\u30eb\u30d9\u30fc\u30b9\u6700\u9069\u5316<\/strong>\u00a0\u306e\u4e00\u624b\u6cd5\u3067\u3042\u308b\u3001<strong>\u30b7\u30df\u30e5\u30ec\u2015\u30c6\u30c3\u30c9\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3092\u7528\u3044\u305f Bayesian optimization of combinatorial structures<\/strong> (<code>BOCS-SA<\/code>) \u3092\u5b9f\u88c5\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u3001\u672c\u8a18\u4e8b\u3067\u306f\u8ad6\u6587\u8457\u8005\u7b49\u306b\u3088\u308b\u5b9f\u88c5\u30b3\u30fc\u30c9 <a href=\"https:\/\/github.com\/baptistar\/BOCS\/\">https:\/\/github.com\/baptistar\/BOCS\/<\/a> \u306f\u4f7f\u7528\u305b\u305a\u3001\u57fa\u672c\u7684\u306b\u3059\u3079\u3066\u30b9\u30af\u30e9\u30c3\u30c1\u3067\u5b9f\u88c5\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u672c\u8a18\u4e8b\u306e\u30b3\u30fc\u30c9\u306f\u8ad6\u6587\u8457\u8005\u7b49\u306e\u30b3\u30fc\u30c9\u306b\u7531\u6765\u3059\u308bGPL\u30e9\u30a4\u30bb\u30f3\u30b9\u306b\u306f\u8a72\u5f53\u3057\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=ebeb3afd-1969-4278-8787-2fb850c8a2b2\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E7%92%B0%E5%A2%83%E8%A8%AD%E5%AE%9A\"><\/span>\u74b0\u5883\u8a2d\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=b700d824-46d7-40c6-a9ed-11259bd3455d\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E3%83%A9%E3%82%A4%E3%83%96%E3%83%A9%E3%83%AA%E3%81%AE%E3%82%A4%E3%83%B3%E3%82%B9%E3%83%88%E3%83%BC%E3%83%AB\"><\/span>\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=a22ff5cf-53d4-4083-80ee-05faa00b9561\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>openjij\n<span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>matplotlib\n<span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>torch\n<span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>tqdm\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=aaa9e174-14ed-4fec-909a-45f1e3920cf7\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E3%83%A9%E3%82%A4%E3%83%96%E3%83%A9%E3%83%AA%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%9D%E3%83%BC%E3%83%88\"><\/span>\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30a4\u30f3\u30dd\u30fc\u30c8<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=41b648e2-c32a-4699-a0dd-f56a5377db72\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"kn\">from<\/span><span class=\"w\"> <\/span><span class=\"nn\">tqdm.notebook<\/span><span class=\"w\"> <\/span><span class=\"kn\">import<\/span> <span class=\"n\">tqdm<\/span>\n<span class=\"kn\">import<\/span><span class=\"w\"> <\/span><span class=\"nn\">numpy<\/span><span class=\"w\"> <\/span><span class=\"k\">as<\/span><span class=\"w\"> <\/span><span class=\"nn\">np<\/span>\n<span class=\"kn\">import<\/span><span class=\"w\"> <\/span><span class=\"nn\">matplotlib.pyplot<\/span><span class=\"w\"> <\/span><span class=\"k\">as<\/span><span class=\"w\"> <\/span><span class=\"nn\">plt<\/span>\n<span class=\"kn\">import<\/span><span class=\"w\"> <\/span><span class=\"nn\">openjij<\/span><span class=\"w\"> <\/span><span class=\"k\">as<\/span><span class=\"w\"> <\/span><span class=\"nn\">oj<\/span>\n<span class=\"kn\">from<\/span><span class=\"w\"> <\/span><span class=\"nn\">typing<\/span><span class=\"w\"> <\/span><span class=\"kn\">import<\/span> <span class=\"n\">Optional<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=0b27e254-4351-458e-8e3d-5a12c2b9bce9\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=0f762663-2bf7-4f35-ad90-bed8390727ba\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E3%83%A2%E3%83%87%E3%83%AB%E3%83%99%E3%83%BC%E3%82%B9%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%A8%E3%81%AF\"><\/span>\u30e2\u30c7\u30eb\u30d9\u30fc\u30b9\u6700\u9069\u5316\u3068\u306f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30e2\u30c7\u30eb\u30d9\u30fc\u30b9\u6700\u9069\u5316\u3067\u306f\u3001\u76ee\u7684\u95a2\u6570\u306e\u5165\u51fa\u529b\u95a2\u4fc2\u3092\u8fd1\u4f3c\u3059\u308b\u4ee3\u7406\u30e2\u30c7\u30eb (surrogate model) \u3068\u547c\u3070\u308c\u308b\u56de\u5e30\u30e2\u30c7\u30eb\u3067\u771f\u306e\u76ee\u7684\u95a2\u6570\u304c\u8fd1\u4f3c\u3067\u304d\u308b\u3068\u4eee\u5b9a\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30b9\u30c6\u30c3\u30d7\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=4b6987c5-be9a-4081-ab38-31712c5bcbcd\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<ol>\n<li>\u4ee3\u7406\u30e2\u30c7\u30eb $\\hat f$ \u3092\u65e2\u77e5\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 $\\mathcal D^{(t-1)}$ \u306b\u30d5\u30a3\u30c3\u30c8\u3055\u305b\u308b<\/li>\n<li>\u7372\u5f97\u95a2\u6570 $\\alpha: \\mathcal X \\to \\mathbb R$ \u3092\u4ee3\u7406\u30e2\u30c7\u30eb $\\hat f$ \u3092\u4f7f\u3063\u3066\u751f\u6210\u3059\u308b<\/li>\n<li>\u8a55\u4fa1\u3059\u308b\u70b9 $x^{(t)}$ \u3092\u7372\u5f97\u95a2\u6570\u3092\u6700\u5c0f\u5316\u3059\u308b\u3053\u3068\u3067\u5f97\u308b: $x^{(t)} \\gets \\mathop{\\rm arg~min}_{x \\in \\mathcal X} \\alpha(x)$<\/li>\n<li>\u76ee\u7684\u95a2\u6570\u306e\u5024 $y^{(t)} = f(x^{(t)})$ \u3092\u5f97\u308b<\/li>\n<li>\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u65b0\u3057\u3044\u30c7\u30fc\u30bf\u3092\u8ffd\u52a0\u3059\u308b: $\\mathcal D^{(t)} \\gets \\mathcal D \\cup \\{(x^{(t)}, y^{(t)})\\}$<\/li>\n<li>\u30b9\u30c6\u30c3\u30d7 $t$ \u3092\u30a4\u30f3\u30af\u30ea\u30e1\u30f3\u30c8<\/li>\n<li>1.-6.\u3092\u7d42\u4e86\u6761\u4ef6\u306b\u9054\u3059\u308b\u307e\u3067\u7e70\u308a\u8fd4\u3059<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=49737680-715e-471c-97f4-4d33da071f2f\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u3088\u3046\u306b\u9593\u63a5\u7684\u306b\u4ee3\u7406\u30e2\u30c7\u30eb\u3092\u4f7f\u3063\u3066\u6700\u9069\u5316\u3059\u308b\u3053\u3068\u3067\u3001\u30b7\u30df\u30e5\u30ec\u2015\u30c6\u30c3\u30c9\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0 (SA, simulated annealing) \u306a\u3069\u306e\u4e00\u822c\u7684\u306a\u30e1\u30bf\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9\u624b\u6cd5\u3068\u6bd4\u3079<strong>\u3001\u76ee\u7684\u95a2\u6570\u3092\u8a55\u4fa1\u3059\u308b\u56de\u6570\u3092\u6e1b\u3089\u305b\u308b<\/strong>\u3068\u671f\u5f85\u3067\u304d\u307e\u3059\u3002\u7279\u306b\u76ee\u7684\u95a2\u6570\u306e\u8a08\u7b97\u30b3\u30b9\u30c8\u304c\u4ee3\u7406\u30e2\u30c7\u30eb\u306e\u66f4\u65b0\u30b9\u30c6\u30c3\u30d7 (\u30b9\u30c6\u30c3\u30d71) \u3084\u7372\u5f97\u95a2\u6570\u306e\u751f\u6210 (\u30b9\u30c6\u30c3\u30d72) \u3088\u308a\u3082\u5927\u304d\u3044\u5834\u5408\u306b\u3001\u30e2\u30c7\u30eb\u30d9\u30fc\u30b9\u6700\u9069\u5316\u6cd5\u306f\u6709\u52b9\u3060\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E4%BB%A3%E7%90%86%E3%83%A2%E3%83%87%E3%83%AB\"><\/span>\u4ee3\u7406\u30e2\u30c7\u30eb<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=d73622a8-ea70-487d-ada9-9d97f76d4a00\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>BOCS\u3067\u306f\u3001\u5165\u529b\u5909\u6570\u9593\u306e2\u6b21\u306e\u9805\u307e\u3067\u3092\u8003\u616e\u3059\u308b\u591a\u9805\u5f0f\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u4ee3\u7406\u30e2\u30c7\u30eb\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f7d98ca7-35a5-4a6c-b267-44711aaae9d5\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\hat f(x; w) = w_0 + \\sum_{i=1}^d w_i x_i + \\sum_{i \\lt j} w_{ij} x_i x_j.<br \/>\n&amp;&amp;<br \/>\nx \\in \\{0, 1\\}^{d}<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f8eb22b5-0dc9-47fa-86a7-19ee463c946b\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5165\u529b $x$ \u306f\u5404\u6210\u5206\u304c $0$ \u307e\u305f\u306f $1$ \u306e $d$ \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3068\u3057\u307e\u3059\u3002\u4e0a\u8a18\u306e\u30e2\u30c7\u30eb\u306f\u5404\u30d1\u30e9\u30e1\u30fc\u30bf $b, w$ \u306b\u3064\u3044\u30661\u6b21\u5f0f\u3067\u3042\u308b\u305f\u3081\u3001\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=61241280-6370-42a5-8d2b-0c9e700e0d6b\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\hat f(\\bm x; \\bm \\beta) = \\bm z^\\top \\bm \\beta<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=9bdb139c-339a-4717-b8b7-969ea036ae63\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u306b\u66f8\u304d\u76f4\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30d9\u30a4\u30ba\u7dda\u5f62\u56de\u5e30\u306e\u65b9\u6cd5\u3067\u30d1\u30e9\u30e1\u30fc\u30bf $\\bm \\beta$ \u306e\u30d9\u30a4\u30ba\u63a8\u5b9a\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3647f1ac-78e7-4358-8ebd-384490317d5c\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\bm z &amp;= [1, x_1, \\dots, x_d, x_1 x_2, \\dots, x_{d-1} x_d]^\\top \\in \\{ 0, 1 \\}^{p}, \\\\<br \/>\n\\bm \\beta &amp;= [w_0, w_1, \\dots, w_d, w_{12}, \\dots, w_{(d-1)d}]^\\top \\in \\mathbb R^{p}, \\\\<br \/>\np &amp;= 1 + d + \\frac{d(d-1)}{2}.<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a7f1ace4-6b67-4373-b284-1b9c01fa8880\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7406\u8ad6\u4e0a\u306f3\u6b21\u4ee5\u4e0a\u306e\u9805\u307e\u3067\u8003\u616e\u3059\u308b\u3053\u3068\u3067\u8868\u73fe\u529b\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u3082\u53ef\u80fd\u3067\u3059\u304c\u3001\u5b9f\u7528\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u500b\u6570 $p$ \u304c\u4ee3\u7406\u30e2\u30c7\u30eb\u306e\u6b21\u6570\u306b\u5bfe\u3057\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u3067\u5897\u52a0\u3059\u308b\u306e\u3067\u3001\u30e2\u30c7\u30eb\u306e\u5b66\u7fd2\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u70b9 $(x,y)$ \u306e\u500b\u6570 $N_{\\rm req} = |\\mathcal D|$ \u3082\u540c\u69d8\u306b\u6307\u6570\u95a2\u6570\u7684\u306b\u5897\u52a0\u3057\u3001\u3055\u3089\u306b\u5b66\u7fd2\u30b3\u30b9\u30c8\u3082\u7206\u767a\u7684\u306b\u5897\u5927\u3057\u3066\u3057\u307e\u3046\u304b\u3089\u3067\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001<strong>\u8868\u73fe\u529b\u3068\u30b3\u30b9\u30c8\u306f\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306e\u95a2\u4fc2\u306b\u3042\u308b<\/strong>\u3068\u8a00\u3048\u307e\u3059\u3002\u5143\u8ad6\u6587\u3067\u306f2\u6b21\u307e\u3067\u306e\u9805\u3092\u8003\u616e\u3059\u308b\u306e\u304c\u6700\u3082\u30d0\u30e9\u30f3\u30b9\u304c\u3088\u3044\u3068\u4e3b\u5f35\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u3053\u3053\u3067\u3082\u305d\u308c\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=1b404ccd-772f-451f-98bf-238c1fad7c14\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u500b\u6570 $p$ \u306f\u3001\u5909\u6570 $x$ \u306e\u6b21\u5143 $d$ \u3092\u7528\u3044\u3066<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=248181f2-6d11-4a14-ab9c-41b72df2845e\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\np = 1 + d + \\binom{d}{2} = 1 + d + \\frac{d (d-1)}{2}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=8b0e07c4-b9bf-431f-acf3-e215ed090518\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u306b\u3088\u308a\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=96626346\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0a\u3001$p, z$ \u3092\u4f5c\u6210\u3059\u308b\u95a2\u6570\u3092\u6e96\u5099\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=857d7ced-963d-489f-9bf4-020bc3490173\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">d_to_p<\/span><span class=\"p\">(<\/span><span class=\"n\">d<\/span><span class=\"p\">:<\/span> <span class=\"nb\">int<\/span><span class=\"p\">)<\/span> <span class=\"o\">-&gt;<\/span> <span class=\"nb\">int<\/span><span class=\"p\">:<\/span>\n    <span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">+<\/span> <span class=\"n\">d<\/span> <span class=\"o\">+<\/span> <span class=\"n\">d<\/span> <span class=\"o\">*<\/span> <span class=\"p\">(<\/span><span class=\"n\">d<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"o\">\/\/<\/span> <span class=\"mi\">2<\/span>\n    <span class=\"k\">return<\/span> <span class=\"n\">p<\/span>\n\n\n<span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">x_to_z<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">)<\/span> <span class=\"o\">-&gt;<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">:<\/span>\n    <span class=\"n\">d<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">d_to_p<\/span><span class=\"p\">(<\/span><span class=\"n\">d<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"n\">z<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">p<\/span><span class=\"p\">,<\/span> <span class=\"n\">dtype<\/span><span class=\"o\">=<\/span><span class=\"nb\">int<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"c1\"># bias<\/span>\n    <span class=\"n\">z<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\n\n    <span class=\"c1\"># linear<\/span>\n    <span class=\"n\">z<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span> <span class=\"p\">:<\/span> <span class=\"n\">d<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">x<\/span>\n\n    <span class=\"c1\"># quadratic<\/span>\n    <span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">j<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">triu_indices<\/span><span class=\"p\">(<\/span><span class=\"n\">d<\/span><span class=\"p\">,<\/span> <span class=\"n\">k<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">z<\/span><span class=\"p\">[<\/span><span class=\"n\">d<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span> <span class=\"p\">:]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">x<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">x<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span>\n    <span class=\"k\">return<\/span> <span class=\"n\">z<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=b2e9ba7b-653a-468b-b9e8-ac5261c67869\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"c1\"># TEST<\/span>\n\n<span class=\"n\">x<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"mi\">10<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">z<\/span> <span class=\"o\">=<\/span> <span class=\"n\">x_to_z<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"z:<\/span><span class=\"se\">\\n<\/span><span class=\"s2\">\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">)<\/span>\n\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"-\"<\/span> <span class=\"o\">*<\/span> <span class=\"mi\">10<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">x_data<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"p\">(<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">z_data<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">apply_along_axis<\/span><span class=\"p\">(<\/span><span class=\"n\">x_to_z<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_data<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"z_data:<\/span><span class=\"se\">\\n<\/span><span class=\"s2\">\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">z_data<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>z:\n [1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0]\n----------\nz_data:\n [[1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n  0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0]\n [1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0\n  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0]\n [1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n [1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0\n  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n [1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0]]\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=c1a596fb-b480-4780-9e91-4bd57625e2a7\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0a\u3092\u4ee3\u7406\u30e2\u30c7\u30eb\u3068\u3057\u3066\u307e\u3068\u3081\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=79f3081e-635e-4113-a732-5b0d72b78863\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">class<\/span><span class=\"w\"> <\/span><span class=\"nc\">BOCSSurrogateModel<\/span><span class=\"p\">:<\/span>\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__init__<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">linear_regressor<\/span><span class=\"p\">,<\/span> <span class=\"n\">remove_duplicate<\/span><span class=\"p\">:<\/span> <span class=\"nb\">bool<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">num_features<\/span> <span class=\"o\">=<\/span> <span class=\"n\">d_to_p<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">)<\/span>\n        <span class=\"n\">coef<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">num_features<\/span><span class=\"p\">,<\/span> <span class=\"n\">dtype<\/span><span class=\"o\">=<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">float64<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">params<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{<\/span><span class=\"s2\">\"coef\"<\/span><span class=\"p\">:<\/span> <span class=\"n\">coef<\/span><span class=\"p\">}<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">linear_regressor<\/span> <span class=\"o\">=<\/span> <span class=\"n\">linear_regressor<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">update<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_data<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_data<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">z_data<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">apply_along_axis<\/span><span class=\"p\">(<\/span><span class=\"n\">x_to_z<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_data<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">linear_regressor<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">(<\/span><span class=\"n\">z_data<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_data<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">params<\/span><span class=\"p\">[<\/span><span class=\"s2\">\"coef\"<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">linear_regressor<\/span><span class=\"o\">.<\/span><span class=\"n\">coef_<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=8369c7cc-d3af-4479-b5e8-46fe7d266bc5\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"c1\"># TEST<\/span>\n\n<span class=\"n\">num_vars<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">16<\/span>\n<span class=\"n\">linear_regressor<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">None<\/span>\n\n<span class=\"n\">bocs_surrogate_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">BOCSSurrogateModel<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">linear_regressor<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">bocs_surrogate_model<\/span><span class=\"o\">.<\/span><span class=\"n\">params<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>{'coef': array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0.])}\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=9e84d49c-2624-4a2a-a365-ec27a3a89df3\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"Thompson%E6%8A%BD%E5%87%BA\"><\/span>Thompson\u62bd\u51fa<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a171203a-322f-4b75-bf48-7247abf74f78\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>BOCS\u306f <strong>Thompson\u62bd\u51fa<\/strong> (Thompson sampling) \u3068\u547c\u3070\u308c\u308b\u624b\u6cd5\u306e1\u3064\u3067\u3059\u3002Thompson\u62bd\u51fa\u306f\u4ee3\u7406\u30e2\u30c7\u30eb\u304c\u30d1\u30e9\u30e1\u30fc\u30bf $\\theta$ \u306b\u7279\u5fb4\u3065\u3051\u3089\u308c\u308b\u95a2\u6570 $\\hat f(x; \\theta)$ \u306e\u5834\u5408\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u624b\u6cd5\u3067\u3001<\/p>\n<ol>\n<li>\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u4e8b\u5f8c\u5206\u5e03 $p(\\tilde \\theta \\mid \\mathcal D)$ \u3092\u8a08\u7b97<\/li>\n<li>\u4e8b\u5f8c\u5206\u5e03\u306b\u5f93\u3046\u30b5\u30f3\u30d7\u30eb $\\tilde{\\theta} \\sim p(\\tilde \\theta \\mid \\mathcal D)$ \u30921\u3064\u5f15\u304f<\/li>\n<li>\u30b5\u30f3\u30d7\u30eb\u3092\u7528\u3044\u305f\u4ee3\u7406\u30e2\u30c7\u30eb $\\hat f(x; \\tilde \\theta)$ \u3092\u7372\u5f97\u95a2\u6570 $\\alpha(x)$ \u3068\u3059\u308b<\/li>\n<\/ol>\n<p>\u3068\u3044\u3046\u30b9\u30c6\u30c3\u30d7\u306b\u3088\u308a\u5f97\u3089\u308c\u308b\u95a2\u6570 $\\alpha(x)$ \u3092\u7372\u5f97\u95a2\u6570\u3068\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=4527db25-7adf-4fc7-9e80-36990798531c\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\alpha(x) = \\hat f(x; \\tilde \\theta) \\quad<br \/>\n\\text{where} \\quad<br \/>\n\\tilde \\theta \\sim p(\\theta \\mid \\mathcal D)<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=089b52a7\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u4ee5\u4e0b\u306e\u78ba\u7387\u898f\u5247\u306b\u5f93\u3063\u3066\u65b0\u3057\u3044\u30c7\u30fc\u30bf\u3092\u8a55\u4fa1\u3059\u308b\u70b9\u3092\u9078\u629e\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\nP(x \\mid \\mathcal D) = \\int d\\theta~ \\delta\\! \\left( x &#8211; \\operatorname*{\\arg\\,\\min}_x \\hat f(x; \\theta) \\right)<br \/>\np (\\theta \\mid \\mathcal D)<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=9bb97e3b-8fd8-4323-8929-7cffd7051966\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Thompson\u62bd\u51fa\u3092\u5b9f\u88c5\u3059\u308b\u306b\u306f\u3001<strong>\u4e8b\u5f8c\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0<\/strong> \u3092\u884c\u3046\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5fc5\u8981\u3067\u3059\u3002\u6b21\u7bc0\u3067\u306fBOCS\u3067\u4f7f\u7528\u3055\u308c\u308b\u30d9\u30a4\u30ba\u7dda\u5f62\u56de\u5e30\u306b\u3088\u308b\u4e8b\u5f8c\u5206\u5e03\u306e\u63a8\u5b9a\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a6514927\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E3%83%99%E3%82%A4%E3%82%BA%E7%B7%9A%E5%BD%A2%E5%9B%9E%E5%B8%B0\"><\/span>\u30d9\u30a4\u30ba\u7dda\u5f62\u56de\u5e30<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=6d1ca453\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7dda\u5f62\u56de\u5e30\u306e\u30d9\u30a4\u30ba\u7684\u306a\u53d6\u308a\u6271\u3044\u65b9\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u7dda\u5f62\u56de\u5e30\u306f\u5165\u529b $\\bm x^{(t)} \\in \\mathbb R^{p}$ \u3068\u51fa\u529b $y^{(t)} \\in \\mathbb R$ \u306e\u95a2\u4fc2\u3092\u6b21\u306e\u3088\u3046\u306b\u30e2\u30c7\u30eb\u5316\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a5907c9f\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\ny^{(t)}<br \/>\n&amp;= \\beta_1 x^{(t)}_1 + \\beta_2 x^{(t)}_2 + \\dots + \\beta_p x^{(t)}_p + \\varepsilon^{(t)} \\\\<br \/>\n&amp;= \\bm x^{(t) \\top} \\bm \\beta + \\varepsilon^{(t)}.<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=939f6ee5\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\bm \\beta \\in \\mathbb R^{p}$ \u306f\u56de\u5e30\u4fc2\u6570\u3001$\\varepsilon^{(t)}$ \u306f\u30ce\u30a4\u30ba\u3067\u3059\u3002\u30ce\u30a4\u30ba\u306b\u306f\u901a\u5e38\u3001\u6b21\u306e\u3088\u3046\u306a\u6b63\u898f\u5206\u5e03\u3092\u4eee\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=5c41a954\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\varepsilon^{(t)} \\sim \\mathcal N(0, \\sigma^2).<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f1b8867f\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u308c\u306f\u51fa\u529b $y^{(t)}$ \u304c\u5e73\u5747 $\\bm x^{(t)\\top} \\bm \\beta$\u3001\u5206\u6563 $\\sigma^2$ \u306e\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3068\u4eee\u5b9a\u3057\u3066\u3044\u308b\u3053\u3068\u3068\u7b49\u4fa1\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f4d39161\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\ny^{(t)} \\mid \\bm x^{(t)}, \\bm \\beta, \\sigma \\sim \\mathcal N(\\bm x^{(t)\\top} \\bm \\beta, \\sigma^2).<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=298e78fa\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e $y^{(t)}$ \u304c\u5f93\u3046\u78ba\u7387\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u6b21\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=da26bc01\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\np(y^{(t)} \\mid \\bm x^{(t)}, \\bm \\beta, \\sigma) = \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\exp \\left( -\\frac{1}{2\\sigma^2} (y^{(t)} &#8211; \\bm x^{(t) \\top} \\bm \\beta)^2 \\right).<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=ad4e18b8\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u884c\u3044\u305f\u3044\u3053\u3068\u306f\u3001\u4fc2\u6570 $\\bm \\beta$ \u3068\u6a19\u6e96\u504f\u5dee $\\sigma$ \u3092\u30c7\u30fc\u30bf $\\mathcal D = \\{(\\bm x^{(t)}, y^{(t)})\\}_{t=1, \\dots, N}$ \u3092\u3082\u3068\u306b\u63a8\u5b9a\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u30d9\u30a4\u30ba\u63a8\u5b9a\u306e\u67a0\u7d44\u307f\u3067\u3053\u308c\u3092\u884c\u30461\u3064\u306e\u65b9\u6cd5\u306f\u300c\u4fc2\u6570 $\\bm \\beta$ \u3068\u6a19\u6e96\u504f\u5dee $\\sigma$ \u306e\u78ba\u7387\u5206\u5e03 $p(\\bm \\beta, \\sigma \\mid \\bm X, \\bm y)$ \u3092\u6c42\u3081\u308b\u300d\u3053\u3068\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u306b\u6b21\u306e\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u3092\u7528\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=75557170\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\np(\\bm \\beta, \\sigma \\mid \\bm X, \\bm y)<br \/>\n&amp;= \\frac{p(\\bm y \\mid \\bm X, \\bm \\beta, \\sigma) p(\\bm \\beta, \\sigma)}{p(\\bm y \\mid \\bm X)} \\\\<br \/>\n&amp;\\propto p(\\bm y \\mid \\bm X, \\bm \\beta, \\sigma) p(\\bm \\beta, \\sigma).<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=37838c16\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u305f\u3060\u3057 $\\bm y=[y^{(1)}, \\dots, y^{(N)}]^\\top, \\bm X=[\\bm x^{(1) \\top}, \\dots, \\bm x^{(N) \\top}]^\\top$ \u3067\u3059\u3002\u3053\u306e\u5f0f\u306b\u3088\u308c\u3070\u3001\u4e8b\u524d\u5206\u5e03 $p(\\bm \\beta, \\sigma)$ \u3092\u8a2d\u5b9a\u3057\u3001\u3053\u308c\u306b\u30e2\u30c7\u30eb\u306e\u78ba\u7387\u5206\u5e03 $p(y^{(t)} \\mid \\bm x^{(t)}, \\bm \\beta, \\sigma)$ \u3092\u639b\u3051\u3001\u66f4\u306b\u5b9a\u6570\u500d\u3057\u3066\u898f\u683c\u5316\u3059\u308c\u3070\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u4e8b\u5f8c\u5206\u5e03 $p(\\bm \\beta, \\sigma \\mid \\bm X, \\bm y)$ \u304c\u6c42\u307e\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3c208724-1579-49bb-aeaf-e8b691a60c8c\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E9%A6%AC%E8%B9%84%E5%88%86%E5%B8%83%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span>\u99ac\u8e44\u5206\u5e03\u306e\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3360c952-5db6-4874-a472-6ce45daef153\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>BOCS\u3067\u306f\u3001\u30b9\u30d1\u30fc\u30b9\u6027\u3092\u4eee\u5b9a\u3059\u308b\u99ac\u8e44\u5206\u5e03 (horseshoe prior) \u3068\u547c\u3070\u308c\u308b\u4e8b\u524d\u5206\u5e03\u3092\u7528\u3044\u307e\u3059\u3002\u99ac\u8e44\u5206\u5e03\u306e\u5b9a\u5f0f\u5316\u306b\u306f [Makalic &amp; Schmidt (2016)] \u306b\u3088\u308b\u6b21\u306e\u5b9a\u5f0f\u5316\u3092\u7528\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=0629d135-71df-48c7-817c-3447f8a76ea1\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\ny \\mid \\bm x, \\bm \\beta, \\sigma<br \/>\n&amp;\\sim \\mathcal N(\\bm x^\\top \\bm \\beta, \\sigma^2), \\\\<br \/>\n\\beta_i \\mid \\sigma, \\lambda_i, \\tau<br \/>\n&amp;\\sim \\mathcal N(0, \\sigma^2 \\tau^2 \\lambda_i^2),<br \/>\n&amp; i=1,\\dots,p, \\\\<br \/>\n\\sigma^2 \\mid a, b<br \/>\n&amp;\\sim \\mathrm{InvGamma}(a, b), \\\\<br \/>\n\\lambda_i<br \/>\n&amp;\\sim \\mathrm{HalfCauchy} (0, 1),<br \/>\n&amp; i=1,\\dots,p, \\\\<br \/>\n\\tau<br \/>\n&amp;\\sim \\mathrm{HalfCauchy} (0, 1).<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=ed163cbe-7f8f-4f04-a786-0111f0a2ed99\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u305f\u3060\u3057 $y \\in \\mathbb R, \\bm x \\in \\mathbb R^p, \\bm \\beta \\in \\mathbb R^p$ \u3067\u3059\u3002$\\mathrm{HalfCauchy}(0, 1)$ \u306f\u4f4d\u7f6e\u30d1\u30e9\u30e1\u30fc\u30bf $0$\u3001\u5c3a\u5ea6\u30d1\u30e9\u30e1\u30fc\u30bf $1$ \u306e <strong>\u534a\u30b3\u30fc\u30b7\u30fc\u5206\u5e03<\/strong> \u3068\u547c\u3070\u308c\u308b\u5206\u5e03\u3067\u3001\u4ee5\u4e0b\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=7a68efe5-af46-4540-a1ab-b57556d4f65e\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\np(x) = \\frac{2}{\\pi} \\frac{1}{1 + x^2}.<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=d29063b7-340f-45d6-b4aa-237468d1f6a6\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"Gibbs%E3%82%B5%E3%83%B3%E3%83%97%E3%83%AA%E3%83%B3%E3%82%B0%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span>Gibbs\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=80c5a272-1822-4f9f-b7b3-02ccb94a3928\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u306b\u5f93\u3063\u3066\u4e8b\u5f8c\u5206\u5e03 $p(\\bm \\beta \\mid \\mathcal D)$ \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u534a\u30b3\u30fc\u30b7\u30fc\u5206\u5e03 $\\mathrm{HalfCauchy} (0, 1)$ \u3068\u6b63\u898f\u5206\u5e03 $\\mathcal N(0, \\sigma^2 \\tau^2 \\lambda_i^2)$ \u306f\u76f8\u6027\u304c\u60aa\u304f\u3001\u305d\u306e\u307e\u307e\u3067\u306f\u89e3\u6790\u7684\u306b\u4e8b\u5f8c\u5206\u5e03\u3092\u5c0e\u51fa\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001[Makalic &amp; Schmidt (2016)] \u306e\u53d6\u6271\u3044\u306b\u5f93\u3044\u3001\u6587\u732e [Wand+ (2011)] \u306b\u8a18\u8f09\u3055\u308c\u3066\u3044\u308b\u5b9a\u7406\u3088\u308a\u5c0e\u304b\u308c\u308b\u4ee5\u4e0b\u306e\u88dc\u984c\u3092\u5229\u7528\u3057\u3066\u3001\u534a\u30b3\u30fc\u30b7\u30fc\u5206\u5e03\u3092\u9006\u30ac\u30f3\u30de\u5206\u5e03\u306b\u66f8\u304d\u63db\u3048\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=45120178-2ebb-469f-aceb-140f8ba450ff\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<hr \/>\n<p><strong>\u88dc\u984c [Wand+ (2011)]<\/strong> $x$ \u304c\u534a\u30b3\u30fc\u30b7\u30fc\u5206\u5e03 $\\mathrm{HalfCauchy} (x \\mid 0, a)$ \u306b\u5f93\u3046\u306a\u3089\u3070\u3001$x^2$ \u306f2\u6bb5\u968e\u306e\u968e\u5c64\u7684\u306a\u9006\u30ac\u30f3\u30de\u5206\u5e03\u306e\u6df7\u5408\u306b\u5f93\u3046\u3002<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\nx^2 \\mid a&#8217; &amp;\\sim \\mathrm{InvGamma} \\left( x^2 \\,\\middle|\\, \\frac{1}{2}, \\frac{1}{a&#8217;} \\right), \\\\<br \/>\na&#8217; \\mid a &amp;\\sim \\mathrm{InvGamma} \\left( a&#8217; \\,\\middle|\\, \\frac{1}{2}, \\frac{1}{a^2} \\right).<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<hr \/>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=ac44f3c0-70ff-4c99-ab38-0e9a620e93df\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u308c\u3092\u7528\u3044\u308c\u3070\u3001$\\lambda_i \\sim \\mathrm{HalfCauchy}(0,1)$ \u3068\u3044\u3046\u90e8\u5206\u306f\u88dc\u52a9\u5909\u6570 $\\nu_i$ \u3092\u5c0e\u5165\u3059\u308b\u3053\u3068\u3067<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=c9b5bf97-bde2-45c7-884e-82f92e045ea5\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\lambda_i^2 \\mid \\nu_i &amp;\\sim \\mathrm{InvGamma} \\left( \\lambda_i^2 \\,\\middle|\\, \\frac{1}{2}, \\frac{1}{\\nu_i} \\right), \\\\<br \/>\n\\nu_i &amp;\\sim \\mathrm{InvGamma} \\left( \\nu_i \\,\\middle|\\, \\frac{1}{2}, 1 \\right)<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=d4efa876-af38-4c65-95ae-fdfc7922579a\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3068\u3044\u3046\u968e\u5c64\u69cb\u9020\u306b\u66f8\u304d\u76f4\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002$\\tau \\sim \\mathrm{HalfCauchy}(0,1)$ \u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u306e\u66f8\u304d\u63db\u3048\u3092\u65bd\u3059\u3053\u3068\u304c\u3067\u304d\u3001\u6700\u7d42\u7684\u306b\u3059\u3079\u3066\u306e\u6761\u4ef6\u4ed8\u304d\u5206\u5e03\u304c\u6b63\u898f\u5206\u5e03\u3068\u9006\u30ac\u30f3\u30de\u5206\u5e03\u306e\u5f62\u3067\u66f8\u304b\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=67db6111-d999-4adf-977c-5aea499a4de0\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\beta_i \\mid \\sigma, \\tau, \\lambda_i<br \/>\n&amp;\\sim \\mathcal{N}(\\beta_i \\mid 0, \\sigma^2 \\tau^2 \\lambda_i^2),<br \/>\n&amp; i &amp;= 1, \\dots, p,<br \/>\n\\\\<br \/>\n\\sigma^2 \\mid a, b<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( \\sigma^2 \\,\\middle|\\, a, b \\right),<br \/>\n\\\\<br \/>\n\\lambda_i^2 \\mid \\nu_i<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( \\lambda_i^2 \\,\\middle|\\, \\frac{1}{2}, \\frac{1}{\\nu_i} \\right),<br \/>\n&amp; i &amp;= 1, \\dots, p,<br \/>\n\\\\<br \/>\n\\nu_i<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( \\nu_i \\,\\middle|\\, \\frac{1}{2}, 1 \\right),<br \/>\n&amp; i &amp;= 1, \\dots, p,<br \/>\n\\\\<br \/>\n\\tau^2 \\mid \\xi<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( \\tau^2 \\,\\middle|\\, \\frac{1}{2}, \\frac{1}{\\xi} \\right),<br \/>\n\\\\<br \/>\n\\xi<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( \\xi \\,\\middle|\\, \\frac{1}{2}, 1 \\right).<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=c3a26b7a-ea73-44e9-8f10-109879c78a16\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u968e\u5c64\u69cb\u9020\u304b\u3089\u3001\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u3067\u5404\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6761\u4ef6\u4ed8\u304d\u4e8b\u5f8c\u5206\u5e03\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=8e297a2d-0c35-428f-b752-1364fc849b6a\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\bm \\beta \\mid \\bm X, \\bm y, \\bm \\beta, \\sigma, \\bm \\lambda, \\tau<br \/>\n&amp;\\sim \\mathcal{N}(\\bm A^{-1} \\bm X^\\top \\bm y, \\sigma^2 \\bm A^{-1}),<br \/>\n\\\\<br \/>\n\\sigma^2 \\mid \\bm X, \\bm y, \\bm \\lambda, \\tau, a, b<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( a + \\frac{N}{2}, b + \\frac{\\bm y^\\top (\\bm I_N + \\bm X \\tau^2 \\operatorname{diag}\\{\\lambda_i^2\\} \\bm X^\\top )^{-1} \\bm y}{2} \\right),<br \/>\n\\\\<br \/>\n\\lambda_i^2 \\mid \\bm \\beta, \\sigma, \\tau, \\bm \\nu<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( 1, \\frac{1}{\\nu_i} + \\frac{1}{2 \\sigma^2} \\frac{\\beta_i^2}{\\tau^2} \\right),<br \/>\n&amp; i &amp;= 1, \\dots, p,<br \/>\n\\\\<br \/>\n\\nu_i \\mid \\bm \\lambda<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( 1, 1 + \\frac{1}{\\lambda_i^2} \\right),<br \/>\n&amp; i &amp;= 1, \\dots, p,<br \/>\n\\\\<br \/>\n\\tau^2 \\mid \\bm \\beta, \\sigma, \\bm \\lambda, \\xi<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( \\frac{p + 1}{2}, \\frac{1}{\\xi} + \\frac{1}{2 \\sigma^2} \\sum_{i=1}^p \\frac{\\beta_i^2}{\\lambda_i^2} \\right),<br \/>\n\\\\<br \/>\n\\xi \\mid \\tau<br \/>\n&amp;\\sim \\mathrm{InvGamma} \\left( 1, 1 + \\frac{1}{\\tau^2} \\right),<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3a991bb6-9b4c-45fc-879d-910b78eed7e2\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u305f\u3060\u3057<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=66f62e8b-81c6-4ba3-af1d-544ab6d38df7\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\bm X &amp;=<br \/>\n\\begin{bmatrix}<br \/>\n\\bm x^{(1) \\top} \\\\ \\bm x^{(2) \\top} \\\\ \\vdots \\\\ \\bm x^{(N) \\top}<br \/>\n\\end{bmatrix} \\in \\mathbb R^{N \\times p},<br \/>\n\\\\<br \/>\ny &amp;=<br \/>\n\\begin{bmatrix}<br \/>\ny^{(1)} \\\\ y^{(2)} \\\\ \\vdots \\\\ y^{(N)}<br \/>\n\\end{bmatrix} \\in \\mathbb R^{N},<br \/>\n\\\\<br \/>\n\\bm A &amp;= \\bm X^\\top \\bm X + \\frac{1}{\\tau^2} \\operatorname{diag}\\left\\{ \\frac{1}{\\lambda_i^2} \\right\\}<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a4e556ee-d8c6-4b39-867d-7dda2ba991ca\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0a\u5c0e\u51fa\u3055\u308c\u305f\u5404\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6761\u4ef6\u4ed8\u304d\u4e8b\u5f8c\u5206\u5e03\u304b\u30891\u30641\u3064\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u3066\u3044\u304fGibbs\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3068\u547c\u3070\u308c\u308b\u65b9\u6cd5\u306b\u3088\u308a\u3001\u4e8b\u5f8c\u5206\u5e03\u306b\u5f93\u3046\u30b5\u30f3\u30d7\u30eb\u3092\u751f\u6210\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=1f890a9e\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">sample_from_inv_gamma<\/span><span class=\"p\">(<\/span><span class=\"n\">shape<\/span><span class=\"p\">,<\/span> <span class=\"n\">scale<\/span><span class=\"p\">):<\/span>\n    <span class=\"k\">return<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">gamma<\/span><span class=\"p\">(<\/span><span class=\"n\">shape<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">scale<\/span><span class=\"p\">)<\/span>\n\n\n<span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">sample_coef<\/span><span class=\"p\">(<\/span><span class=\"n\">sigma2<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">Phi<\/span> <span class=\"o\">=<\/span> <span class=\"n\">X<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">sigma2<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">alpha<\/span> <span class=\"o\">=<\/span> <span class=\"n\">y<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">sigma2<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">delta<\/span> <span class=\"o\">=<\/span> <span class=\"n\">tau2<\/span> <span class=\"o\">*<\/span> <span class=\"n\">lamb2<\/span> <span class=\"o\">*<\/span> <span class=\"n\">sigma2<\/span>\n\n    <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Phi<\/span><span class=\"o\">.<\/span><span class=\"n\">shape<\/span>\n    <span class=\"n\">u<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.0<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">delta<\/span><span class=\"p\">),<\/span> <span class=\"n\">p<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">d<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.0<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">v<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Phi<\/span> <span class=\"o\">@<\/span> <span class=\"n\">u<\/span> <span class=\"o\">+<\/span> <span class=\"n\">d<\/span>\n    <span class=\"k\">try<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">w<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linalg<\/span><span class=\"o\">.<\/span><span class=\"n\">solve<\/span><span class=\"p\">((<\/span><span class=\"n\">delta<\/span> <span class=\"o\">*<\/span> <span class=\"n\">Phi<\/span><span class=\"p\">)<\/span> <span class=\"o\">@<\/span> <span class=\"n\">Phi<\/span><span class=\"o\">.<\/span><span class=\"n\">T<\/span> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">eye<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">),<\/span> <span class=\"n\">alpha<\/span> <span class=\"o\">-<\/span> <span class=\"n\">v<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">except<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linalg<\/span><span class=\"o\">.<\/span><span class=\"n\">LinAlgError<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">w<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linalg<\/span><span class=\"o\">.<\/span><span class=\"n\">lstsq<\/span><span class=\"p\">((<\/span><span class=\"n\">delta<\/span> <span class=\"o\">*<\/span> <span class=\"n\">Phi<\/span><span class=\"p\">)<\/span> <span class=\"o\">@<\/span> <span class=\"n\">Phi<\/span><span class=\"o\">.<\/span><span class=\"n\">T<\/span> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">eye<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">),<\/span> <span class=\"n\">alpha<\/span> <span class=\"o\">-<\/span> <span class=\"n\">v<\/span><span class=\"p\">,<\/span> <span class=\"n\">rcond<\/span><span class=\"o\">=<\/span><span class=\"kc\">None<\/span><span class=\"p\">)[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\n    <span class=\"n\">coef_new<\/span> <span class=\"o\">=<\/span> <span class=\"n\">u<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"n\">delta<\/span> <span class=\"o\">*<\/span> <span class=\"n\">Phi<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">T<\/span> <span class=\"o\">@<\/span> <span class=\"n\">w<\/span>\n\n    <span class=\"k\">return<\/span> <span class=\"n\">coef_new<\/span>\n\n\n<span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">sample_sigma2<\/span><span class=\"p\">(<\/span><span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">X<\/span><span class=\"o\">.<\/span><span class=\"n\">shape<\/span>\n    <span class=\"n\">shape<\/span> <span class=\"o\">=<\/span> <span class=\"n\">a<\/span> <span class=\"o\">+<\/span> <span class=\"n\">N<\/span> <span class=\"o\">\/<\/span> <span class=\"mi\">2<\/span>\n\n    <span class=\"n\">XDX_In<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"n\">tau2<\/span> <span class=\"o\">*<\/span> <span class=\"n\">lamb2<\/span> <span class=\"o\">*<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span> <span class=\"o\">@<\/span> <span class=\"n\">X<\/span><span class=\"o\">.<\/span><span class=\"n\">T<\/span> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">eye<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">scale<\/span> <span class=\"o\">=<\/span> <span class=\"n\">b<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span> <span class=\"o\">@<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linalg<\/span><span class=\"o\">.<\/span><span class=\"n\">solve<\/span><span class=\"p\">(<\/span><span class=\"n\">XDX_In<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span> <span class=\"o\">\/<\/span> <span class=\"mi\">2<\/span>\n\n    <span class=\"n\">sigma2_new<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sample_from_inv_gamma<\/span><span class=\"p\">(<\/span><span class=\"n\">shape<\/span><span class=\"p\">,<\/span> <span class=\"n\">scale<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">return<\/span> <span class=\"n\">sigma2_new<\/span>\n\n\n<span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">sample_lamb2<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">shape<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span>\n    <span class=\"n\">scale<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">+<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">lamb2<\/span>\n    <span class=\"n\">nu<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sample_from_inv_gamma<\/span><span class=\"p\">(<\/span><span class=\"n\">shape<\/span><span class=\"p\">,<\/span> <span class=\"n\">scale<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"n\">shape<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span>\n    <span class=\"n\">scale<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">nu<\/span> <span class=\"o\">+<\/span> <span class=\"n\">coef<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">tau2<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">sigma2<\/span> <span class=\"o\">\/<\/span> <span class=\"mi\">2<\/span>\n    <span class=\"n\">lamb2_new<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sample_from_inv_gamma<\/span><span class=\"p\">(<\/span><span class=\"n\">shape<\/span><span class=\"p\">,<\/span> <span class=\"n\">scale<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">return<\/span> <span class=\"n\">lamb2_new<\/span>\n\n\n<span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">sample_tau2<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">shape<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span>\n    <span class=\"n\">scale<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">+<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">tau2<\/span>\n    <span class=\"n\">xi<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sample_from_inv_gamma<\/span><span class=\"p\">(<\/span><span class=\"n\">shape<\/span><span class=\"p\">,<\/span> <span class=\"n\">scale<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">shape<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"n\">p<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"o\">\/<\/span> <span class=\"mi\">2<\/span>\n    <span class=\"n\">scale<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">xi<\/span> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">)<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">sigma2<\/span> <span class=\"o\">\/<\/span> <span class=\"mi\">2<\/span>\n    <span class=\"n\">tau2_new<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sample_from_inv_gamma<\/span><span class=\"p\">(<\/span><span class=\"n\">shape<\/span><span class=\"p\">,<\/span> <span class=\"n\">scale<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">return<\/span> <span class=\"n\">tau2_new<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=363dc4c9-2047-4879-87aa-3003c0e8df67\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u3046\u3057\u3066\u4f5c\u6210\u3055\u308c\u305f\u5404\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u95a2\u6570\u3092\u307e\u3068\u3081\u3066\u30eb\u30fc\u30d7\u3055\u305b\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=1221015b-3a18-428d-b95a-9c38cf22aa92\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">markov_transition<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">X<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">y<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">coef<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">sigma2<\/span><span class=\"p\">:<\/span> <span class=\"nb\">float<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">lamb2<\/span><span class=\"p\">:<\/span> <span class=\"nb\">float<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">tau2<\/span><span class=\"p\">:<\/span> <span class=\"nb\">float<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">a_sigma2<\/span><span class=\"p\">:<\/span> <span class=\"nb\">float<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">b_sigma2<\/span><span class=\"p\">:<\/span> <span class=\"nb\">float<\/span><span class=\"p\">,<\/span>\n<span class=\"p\">):<\/span>\n    <span class=\"n\">tau2_new<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sample_tau2<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">sigma2_new<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sample_sigma2<\/span><span class=\"p\">(<\/span><span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2_new<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"n\">a_sigma2<\/span><span class=\"p\">,<\/span> <span class=\"n\">b_sigma2<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">coef_new<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sample_coef<\/span><span class=\"p\">(<\/span><span class=\"n\">sigma2_new<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2_new<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">lamb2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sample_lamb2<\/span><span class=\"p\">(<\/span><span class=\"n\">coef_new<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2_new<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2_new<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"k\">return<\/span> <span class=\"n\">coef_new<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2_new<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2_new<\/span>\n\n\n<span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">horseshoe_gibbs_sampling<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">X<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">y<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">coef<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">sigma2<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">tau2<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">a_sigma2<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">b_sigma2<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">max_iter<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">show_progress_bar<\/span><span class=\"p\">:<\/span> <span class=\"nb\">bool<\/span><span class=\"p\">,<\/span>\n<span class=\"p\">):<\/span>\n    <span class=\"n\">coefs<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">((<\/span><span class=\"n\">max_iter<\/span><span class=\"p\">,<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"p\">)))<\/span>\n    <span class=\"n\">sigma2s<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">max_iter<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">lamb2s<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">((<\/span><span class=\"n\">max_iter<\/span><span class=\"p\">,<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"p\">)))<\/span>\n    <span class=\"n\">tau2s<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">max_iter<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"k\">if<\/span> <span class=\"n\">show_progress_bar<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">iterator<\/span> <span class=\"o\">=<\/span> <span class=\"n\">tqdm<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">max_iter<\/span><span class=\"p\">))<\/span>\n    <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">iterator<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">max_iter<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">mcs<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">iterator<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">coef<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">markov_transition<\/span><span class=\"p\">(<\/span>\n            <span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"n\">coef<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2<\/span><span class=\"p\">,<\/span> <span class=\"n\">a_sigma2<\/span><span class=\"p\">,<\/span> <span class=\"n\">b_sigma2<\/span>\n        <span class=\"p\">)<\/span>\n\n        <span class=\"n\">coefs<\/span><span class=\"p\">[<\/span><span class=\"n\">mcs<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">coef<\/span>\n        <span class=\"n\">sigma2s<\/span><span class=\"p\">[<\/span><span class=\"n\">mcs<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sigma2<\/span>\n        <span class=\"n\">lamb2s<\/span><span class=\"p\">[<\/span><span class=\"n\">mcs<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">lamb2<\/span>\n        <span class=\"n\">tau2s<\/span><span class=\"p\">[<\/span><span class=\"n\">mcs<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">tau2<\/span>\n\n    <span class=\"k\">return<\/span> <span class=\"n\">coefs<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2s<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2s<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2s<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=42247312-f411-443f-946e-6b88b732532c\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">class<\/span><span class=\"w\"> <\/span><span class=\"nc\">HorseshoeGibbs<\/span><span class=\"p\">:<\/span>\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__init__<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">max_iter<\/span><span class=\"p\">:<\/span> <span class=\"nb\">int<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">50<\/span><span class=\"p\">,<\/span> <span class=\"n\">warm_start<\/span><span class=\"p\">:<\/span> <span class=\"nb\">bool<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"n\">show_progress_bar<\/span><span class=\"p\">:<\/span> <span class=\"nb\">bool<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">):<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">max_iter<\/span> <span class=\"o\">=<\/span> <span class=\"n\">max_iter<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">warm_start<\/span> <span class=\"o\">=<\/span> <span class=\"n\">warm_start<\/span>\n\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">coef_<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">None<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">sigma2_<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">None<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">lamb2_<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">None<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">tau2_<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">None<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">hyperparams<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{<\/span>\n            <span class=\"s2\">\"a_sigma2\"<\/span><span class=\"p\">:<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span>\n            <span class=\"s2\">\"b_sigma2\"<\/span><span class=\"p\">:<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span>\n        <span class=\"p\">}<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">config<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{<\/span>\n            <span class=\"s2\">\"show_progress_bar\"<\/span><span class=\"p\">:<\/span> <span class=\"n\">show_progress_bar<\/span><span class=\"p\">,<\/span>\n        <span class=\"p\">}<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">is_initilized<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">initialize_params<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_features<\/span><span class=\"p\">):<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">coef_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">num_features<\/span><span class=\"p\">,<\/span> <span class=\"n\">dtype<\/span><span class=\"o\">=<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">float64<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">sigma2_<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">lamb2_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">uniform<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.0<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_features<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">astype<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">float64<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">tau2_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">uniform<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.0<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">is_initilized<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">fit<\/span><span class=\"p\">(<\/span>\n        <span class=\"bp\">self<\/span><span class=\"p\">,<\/span>\n        <span class=\"n\">X<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">,<\/span>\n        <span class=\"n\">y<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">,<\/span>\n        <span class=\"n\">return_samples<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">,<\/span>\n    <span class=\"p\">):<\/span>\n        <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">is_initilized<\/span> <span class=\"ow\">or<\/span> <span class=\"ow\">not<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">warm_start<\/span><span class=\"p\">:<\/span>\n            <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">initialize_params<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"o\">.<\/span><span class=\"n\">shape<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">])<\/span>\n\n        <span class=\"n\">coef<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">coef_<\/span>\n        <span class=\"n\">sigma2<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">sigma2_<\/span>\n        <span class=\"n\">lamb2<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">lamb2_<\/span>\n        <span class=\"n\">tau2<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">tau2_<\/span>\n\n        <span class=\"n\">coefs<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2s<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2s<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2s<\/span> <span class=\"o\">=<\/span> <span class=\"n\">horseshoe_gibbs_sampling<\/span><span class=\"p\">(<\/span>\n            <span class=\"n\">X<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">y<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">coef<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">sigma2<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">lamb2<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">tau2<\/span><span class=\"p\">,<\/span>\n            <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">hyperparams<\/span><span class=\"p\">[<\/span><span class=\"s2\">\"a_sigma2\"<\/span><span class=\"p\">],<\/span>\n            <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">hyperparams<\/span><span class=\"p\">[<\/span><span class=\"s2\">\"b_sigma2\"<\/span><span class=\"p\">],<\/span>\n            <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">max_iter<\/span><span class=\"p\">,<\/span>\n            <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">config<\/span><span class=\"p\">[<\/span><span class=\"s2\">\"show_progress_bar\"<\/span><span class=\"p\">],<\/span>\n        <span class=\"p\">)<\/span>\n\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">coef_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">coefs<\/span><span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">sigma2_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sigma2s<\/span><span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">lamb2_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">lamb2s<\/span><span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">tau2_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">tau2s<\/span><span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span>\n\n        <span class=\"k\">if<\/span> <span class=\"n\">return_samples<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">return<\/span> <span class=\"n\">coefs<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2s<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2s<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2s<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=c7561f5b-795d-4839-a337-27d92bb7568d\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"c1\"># TEST<\/span>\n<span class=\"n\">num_features<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">50<\/span>\n<span class=\"n\">num_samples<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">50<\/span>\n\n<span class=\"n\">coef_raw<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"n\">num_features<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">coef_mask<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"n\">num_features<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">coef_true<\/span> <span class=\"o\">=<\/span> <span class=\"n\">coef_raw<\/span> <span class=\"o\">*<\/span> <span class=\"n\">coef_mask<\/span>\n\n<span class=\"n\">x_data<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">num_samples<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_features<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">y_data<\/span> <span class=\"o\">=<\/span> <span class=\"n\">x_data<\/span> <span class=\"o\">@<\/span> <span class=\"n\">coef_true<\/span> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"n\">num_samples<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">horseshoe<\/span> <span class=\"o\">=<\/span> <span class=\"n\">HorseshoeGibbs<\/span><span class=\"p\">(<\/span><span class=\"n\">max_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">400<\/span><span class=\"p\">,<\/span> <span class=\"n\">show_progress_bar<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">coefs<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma2s<\/span><span class=\"p\">,<\/span> <span class=\"n\">lamb2s<\/span><span class=\"p\">,<\/span> <span class=\"n\">tau2s<\/span> <span class=\"o\">=<\/span> <span class=\"n\">horseshoe<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">(<\/span><span class=\"n\">x_data<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_data<\/span><span class=\"p\">,<\/span> <span class=\"n\">return_samples<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">axes<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"n\">figsize<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mi\">6<\/span><span class=\"p\">,<\/span><span class=\"mi\">6<\/span><span class=\"p\">),<\/span> <span class=\"n\">dpi<\/span><span class=\"o\">=<\/span><span class=\"mi\">150<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">coefs<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$\\beta$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">][<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">sigma2s<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">][<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yscale<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"log\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">][<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$\\sigma^2$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">lamb2s<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yscale<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"log\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$\\lambda^2$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">tau2s<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yscale<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"log\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">axes<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$\\tau^2$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">fig<\/span><span class=\"o\">.<\/span><span class=\"n\">tight_layout<\/span><span class=\"p\">()<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_text output_subarea\">\n<pre>  0%|          | 0\/400 [00:00&lt;?, ?it\/s]<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea\"><img decoding=\"async\" alt=\"No description has been provided for this image\" 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\/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=901fc3f2-2924-4a0b-a7c4-0e73b8c8f603\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E5%A4%9A%E5%A4%89%E9%87%8F%E6%AD%A3%E8%A6%8F%E5%88%86%E5%B8%83%E3%81%8B%E3%82%89%E3%81%AE%E5%8A%B9%E7%8E%87%E7%9A%84%E3%81%AA%E3%82%B5%E3%83%B3%E3%83%97%E3%83%AA%E3%83%B3%E3%82%B0\"><\/span>\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03\u304b\u3089\u306e\u52b9\u7387\u7684\u306a\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f1d70bee-cd0c-4742-86d3-a47f82b51bd7\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4e0a\u8ff0\u306eGibbs\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306b\u304a\u3044\u3066\u30dc\u30c8\u30eb\u30cd\u30c3\u30af\u3068\u306a\u308b\u306e\u304c $\\bm \\beta \\mid \\mathcal D, \\bm \\beta \\setminus \\{\\theta\\}$ \u306e\u30b5\u30f3\u30d7\u30eb\u3067\u3001\u3053\u306e\u90e8\u5206\u306f (1) \u9006\u884c\u5217 $A^{-1}$ \u306e\u8a08\u7b97\u3001(2)\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03 $\\mathcal{N}(A^{-1} X^\\top y, \\sigma^2 A^{-1})$ \u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3001\u306e\u3044\u305a\u308c\u3082 $\\mathcal O(p^3) = \\mathcal O(d^6)$ \u3082\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\u8981\u6c42\u3057\u307e\u3059\u3002\u3053\u306e\u90e8\u5206\u3092\u9ad8\u901f\u5316\u3059\u308b\u305f\u3081\u306b\u3001\u5148\u7a0b\u306e\u30b3\u30fc\u30c9\u3067\u306f [Bhattacharya+ (2016)] \u306b\u3088\u308b\u4ee5\u4e0b\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=9bfa014b-a09b-4e34-82b9-d87c314d653c\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<hr \/>\n<p><strong>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 [Bhattacharya+ (2016)]<\/strong>: \u4ee5\u4e0b\u306e\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03\u3092\u8003\u3048\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=2c7fd161-a205-40cc-ada6-4cbf2dd244cf\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\bm \\beta \\sim \\mathcal N(m, V)<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=40f05b6c-32e8-412c-8fa5-74b08bba8802\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u305f\u3060\u3057<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f29e057c-875a-42ac-a0e2-036c7e8b2779\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\nm &amp;= V \\Phi^\\top \\alpha &amp;&amp; \\in \\mathbb{R}^{p}, \\\\<br \/>\nV &amp;= \\left( \\Phi^\\top \\Phi + \\Delta^{-1} \\right)^{-1} &amp;&amp; \\in \\mathbb{R}^{p \\times p}<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=b6975edd-8ee9-4d95-9b35-8788e1fcf515\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3067\u3042\u308a\u3001$\\Phi \\in \\mathbb R^{N \\times p}$\u3001$\\alpha \\in \\mathbb R^N$\u3001$\\Delta \\in \\mathbb R^{p \\times p}$\u3001\u3055\u3089\u306b $\\Delta$ \u306f\u6b63\u5b9a\u5024\u884c\u5217\u3067\u3042\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=d417f2f2-8639-41ef-95c8-47c8f8825e5e\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u5206\u5e03\u306b\u5f93\u3046\u30b5\u30f3\u30d7\u30eb $\\bm \\beta \\in \\mathbb R^p$ \u306f\u3001\u4ee5\u4e0b\u306e\u65b9\u6cd5\u306b\u3088\u308a\u751f\u6210\u53ef\u80fd\u3067\u3042\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a3271995-3d03-461b-a398-4fb04f0686e4\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<ol>\n<li>$u \\in \\mathbb R^p$ \u3092\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03 $\\mathcal N(0, \\Delta)$ \u304b\u3089\u30b5\u30f3\u30d7\u30eb\u3059\u308b<\/li>\n<li>$v \\in \\mathbb R^N$ \u3092\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03 $\\mathcal N(\\Phi u, I)$ \u304b\u3089\u30b5\u30f3\u30d7\u30eb\u3059\u308b<\/li>\n<li>\u7dda\u5f62\u65b9\u7a0b\u5f0f $(\\Phi \\Delta \\Phi^\\top + I) w = (\\alpha &#8211; v)$ \u3092 $w$ \u306b\u3064\u3044\u3066\u89e3\u304f<\/li>\n<li>$\\bm \\beta = u + \\Delta \\Phi^\\top w$ \u3092\u8a08\u7b97\u3059\u308b<\/li>\n<\/ol>\n<hr \/>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=59b695bc-c02d-4e1e-98e5-60caf885d217\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6b63\u5f53\u6027\u306fSherman\u2013Morrison\u2013Woodbury\u306e\u516c\u5f0f\u306b\u3088\u308a\u793a\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=09e4fbb1-77ac-4541-9a76-6764e864ec36\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b $\\bm \\beta \\mid \\cdot \\sim \\mathcal{N}(\\bm A^{-1} \\bm X^\\top \\bm y, \\sigma^2 \\bm A^{-1})$ \u3092\u5f53\u3066\u306f\u3081\u308b\u3068\u3001<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=16e15d64-398f-4e7b-80f6-ccf0d2c9cb90\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\Phi = \\frac{X}{\\sigma}, \\quad<br \/>\n\\alpha = \\frac{y}{\\sigma}, \\quad<br \/>\n\\Delta = \\mathop{\\rm diag} \\left\\{ \\tau_i^2 \\lambda^2 \\sigma^2 \\right\\}<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=e53b0896-f145-4965-85c2-a1f45cd79c53\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=c5e32582-668b-423b-a687-37e15db21fd1\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0a\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u304a\u3044\u3066\u3001\u6700\u5927\u306e\u30dc\u30c8\u30eb\u30cd\u30c3\u30af\u3068\u306a\u308b\u306e\u306f\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u90e8\u5206\u3067\u3059\u3002\u8a73\u7d30\u306f\u7701\u7565\u3057\u307e\u3059\u304c\u3001\u884c\u5217 $\\Delta$ \u304c\u30b9\u30d1\u30fc\u30b9\u306a\u5834\u5408\u306b\u306f $\\mathcal O(p N^2)$ \u304c\u3001$\\Delta$ \u304c\u30b9\u30d1\u30fc\u30b9\u3067\u306a\u3044\u5834\u5408\u306b\u306f $\\mathcal O(p^2 N)$ \u304c\u652f\u914d\u7684\u306b\u306a\u308a\u307e\u3059\u3002\u4eca\u56de\u306e\u8a2d\u5b9a\u3067\u306f\u3044\u305a\u308c\u306b\u305b\u3088 $\\mathcal O(p^3)$ \u306b\u6bd4\u3079\u308c\u3070 $p$ \u3078\u306e\u4f9d\u5b58\u6027\u304c\u5c0f\u3055\u304f\u306a\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=bf0d9d2d-6795-4870-ae1c-b89d1a98b065\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><code>sample_theta()<\/code> \u95a2\u6570\u3067\u306f\u3001\u4ee5\u4e0a\u306e\u30ed\u30b8\u30c3\u30af\u3092\u7528\u3044\u3066\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u9ad8\u901f\u5316\u3059\u308b\u3088\u3046\u5de5\u592b\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a72f3796-edbc-4dce-a55f-f8908baf4c66\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E7%8D%B2%E5%BE%97%E9%96%A2%E6%95%B0%E3%81%AE%E6%9C%80%E9%81%A9%E5%8C%96\"><\/span>\u7372\u5f97\u95a2\u6570\u306e\u6700\u9069\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=9c90580c-d91e-4039-afa8-26f52f3ce93b\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f97\u3089\u308c\u305f\u30b5\u30f3\u30d7\u30eb $\\tilde{\\bm \\beta} \\sim p(\\bm \\beta | \\mathcal D)$ \u3092\u7528\u3044\u305f2\u6b21\u591a\u9805\u5f0f\u30e2\u30c7\u30eb $\\alpha(\\bm x) = \\hat f(\\bm x; \\tilde{\\bm \\beta})$ \u3092\u6700\u5c0f\u5316\u3059\u308b\u5165\u529b $x^{(t+1)} = \\mathop{\\rm arg~min}_x \\alpha(x)$ \u304c\u3001\u6b21\u306b\u5165\u529b\u3059\u308b\u30b5\u30f3\u30d7\u30eb\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u304b\u3089\u306f\u3001\u3053\u306e\u5165\u529b\u3092\u63a2\u7d22\u3059\u308b\u30ed\u30b8\u30c3\u30af\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=b37323f2-401c-47ea-9db4-2cc3a6f6c6cd\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>2\u6b21\u591a\u9805\u5f0f\u30e2\u30c7\u30eb\u304c\u3001\u6b21\u5f0f\u3067\u8868\u3055\u308c\u308b\u3088\u3046\u306aQUBO (quadratic unconstrained binary optimization, \u4e8c\u6b21\u7121\u5236\u7d04\u4e8c\u5024\u6700\u9069\u5316\u554f\u984c) \u5f62\u5f0f\u306b\u66f8\u304d\u76f4\u305b\u308b\u70b9\u306b\u6ce8\u76ee\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=6a9b63a3-0fa8-4ef9-a4c1-4fa4e615ae72\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\mathop{\\rm minimize}\\limits_{\\bm x \\in \\{0, 1\\}^d} \\quad \\bm x^\\top \\bm Q \\bm x<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=5edacc12-9913-4dd7-9ecc-fe39de20b1dd\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u3053\u3068\u3092\u7528\u3044\u3066\u56de\u5e30\u4fc2\u6570\u3092QUBO\u884c\u5217\u306b\u5909\u63db\u3057\u3001SA\u3067\u4f4e\u30a8\u30cd\u30eb\u30ae\u30fc\u72b6\u614b\u3092\u30b5\u30f3\u30d7\u30eb\u3059\u308b\u3053\u3068\u3067\u6b21\u306e\u5165\u529b\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=d953c409-e7cd-4a4d-900f-dc14d71ab5ae\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SA\u306b\u3088\u308b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306f <code>openjij<\/code> \u306b\u3088\u308b\u5b9f\u88c5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=019d4a70-f465-4cb4-b0ef-8ae216ace1a5\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">calc_num_vars_from_num_features<\/span><span class=\"p\">(<\/span><span class=\"n\">num_features<\/span><span class=\"p\">:<\/span> <span class=\"nb\">int<\/span><span class=\"p\">)<\/span> <span class=\"o\">-&gt;<\/span> <span class=\"nb\">int<\/span><span class=\"p\">:<\/span>\n    <span class=\"k\">return<\/span> <span class=\"nb\">int<\/span><span class=\"p\">((<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">8<\/span> <span class=\"o\">*<\/span> <span class=\"n\">num_features<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">7<\/span><span class=\"p\">))<\/span> <span class=\"o\">\/\/<\/span> <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\n\n\n<span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">calc_Q_from_coef<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">)<\/span> <span class=\"o\">-&gt;<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">:<\/span>\n    <span class=\"n\">num_features<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">num_vars<\/span> <span class=\"o\">=<\/span> <span class=\"n\">calc_num_vars_from_num_features<\/span><span class=\"p\">(<\/span><span class=\"n\">num_features<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">Q<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">((<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">))<\/span>\n    <span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">j<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">diag_indices<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">Q<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">coef<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span> <span class=\"p\">:<\/span> <span class=\"n\">num_vars<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">]<\/span>\n    <span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">j<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">triu_indices<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">k<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">Q<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">coef<\/span><span class=\"p\">[<\/span><span class=\"n\">num_vars<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span> <span class=\"p\">:]<\/span>\n    <span class=\"k\">return<\/span> <span class=\"n\">Q<\/span>\n\n\n<span class=\"k\">class<\/span><span class=\"w\"> <\/span><span class=\"nc\">BOCSAcquisitionFunction<\/span><span class=\"p\">:<\/span>\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__init__<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">optimizer<\/span><span class=\"p\">:<\/span> <span class=\"n\">oj<\/span><span class=\"o\">.<\/span><span class=\"n\">SASampler<\/span><span class=\"o\">.<\/span><span class=\"n\">sample_qubo<\/span><span class=\"p\">):<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">optimizer<\/span> <span class=\"o\">=<\/span> <span class=\"n\">optimizer<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">build<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">surrogate_model<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">coef<\/span> <span class=\"o\">=<\/span> <span class=\"n\">surrogate_model<\/span><span class=\"o\">.<\/span><span class=\"n\">params<\/span><span class=\"p\">[<\/span><span class=\"s2\">\"coef\"<\/span><span class=\"p\">]<\/span>\n        <span class=\"n\">Q<\/span> <span class=\"o\">=<\/span> <span class=\"n\">calc_Q_from_coef<\/span><span class=\"p\">(<\/span><span class=\"n\">coef<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">Q<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Q<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">optimize<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">)<\/span> <span class=\"o\">-&gt;<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">response<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">optimizer<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">Q<\/span><span class=\"p\">)<\/span>\n        <span class=\"n\">optimal_x<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">(<\/span><span class=\"nb\">list<\/span><span class=\"p\">(<\/span><span class=\"n\">response<\/span><span class=\"o\">.<\/span><span class=\"n\">first<\/span><span class=\"o\">.<\/span><span class=\"n\">sample<\/span><span class=\"o\">.<\/span><span class=\"n\">values<\/span><span class=\"p\">()),<\/span> <span class=\"n\">dtype<\/span><span class=\"o\">=<\/span><span class=\"nb\">int<\/span><span class=\"p\">)<\/span>\n        <span class=\"k\">return<\/span> <span class=\"n\">optimal_x<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=ea430e44-9558-4725-adfb-b2fd7c8774e7\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"c1\"># TEST \u771f\u306eQ_true\u3068\u63a8\u5b9a\u3055\u308c\u305fQ\u306e\u985e\u4f3c\u5ea6\u3092\u8a08\u7b97<\/span>\n\n<span class=\"n\">num_vars<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">10<\/span>\n<span class=\"n\">num_samples<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">250<\/span>\n\n<span class=\"n\">Q_true<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">triu<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">)))<\/span>\n<span class=\"n\">x_data<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">num_samples<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">y_data<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">einsum<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"di,dj,ij-&gt;d\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_data<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_data<\/span><span class=\"p\">,<\/span> <span class=\"n\">Q_true<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span>\n    <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"n\">num_samples<\/span>\n<span class=\"p\">)<\/span>\n\n<span class=\"n\">horseshoe_linear_regressor<\/span> <span class=\"o\">=<\/span> <span class=\"n\">HorseshoeGibbs<\/span><span class=\"p\">(<\/span><span class=\"n\">max_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">20<\/span><span class=\"p\">,<\/span> <span class=\"n\">show_progress_bar<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">bocs_surrogate_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">BOCSSurrogateModel<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">linear_regressor<\/span><span class=\"o\">=<\/span><span class=\"n\">horseshoe_linear_regressor<\/span>\n<span class=\"p\">)<\/span>\n<span class=\"n\">bocs_acquis_func<\/span> <span class=\"o\">=<\/span> <span class=\"n\">BOCSAcquisitionFunction<\/span><span class=\"p\">(<\/span><span class=\"n\">oj<\/span><span class=\"o\">.<\/span><span class=\"n\">SASampler<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">sample_qubo<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">bocs_surrogate_model<\/span><span class=\"o\">.<\/span><span class=\"n\">update<\/span><span class=\"p\">(<\/span><span class=\"n\">x_data<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_data<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">bocs_acquis_func<\/span><span class=\"o\">.<\/span><span class=\"n\">build<\/span><span class=\"p\">(<\/span><span class=\"n\">bocs_surrogate_model<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">x_next<\/span> <span class=\"o\">=<\/span> <span class=\"n\">bocs_acquis_func<\/span><span class=\"o\">.<\/span><span class=\"n\">optimize<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">y_next<\/span> <span class=\"o\">=<\/span> <span class=\"n\">x_next<\/span> <span class=\"o\">@<\/span> <span class=\"n\">Q_true<\/span> <span class=\"o\">@<\/span> <span class=\"n\">x_next<\/span>\n\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"x_next:\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_next<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"y_next:\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_next<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span>\n    <span class=\"s2\">\"similarity:\"<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">Q_true<\/span> <span class=\"o\">*<\/span> <span class=\"n\">bocs_acquis_func<\/span><span class=\"o\">.<\/span><span class=\"n\">Q<\/span><span class=\"p\">)<\/span>\n    <span class=\"o\">\/<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">Q_true<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">bocs_acquis_func<\/span><span class=\"o\">.<\/span><span class=\"n\">Q<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)),<\/span>\n<span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>x_next: [0 1 0 1 1 0 0 0 1 0]\ny_next: -19.367115987530514\nsimilarity: 0.9999814907528135\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=6c89bed9-3254-422e-b217-beccbfc65bb3\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E5%AE%9F%E9%A8%93\"><\/span>\u5b9f\u9a13<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=68e23510-945b-4308-9aa8-aae493ec5b45\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0a\u3067 <code>BOCS-SA<\/code> \u306b\u5fc5\u8981\u306a\u6a5f\u80fd\u3092\u6e96\u5099\u3067\u304d\u305f\u306e\u3067\u3001\u3044\u304f\u3064\u304b\u306e\u554f\u984c\u3092\u4f5c\u6210\u3057\u3066\u30c6\u30b9\u30c8\u3092\u884c\u3044\u307e\u3057\u3087\u3046\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=acee4cd3-22e3-48eb-86f5-7b81c81b2da3\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"RandomQUBO\"><\/span>RandomQUBO<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a84ce9e9-04c3-4bf6-a222-3ff78463a3d3\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u307e\u305a\u3001\u7c21\u5358\u306a\u4f8b\u984c\u3068\u3057\u3066\u3001\u30e9\u30f3\u30c0\u30e0\u306b\u751f\u6210\u3055\u308c\u305fQUBO\u5f62\u5f0f\u306e\u76ee\u7684\u95a2\u6570\u306e\u6700\u9069\u89e3\u3092\u63a2\u7d22\u3059\u308b\u554f\u984c\u3092\u53d6\u308a\u6271\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=4ba8a026-5581-4817-a19f-289b6d8b3762\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">class<\/span><span class=\"w\"> <\/span><span class=\"nc\">RandomQUBO<\/span><span class=\"p\">:<\/span>\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__init__<\/span><span class=\"p\">(<\/span>\n        <span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">noise_variance<\/span><span class=\"p\">:<\/span> <span class=\"nb\">float<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.0<\/span><span class=\"p\">,<\/span> <span class=\"n\">seed<\/span><span class=\"p\">:<\/span> <span class=\"n\">Optional<\/span><span class=\"p\">[<\/span><span class=\"nb\">int<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">None<\/span>\n    <span class=\"p\">):<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">noise_variance<\/span> <span class=\"o\">=<\/span> <span class=\"n\">noise_variance<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">rng<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">default_rng<\/span><span class=\"p\">(<\/span><span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">Q<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">))<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">energy<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">):<\/span>\n        <span class=\"k\">return<\/span> <span class=\"n\">x<\/span> <span class=\"o\">@<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">Q<\/span> <span class=\"o\">@<\/span> <span class=\"n\">x<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__call__<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">):<\/span>\n        <span class=\"k\">return<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">noise_variance<\/span><span class=\"p\">))<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=233d8069-4375-47cc-9135-2079895c029c\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SA\u306b\u3088\u308a\u3053\u306e\u30e2\u30c7\u30eb\u306e\u6700\u5c0f\u5316\u554f\u984c\u306e\u6700\u9069\u89e3\u3092\u63a2\u7d22\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=90bde248-e09c-47d4-a596-1a7d03b1ee06\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"c1\"># TEST<\/span>\n\n<span class=\"n\">seed<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n<span class=\"n\">rng<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">default_rng<\/span><span class=\"p\">(<\/span><span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">num_vars<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">16<\/span>\n<span class=\"n\">num_init_samples<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">5<\/span>\n<span class=\"n\">noise_variance<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>\n\n<span class=\"n\">random_qubo<\/span> <span class=\"o\">=<\/span> <span class=\"n\">RandomQUBO<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">noise_variance<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"n\">seed<\/span><span class=\"o\">=<\/span><span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">Q<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random_qubo<\/span><span class=\"o\">.<\/span><span class=\"n\">Q<\/span>\n\n<span class=\"n\">response<\/span> <span class=\"o\">=<\/span> <span class=\"n\">oj<\/span><span class=\"o\">.<\/span><span class=\"n\">SASampler<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">sample_qubo<\/span><span class=\"p\">(<\/span><span class=\"n\">Q<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_reads<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">response<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">GS_energy<\/span> <span class=\"o\">=<\/span> <span class=\"n\">response<\/span><span class=\"o\">.<\/span><span class=\"n\">first<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span>\n<span class=\"n\">GS_sample<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">list<\/span><span class=\"p\">(<\/span><span class=\"n\">response<\/span><span class=\"o\">.<\/span><span class=\"n\">first<\/span><span class=\"o\">.<\/span><span class=\"n\">sample<\/span><span class=\"o\">.<\/span><span class=\"n\">values<\/span><span class=\"p\">())<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"Approximate groudstate:\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">GS_sample<\/span><span class=\"p\">,<\/span> <span class=\"n\">GS_energy<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>   0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15     energy num_oc.\n0  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n1  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n2  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n3  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n4  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n5  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n6  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n7  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n8  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n9  1  1  0  0  0  0  1  0  0  1  1  1  1  1  1  1 -25.135564       1\n['BINARY', 10 rows, 10 samples, 16 variables]\nApproximate groudstate: [1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1] -25.13556376452084\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=c956148f-abf7-4594-ae29-9820a0eceeae\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0a\u306e\u76ee\u7684\u95a2\u6570\u3068\u3001\u4ee3\u7406\u30e2\u30c7\u30eb\u3001\u7372\u5f97\u95a2\u6570\u3001\u30bd\u30eb\u30d0\u30fc\u3092\u6307\u5b9a\u3057\u3001\u30d9\u30a4\u30ba\u6700\u9069\u5316\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=49fdf8a8-efe2-41c9-89bb-7eaf4b455d86\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">surrogate_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">BOCSSurrogateModel<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">linear_regressor<\/span><span class=\"o\">=<\/span><span class=\"n\">HorseshoeGibbs<\/span><span class=\"p\">(<\/span><span class=\"n\">max_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">)<\/span>\n<span class=\"p\">)<\/span>\n<span class=\"n\">acquisition_function<\/span> <span class=\"o\">=<\/span> <span class=\"n\">BOCSAcquisitionFunction<\/span><span class=\"p\">(<\/span><span class=\"n\">oj<\/span><span class=\"o\">.<\/span><span class=\"n\">SASampler<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">sample_qubo<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">X<\/span> <span class=\"o\">=<\/span> <span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">num_init_samples<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">([<\/span><span class=\"n\">random_qubo<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"k\">for<\/span> <span class=\"n\">x<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">X<\/span><span class=\"p\">])<\/span>\n\n<span class=\"c1\"># bayesian optimization loop<\/span>\n<span class=\"n\">y_best<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">inf<\/span>\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">tqdm<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">120<\/span><span class=\"p\">)):<\/span>\n    <span class=\"n\">surrogate_model<\/span><span class=\"o\">.<\/span><span class=\"n\">update<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">acquisition_function<\/span><span class=\"o\">.<\/span><span class=\"n\">build<\/span><span class=\"p\">(<\/span><span class=\"n\">surrogate_model<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">x_next<\/span> <span class=\"o\">=<\/span> <span class=\"n\">acquisition_function<\/span><span class=\"o\">.<\/span><span class=\"n\">optimize<\/span><span class=\"p\">()<\/span>\n    <span class=\"n\">y_next<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random_qubo<\/span><span class=\"p\">(<\/span><span class=\"n\">x_next<\/span><span class=\"p\">)<\/span>  <span class=\"c1\"># \u95a2\u6570\u306e \u201c\u89b3\u6e2c\u5024\u201d \u3092\u8a18\u9332<\/span>\n\n    <span class=\"n\">X<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">vstack<\/span><span class=\"p\">([<\/span><span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_next<\/span><span class=\"p\">])<\/span>\n    <span class=\"n\">y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">hstack<\/span><span class=\"p\">([<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_next<\/span><span class=\"p\">])<\/span>\n\n    <span class=\"n\">y_best<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">y_best<\/span><span class=\"p\">,<\/span> <span class=\"n\">random_qubo<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span><span class=\"p\">(<\/span><span class=\"n\">x_next<\/span><span class=\"p\">))<\/span>  <span class=\"c1\"># \u95a2\u6570\u306e\u771f\u306e\u5024\u3092\u8a18\u9332<\/span>\n\n    <span class=\"k\">if<\/span> <span class=\"n\">i<\/span> <span class=\"o\">%<\/span> <span class=\"mi\">10<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">tqdm<\/span><span class=\"o\">.<\/span><span class=\"n\">write<\/span><span class=\"p\">(<\/span><span class=\"sa\">f<\/span><span class=\"s2\">\"iteration <\/span><span class=\"si\">{<\/span><span class=\"n\">i<\/span><span class=\"si\">:<\/span><span class=\"s2\">4<\/span><span class=\"si\">}<\/span><span class=\"s2\">: y_best = <\/span><span class=\"si\">{<\/span><span class=\"n\">y_best<\/span><span class=\"si\">:<\/span><span class=\"s2\">6.3<\/span><span class=\"si\">}<\/span><span class=\"s2\">: x_next = <\/span><span class=\"si\">{<\/span><span class=\"n\">x_next<\/span><span class=\"si\">}<\/span><span class=\"s2\">\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_text output_subarea\">\n<pre>  0%|          | 0\/120 [00:00&lt;?, ?it\/s]<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>iteration    0: y_best =  0.989: x_next = [1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1]\niteration   10: y_best =  -16.5: x_next = [0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1]\niteration   20: y_best =  -23.6: x_next = [1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1]\niteration   30: y_best =  -25.1: x_next = [1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1]\niteration   40: y_best =  -25.1: x_next = [1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1]\niteration   50: y_best =  -25.1: x_next = [1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1]\niteration   60: y_best =  -25.1: x_next = [1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1]\niteration   70: y_best =  -25.1: x_next = [1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1]\niteration   80: y_best =  -25.1: x_next = [1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1]\niteration   90: y_best =  -25.1: x_next = [1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1]\niteration  100: y_best =  -25.1: x_next = [1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1]\niteration  110: y_best =  -25.1: x_next = [1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1]\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=dbacbfd2-2663-4082-ad7f-5496a2eb570f\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f97\u3089\u308c\u305f\u7d50\u679c\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=944c51e4-7a82-4190-b1fd-2301095b4c29\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">plot_x<\/span> <span class=\"o\">=<\/span> <span class=\"n\">X<\/span>\n<span class=\"n\">plot_y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">apply_along_axis<\/span><span class=\"p\">(<\/span><span class=\"n\">random_qubo<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">plot_min_y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">([<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">[:<\/span><span class=\"n\">i<\/span><span class=\"p\">])<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)])<\/span>\n\n<span class=\"n\">fig<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">figure<\/span><span class=\"p\">(<\/span><span class=\"n\">figsize<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mi\">6<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">fig<\/span><span class=\"o\">.<\/span><span class=\"n\">add_subplot<\/span><span class=\"p\">()<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_min_y<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_min_y<\/span> <span class=\"o\">-<\/span> <span class=\"n\">GS_energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"blue\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">scatter<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_y<\/span> <span class=\"o\">-<\/span> <span class=\"n\">GS_energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"red\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"x\"<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"RandomQUBO\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"iteration $t$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$f(x^{(t)}) - f^\\ast$\"<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">()<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea\"><img decoding=\"async\" alt=\"No description has been provided for this image\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=b292cd73-9652-4faf-93ab-7e0fa57b2a72\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4eca\u56de\u306f $d=16$ \u3068\u3044\u3046\u5c0f\u898f\u6a21\u306a\u8a2d\u5b9a\u306a\u306e\u3067\u3001\u6bd4\u8f03\u7684\u7c21\u5358\u306b\u6700\u9069\u89e3\u3092\u767a\u898b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u3044\u307e\u3059\u3002\u6700\u7d42\u7684\u306b\u306f $t=30$ \u7a0b\u5ea6\u3067\u6700\u9069\u89e3\u306b\u5230\u9054\u3057\u3066\u304a\u308a\u3001BOCS\u304c\u4e0a\u624b\u304f\u6a5f\u80fd\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=81ad5790-c82f-40c1-8e70-23479f5c9f75\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"RandomHUBO\"><\/span>RandomHUBO<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=5e8d9d3d-4546-4546-b022-d61471fb708b\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>3\u5bfe\u76f8\u4e92\u4f5c\u7528\u3092\u6301\u3064\u9ad8\u6b21\u51432\u5024\u6700\u9069\u5316\u3082\u884c\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u76ee\u7684\u95a2\u6570\u3068\u3057\u3066<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3bb38161-adb9-481c-b62a-078e6267f85a\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\nf(x) = \\sum_{i,j,k} Q_{ijk} x_i x_j x_k<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a936a382-b2f7-4543-afce-d7918d57de22\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3092\u4eee\u5b9a\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=7171aa68-0a16-46d3-b10e-20865076e4ee\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">class<\/span><span class=\"w\"> <\/span><span class=\"nc\">RandomHUBO<\/span><span class=\"p\">:<\/span>\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__init__<\/span><span class=\"p\">(<\/span>\n        <span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">noise_variance<\/span><span class=\"p\">:<\/span> <span class=\"nb\">float<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.0<\/span><span class=\"p\">,<\/span> <span class=\"n\">seed<\/span><span class=\"p\">:<\/span> <span class=\"n\">Optional<\/span><span class=\"p\">[<\/span><span class=\"nb\">int<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">None<\/span>\n    <span class=\"p\">):<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">noise_variance<\/span> <span class=\"o\">=<\/span> <span class=\"n\">noise_variance<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">rng<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">default_rng<\/span><span class=\"p\">(<\/span><span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">Q<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">))<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">energy<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">):<\/span>\n        <span class=\"k\">return<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">einsum<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"ijk,i,j,k\"<\/span><span class=\"p\">,<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">Q<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__call__<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">):<\/span>\n        <span class=\"k\">return<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">noise_variance<\/span><span class=\"p\">))<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=5f0a5021-433c-4baf-a573-0f4bb7745f12\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">seed<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n<span class=\"n\">rng<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">default_rng<\/span><span class=\"p\">(<\/span><span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">num_vars<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">16<\/span>\n<span class=\"n\">num_init_samples<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">5<\/span>\n<span class=\"n\">noise_variance<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.0<\/span>\n\n<span class=\"n\">random_hubo<\/span> <span class=\"o\">=<\/span> <span class=\"n\">RandomHUBO<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">noise_variance<\/span><span class=\"p\">,<\/span> <span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">surrogate_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">BOCSSurrogateModel<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">linear_regressor<\/span><span class=\"o\">=<\/span><span class=\"n\">HorseshoeGibbs<\/span><span class=\"p\">(<\/span><span class=\"n\">max_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">)<\/span>\n<span class=\"p\">)<\/span>\n<span class=\"n\">acquisition_function<\/span> <span class=\"o\">=<\/span> <span class=\"n\">BOCSAcquisitionFunction<\/span><span class=\"p\">(<\/span>\n    <span class=\"k\">lambda<\/span> <span class=\"n\">Q<\/span><span class=\"p\">:<\/span> <span class=\"n\">oj<\/span><span class=\"o\">.<\/span><span class=\"n\">SASampler<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">sample_qubo<\/span><span class=\"p\">(<\/span><span class=\"n\">Q<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_reads<\/span><span class=\"o\">=<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_sweeps<\/span><span class=\"o\">=<\/span><span class=\"mi\">2500<\/span><span class=\"p\">)<\/span>\n<span class=\"p\">)<\/span>\n\n<span class=\"n\">X<\/span> <span class=\"o\">=<\/span> <span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">num_init_samples<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">([<\/span><span class=\"n\">random_hubo<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"k\">for<\/span> <span class=\"n\">x<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">X<\/span><span class=\"p\">])<\/span>\n\n<span class=\"c1\"># bayesian optimization loop<\/span>\n<span class=\"n\">y_best<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">inf<\/span>\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">tqdm<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">150<\/span><span class=\"p\">)):<\/span>\n    <span class=\"n\">surrogate_model<\/span><span class=\"o\">.<\/span><span class=\"n\">update<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">acquisition_function<\/span><span class=\"o\">.<\/span><span class=\"n\">build<\/span><span class=\"p\">(<\/span><span class=\"n\">surrogate_model<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">x_next<\/span> <span class=\"o\">=<\/span> <span class=\"n\">acquisition_function<\/span><span class=\"o\">.<\/span><span class=\"n\">optimize<\/span><span class=\"p\">()<\/span>\n    <span class=\"n\">y_next<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random_hubo<\/span><span class=\"p\">(<\/span><span class=\"n\">x_next<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"n\">X<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">vstack<\/span><span class=\"p\">([<\/span><span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_next<\/span><span class=\"p\">])<\/span>\n    <span class=\"n\">y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">hstack<\/span><span class=\"p\">([<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_next<\/span><span class=\"p\">])<\/span>\n\n    <span class=\"n\">y_best<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">y_best<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_next<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"k\">if<\/span> <span class=\"n\">i<\/span> <span class=\"o\">%<\/span> <span class=\"mi\">10<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">tqdm<\/span><span class=\"o\">.<\/span><span class=\"n\">write<\/span><span class=\"p\">(<\/span>\n            <span class=\"sa\">f<\/span><span class=\"s2\">\"iteration <\/span><span class=\"si\">{<\/span><span class=\"n\">i<\/span><span class=\"si\">:<\/span><span class=\"s2\">4<\/span><span class=\"si\">}<\/span><span class=\"s2\">: y_best = <\/span><span class=\"si\">{<\/span><span class=\"n\">y_best<\/span><span class=\"si\">:<\/span><span class=\"s2\">6.3<\/span><span class=\"si\">}<\/span><span class=\"s2\">: x_next = <\/span><span class=\"si\">{<\/span><span class=\"n\">x_next<\/span><span class=\"si\">}<\/span><span class=\"s2\">\"<\/span>\n        <span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_text output_subarea\">\n<pre>  0%|          | 0\/150 [00:00&lt;?, ?it\/s]<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>iteration    0: y_best =  -13.6: x_next = [1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0]\niteration   10: y_best = -1.06e+02: x_next = [1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0]\niteration   20: y_best = -1.33e+02: x_next = [0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1]\niteration   30: y_best = -1.33e+02: x_next = [0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0]\niteration   40: y_best = -1.33e+02: x_next = [1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0]\niteration   50: y_best = -1.33e+02: x_next = [0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1]\niteration   60: y_best = -1.46e+02: x_next = [1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1]\niteration   70: y_best = -1.46e+02: x_next = [0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 0]\niteration   80: y_best = -1.46e+02: x_next = [0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0]\niteration   90: y_best = -1.46e+02: x_next = [1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1]\niteration  100: y_best = -1.46e+02: x_next = [0 1 1 1 0 0 1 1 0 0 1 0 1 1 1 1]\niteration  110: y_best = -1.46e+02: x_next = [1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1]\niteration  120: y_best = -1.46e+02: x_next = [1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1]\niteration  130: y_best = -1.46e+02: x_next = [1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1]\niteration  140: y_best = -1.46e+02: x_next = [1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1]\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=9a2f27ac-93d3-4807-8005-5ee941f95629\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u6bd4\u8f03\u5bfe\u8c61\u3068\u3057\u3066\u30e9\u30f3\u30c0\u30e0\u306b\u63a2\u7d22\u3059\u308b\u65b9\u6cd5\u3067\u3082\u5b9f\u9a13\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=3ecdd0aa-c6ba-44f3-8120-6d45a1e532cd\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">rng<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">default_rng<\/span><span class=\"p\">(<\/span><span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">X_rand<\/span> <span class=\"o\">=<\/span> <span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mi\">150<\/span> <span class=\"o\">+<\/span> <span class=\"n\">num_init_samples<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">))<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3b3964bf-bb65-41bb-924a-7e1caf5d1b40\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f97\u3089\u308c\u305f\u7d50\u679c\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=20abe25a-d435-45d3-8361-5c57046ba66b\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">plot_x<\/span> <span class=\"o\">=<\/span> <span class=\"n\">X<\/span>\n<span class=\"n\">plot_y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">apply_along_axis<\/span><span class=\"p\">(<\/span><span class=\"n\">random_hubo<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plot_min_y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">([<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">[:<\/span><span class=\"n\">i<\/span><span class=\"p\">])<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)])<\/span>\n\n<span class=\"n\">plot_X_rand<\/span> <span class=\"o\">=<\/span> <span class=\"n\">X_rand<\/span>\n<span class=\"n\">plot_y_rand<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">apply_along_axis<\/span><span class=\"p\">(<\/span><span class=\"n\">random_hubo<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">X_rand<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plot_min_y_rand<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">(<\/span>\n    <span class=\"p\">[<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y_rand<\/span><span class=\"p\">[:<\/span><span class=\"n\">i<\/span><span class=\"p\">])<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y_rand<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)]<\/span>\n<span class=\"p\">)<\/span>\n\n<span class=\"n\">fig<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">figure<\/span><span class=\"p\">(<\/span><span class=\"n\">figsize<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mi\">6<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">fig<\/span><span class=\"o\">.<\/span><span class=\"n\">add_subplot<\/span><span class=\"p\">()<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_min_y_rand<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_min_y_rand<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"red\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">scatter<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y_rand<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_y_rand<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"red\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"^\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"Random\"<\/span>\n<span class=\"p\">)<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_min_y<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_min_y<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"blue\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">scatter<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_y<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"blue\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"x\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"BOCS\"<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">vlines<\/span><span class=\"p\">(<\/span><span class=\"n\">num_init_samples<\/span><span class=\"p\">,<\/span> <span class=\"nb\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">),<\/span> <span class=\"nb\">max<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">),<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"black\"<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"RandomHUBO\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"iteration $t$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$f(x^{(t)})$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">()<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea\"><img decoding=\"async\" alt=\"No description has been provided for this image\" 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\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\/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=5745a199-c8e8-45a8-9c07-0c4a27b79d3b\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>BOCS\u3067\u306f\u76ee\u7684\u95a2\u6570\u5024\u306e\u4f4e\u3044\u9818\u57df\u3092\u4e2d\u5fc3\u306b\u30b5\u30f3\u30d7\u30eb\u3092\u96c6\u3081\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=a8dc42f3-7f3b-47d9-98a3-832456273977\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"RandomMLP\"><\/span>RandomMLP<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=c1e0ffeb-10d1-4fb4-9b01-5dd036894f07\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u66f4\u306b\u3082\u30461\u3064\u7c21\u5358\u306a\u4f8b\u3068\u3057\u3066\u3001\u591a\u5c64\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u6700\u9069\u5316\u3092\u884c\u3063\u3066\u307f\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u5f8c\u306e\u62e1\u5f35\u6027\u3082\u8003\u3048\u3066\u3001\u591a\u5c64\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306fPyTorch\u3067\u5b9f\u88c5\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=47ac70ca-cc8d-4332-8fed-4565a97ca278\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"kn\">import<\/span><span class=\"w\"> <\/span><span class=\"nn\">torch<\/span>\n<span class=\"kn\">import<\/span><span class=\"w\"> <\/span><span class=\"nn\">torch.nn<\/span><span class=\"w\"> <\/span><span class=\"k\">as<\/span><span class=\"w\"> <\/span><span class=\"nn\">nn<\/span>\n\n\n<span class=\"k\">class<\/span><span class=\"w\"> <\/span><span class=\"nc\">RandomMLP<\/span><span class=\"p\">(<\/span><span class=\"n\">nn<\/span><span class=\"o\">.<\/span><span class=\"n\">Module<\/span><span class=\"p\">):<\/span>\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__init__<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">dim_in<\/span><span class=\"p\">,<\/span> <span class=\"n\">dim_hidden<\/span><span class=\"p\">):<\/span>\n        <span class=\"nb\">super<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"fm\">__init__<\/span><span class=\"p\">()<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">fc1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">nn<\/span><span class=\"o\">.<\/span><span class=\"n\">Linear<\/span><span class=\"p\">(<\/span><span class=\"n\">dim_in<\/span><span class=\"p\">,<\/span> <span class=\"n\">dim_hidden<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">fc2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">nn<\/span><span class=\"o\">.<\/span><span class=\"n\">Linear<\/span><span class=\"p\">(<\/span><span class=\"n\">dim_hidden<\/span><span class=\"p\">,<\/span> <span class=\"n\">dim_hidden<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">fc3<\/span> <span class=\"o\">=<\/span> <span class=\"n\">nn<\/span><span class=\"o\">.<\/span><span class=\"n\">Linear<\/span><span class=\"p\">(<\/span><span class=\"n\">dim_hidden<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">forward<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">:<\/span> <span class=\"n\">torch<\/span><span class=\"o\">.<\/span><span class=\"n\">Tensor<\/span><span class=\"p\">)<\/span> <span class=\"o\">-&gt;<\/span> <span class=\"n\">torch<\/span><span class=\"o\">.<\/span><span class=\"n\">Tensor<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">x<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">fc1<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span>\n        <span class=\"n\">x<\/span> <span class=\"o\">=<\/span> <span class=\"n\">torch<\/span><span class=\"o\">.<\/span><span class=\"n\">relu<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span>\n        <span class=\"n\">x<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">fc2<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span>\n        <span class=\"n\">x<\/span> <span class=\"o\">=<\/span> <span class=\"n\">torch<\/span><span class=\"o\">.<\/span><span class=\"n\">relu<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span>\n        <span class=\"n\">x<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">fc3<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"k\">return<\/span> <span class=\"n\">x<\/span>\n\n\n<span class=\"k\">class<\/span><span class=\"w\"> <\/span><span class=\"nc\">RandomMLPWrapper<\/span><span class=\"p\">:<\/span>\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__init__<\/span><span class=\"p\">(<\/span>\n        <span class=\"bp\">self<\/span><span class=\"p\">,<\/span>\n        <span class=\"n\">random_mlp_model<\/span><span class=\"p\">:<\/span> <span class=\"n\">RandomMLP<\/span><span class=\"p\">,<\/span>\n        <span class=\"n\">noise_variance<\/span><span class=\"p\">:<\/span> <span class=\"nb\">float<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.0<\/span><span class=\"p\">,<\/span>\n        <span class=\"n\">seed<\/span><span class=\"p\">:<\/span> <span class=\"n\">Optional<\/span><span class=\"p\">[<\/span><span class=\"nb\">int<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">None<\/span><span class=\"p\">,<\/span>\n    <span class=\"p\">):<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">noise_variance<\/span> <span class=\"o\">=<\/span> <span class=\"n\">noise_variance<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">rng<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">default_rng<\/span><span class=\"p\">(<\/span><span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n        <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random_mlp_model<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">energy<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">x<\/span> <span class=\"o\">=<\/span> <span class=\"n\">torch<\/span><span class=\"o\">.<\/span><span class=\"n\">from_numpy<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">float<\/span><span class=\"p\">()<\/span>\n        <span class=\"n\">y<\/span> <span class=\"o\">=<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">model<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span>\n        <span class=\"n\">y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">y<\/span><span class=\"o\">.<\/span><span class=\"n\">detach<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">numpy<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">item<\/span><span class=\"p\">()<\/span>\n        <span class=\"k\">return<\/span> <span class=\"n\">y<\/span>\n\n    <span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"fm\">__call__<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">:<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">ndarray<\/span><span class=\"p\">):<\/span>\n        <span class=\"k\">return<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"bp\">self<\/span><span class=\"o\">.<\/span><span class=\"n\">noise_variance<\/span><span class=\"p\">))<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=ff4fb99a-05c8-4656-a892-8ae4d6bb9af5\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">seed<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n<span class=\"n\">rng<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">default_rng<\/span><span class=\"p\">(<\/span><span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">num_vars<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">32<\/span>\n<span class=\"n\">dim_hidden<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">64<\/span>\n<span class=\"n\">num_init_samples<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">25<\/span>\n<span class=\"n\">noise_variance<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.0<\/span>\n\n<span class=\"n\">random_mlp_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">RandomMLP<\/span><span class=\"p\">(<\/span><span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">dim_hidden<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">random_mlp<\/span> <span class=\"o\">=<\/span> <span class=\"n\">RandomMLPWrapper<\/span><span class=\"p\">(<\/span><span class=\"n\">random_mlp_model<\/span><span class=\"p\">,<\/span> <span class=\"n\">noise_variance<\/span><span class=\"p\">,<\/span> <span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">surrogate_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">BOCSSurrogateModel<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">num_vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">linear_regressor<\/span><span class=\"o\">=<\/span><span class=\"n\">HorseshoeGibbs<\/span><span class=\"p\">(<\/span><span class=\"n\">max_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">50<\/span><span class=\"p\">)<\/span>\n<span class=\"p\">)<\/span>\n<span class=\"n\">acquisition_function<\/span> <span class=\"o\">=<\/span> <span class=\"n\">BOCSAcquisitionFunction<\/span><span class=\"p\">(<\/span>\n    <span class=\"k\">lambda<\/span> <span class=\"n\">Q<\/span><span class=\"p\">:<\/span> <span class=\"n\">oj<\/span><span class=\"o\">.<\/span><span class=\"n\">SASampler<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">sample_qubo<\/span><span class=\"p\">(<\/span><span class=\"n\">Q<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_reads<\/span><span class=\"o\">=<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_sweeps<\/span><span class=\"o\">=<\/span><span class=\"mi\">2500<\/span><span class=\"p\">)<\/span>\n<span class=\"p\">)<\/span>\n\n<span class=\"n\">X<\/span> <span class=\"o\">=<\/span> <span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">num_init_samples<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">([<\/span><span class=\"n\">random_mlp<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"k\">for<\/span> <span class=\"n\">x<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">X<\/span><span class=\"p\">])<\/span>\n\n<span class=\"c1\"># bayesian optimization loop<\/span>\n<span class=\"n\">y_best<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">inf<\/span>\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">tqdm<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">200<\/span><span class=\"p\">)):<\/span>\n    <span class=\"n\">surrogate_model<\/span><span class=\"o\">.<\/span><span class=\"n\">update<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">acquisition_function<\/span><span class=\"o\">.<\/span><span class=\"n\">build<\/span><span class=\"p\">(<\/span><span class=\"n\">surrogate_model<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">x_next<\/span> <span class=\"o\">=<\/span> <span class=\"n\">acquisition_function<\/span><span class=\"o\">.<\/span><span class=\"n\">optimize<\/span><span class=\"p\">()<\/span>\n    <span class=\"n\">y_next<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random_mlp<\/span><span class=\"p\">(<\/span><span class=\"n\">x_next<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"n\">X<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">vstack<\/span><span class=\"p\">([<\/span><span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_next<\/span><span class=\"p\">])<\/span>\n    <span class=\"n\">y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">hstack<\/span><span class=\"p\">([<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_next<\/span><span class=\"p\">])<\/span>\n\n    <span class=\"n\">y_best<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">y_best<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_next<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"k\">if<\/span> <span class=\"n\">i<\/span> <span class=\"o\">%<\/span> <span class=\"mi\">10<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">tqdm<\/span><span class=\"o\">.<\/span><span class=\"n\">write<\/span><span class=\"p\">(<\/span>\n            <span class=\"s2\">\"iter: <\/span><span class=\"si\">{:3d}<\/span><span class=\"s2\">, y_next: <\/span><span class=\"si\">{:10.3e}<\/span><span class=\"s2\">, y_best: <\/span><span class=\"si\">{:10.3e}<\/span><span class=\"s2\">\"<\/span><span class=\"o\">.<\/span><span class=\"n\">format<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_next<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_best<\/span><span class=\"p\">)<\/span>\n        <span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_text output_subarea\">\n<pre>  0%|          | 0\/200 [00:00&lt;?, ?it\/s]<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>iter:   0, y_next: -7.936e-02, y_best: -7.936e-02\niter:  10, y_next: -3.761e-02, y_best: -1.563e-01\niter:  20, y_next: -1.354e-01, y_best: -1.563e-01\niter:  30, y_next: -1.663e-01, y_best: -1.663e-01\niter:  40, y_next: -7.705e-02, y_best: -1.663e-01\niter:  50, y_next: -9.314e-02, y_best: -1.663e-01\niter:  60, y_next: -1.062e-01, y_best: -1.663e-01\niter:  70, y_next: -1.096e-01, y_best: -1.663e-01\niter:  80, y_next: -4.958e-02, y_best: -1.663e-01\niter:  90, y_next: -1.010e-01, y_best: -1.663e-01\niter: 100, y_next: -1.407e-01, y_best: -1.663e-01\niter: 110, y_next: -1.387e-01, y_best: -1.663e-01\niter: 120, y_next: -1.191e-01, y_best: -1.663e-01\niter: 130, y_next: -8.210e-02, y_best: -1.949e-01\niter: 140, y_next: -6.145e-02, y_best: -1.949e-01\niter: 150, y_next: -9.874e-02, y_best: -1.949e-01\niter: 160, y_next: -8.823e-02, y_best: -1.949e-01\niter: 170, y_next: -1.241e-01, y_best: -1.949e-01\niter: 180, y_next: -9.590e-02, y_best: -1.949e-01\niter: 190, y_next: -9.159e-02, y_best: -1.949e-01\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=7cf6290e-bb86-4eca-bfb4-9835f6bbb47a\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30e9\u30f3\u30c0\u30e0\u306b\u63a2\u7d22\u3059\u308b\u65b9\u6cd5\u3082\u5b9f\u9a13\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=3139fb3f-6bdb-4a67-9125-36d9bd6c913b\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">rng<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">default_rng<\/span><span class=\"p\">(<\/span><span class=\"n\">seed<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">X_rand<\/span> <span class=\"o\">=<\/span> <span class=\"n\">rng<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mi\">200<\/span> <span class=\"o\">+<\/span> <span class=\"n\">num_init_samples<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_vars<\/span><span class=\"p\">))<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3f5e54fd-2d66-46a8-9393-daca477f5426\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f97\u3089\u308c\u305f\u7d50\u679c\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=e11f6071-382f-4b3e-8dc6-dbd32b0eb8ea\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">plot_x<\/span> <span class=\"o\">=<\/span> <span class=\"n\">X<\/span>\n<span class=\"n\">plot_y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">apply_along_axis<\/span><span class=\"p\">(<\/span><span class=\"n\">random_mlp<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plot_min_y<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">([<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">[:<\/span><span class=\"n\">i<\/span><span class=\"p\">])<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)])<\/span>\n\n<span class=\"n\">plot_X_rand<\/span> <span class=\"o\">=<\/span> <span class=\"n\">X_rand<\/span>\n<span class=\"n\">plot_y_rand<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">apply_along_axis<\/span><span class=\"p\">(<\/span><span class=\"n\">random_mlp<\/span><span class=\"o\">.<\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">X_rand<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plot_min_y_rand<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">(<\/span>\n    <span class=\"p\">[<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y_rand<\/span><span class=\"p\">[:<\/span><span class=\"n\">i<\/span><span class=\"p\">])<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y_rand<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)]<\/span>\n<span class=\"p\">)<\/span>\n\n<span class=\"n\">fig<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">figure<\/span><span class=\"p\">(<\/span><span class=\"n\">figsize<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mi\">6<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">fig<\/span><span class=\"o\">.<\/span><span class=\"n\">add_subplot<\/span><span class=\"p\">()<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_min_y_rand<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_min_y_rand<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"red\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">scatter<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y_rand<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_y_rand<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"red\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"^\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"Random\"<\/span>\n<span class=\"p\">)<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_min_y<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_min_y<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"blue\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">scatter<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">)),<\/span> <span class=\"n\">plot_y<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"blue\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"x\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"BOCS\"<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">vlines<\/span><span class=\"p\">(<\/span><span class=\"n\">num_init_samples<\/span><span class=\"p\">,<\/span> <span class=\"nb\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">),<\/span> <span class=\"nb\">max<\/span><span class=\"p\">(<\/span><span class=\"n\">plot_y<\/span><span class=\"p\">),<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"black\"<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"RandomMLP\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"iteration $t$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$f(x^{(t)})$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">()<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea\"><img decoding=\"async\" alt=\"No description has been provided for this image\" 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obBMBgHq2DvlFY5pTwxBEGkNXV1AL16YY6OSNa5FSsAskNvI0gpGZEnhlDDMzdOr4Oi7DVcuAyCuREBk72Gb6eob4IgCA8YPz4iYBCcRU6YkOojyhhIxKQZ+XPGw7i6i1Tb8HV+Cd1UBEEQnlhhHngAHSojr9F9AV\/jdsJzSMSkE3V13AcGl5BE8DVup5uKIHSi+TRQNB9h2QqjeGbU15M1xkdIxKQR5S9+CoPLx0aWkOB3KIGB\/BlfDy57G8pfmpzqQySIYEbzCaRDNB8JtBRZYRTIGuMbJGLShLWr62DwHX1iAmYmDIaBMI8\/x4TM7YfzzxFEpqOO5osLGdE5Ht\/Hz4WNdBdogbbCKJA1xjdIxKQJLZfNg9y6P2ICJh8i0zB8VoQMvo+fI4hMB4vlYbQeBpIoQmbuXCG6LxrNp1dsL8iks0ALhRVGgawxvkAh1ukSYl1TA5UTvoDqSgZd2+5IeHvtlmbQMicLci48BWskgJ9QiDURVMSBXSGV6Qg8SbdQFEldMmyYWqCF+fcFAjyJxx6b\/HPFxZGLQXgyhpKISaM8MUGFRAwRZNACM2hQ\/HVJCSbFhNCTrgItMNTUAEyeHHnWAyeMZ5zh+8Qxk8ZQysZDEETGggM9WihE8HU6DPR4\/GiBEQUavg777woMKEzOPz\/VR5HxkE8MQRAZiXbJBS0woo+M1ik2XQRa2H8XQYiQiCEIIuPAMGOtEy8uIWmdffXClINOugs0glAgEUMQRMbRsiVAbm6ijwgv3REVMvg+fi5spLtAIwgR8okhCCLjwEruU6dGwoy1YdQoZGbNigiYMFZ8VwQaIhNoKGDCKtAIQguJGIJQwEC9xYsB+vTRz\/1ApA0oUPREShjzw2SCQCMCCEttv0nLSQSh8M47AP36Abz7bqqPhCAcgQJFT4jhdhIwRLr0myRiCELMvolQlk2CIIhQ9JskYghCrIGCUM0TgiAyfYlo0aLEmlAB7DdJxBCEtgYK1TwhCCKTecfEElFA+k0SMQShrURLFWgJgshU6kwuEQWk3yQRQ2Q2epVoyRpDEEQmMt7EElGA+k0SMURmo51NKJA1JrPW9gmCANNLRAHqN0nEhITKSiHDpqZjxu34PmERvdmEAlljwg+FzfsPCcfwjSkacbKW5UEltJKLkoD1myRiQtLYhg4FOOaYaM0ToWPG17gd3ychY5E5c+SzCQXlBsbPEeEjAOGfGSkqSDiGb0wR7pdyyIdjYBYMhakRIaMVJQHrNyljbwjAzJsbNyo1TxjMrB0NmEm8\/J+jYXD2JbBqVVbsc5TEygIDBgC8\/z7A8uUA3bvLZxaNG0c+R6TH2v6ll0LGgaLisssAxo3z\/vdrheOFFwJk0zAT7DEFIuUpZo6H8tJaGAwzYRXsHfkctISc+ir1\/YP94cSJADU1+l\/gZ7\/JCE+orKxEmcqf3aCsjLGiIpS+jBXBb6wEBvBn\/roo8n5Q2bZtGz8X+MD\/B4qxYyMnddy4VB8J4Sa1tYx1785YVlbk+jZoELlRcHsmngelo\/D69yv3k\/Kg+yqwlIljSlE9K+l8bnxMgd9YGXSNX8cU3D9mx1BaTgoJvHjb9Dooyl7DVfIgmMuf8TVuV4q8ERag5Yb0JSDhnynHz2RkAckbQphDrNiO1vxB6ydFxhT4HWbCYMiHtaFYWs9CJZPqg0hHqqqqICcnByorK6FVq1bu7HTcOJh72StcwCiUwEAYOO7GQJvJt2\/fDi1atOD\/37ZtGzRv3hwCAZrX0cwuvg7weSRMgoNmr14Aq1er1+1xUC0sBFixIjOWOLTnwevfr72fxO10XwWWuXMBBg2Kvy65byoM7PWXfInojDMizwEaQ0nEhEXE1NVBedExMLh8bGy9EuGqueByyP99ZmA75kCKmNraSIe+fr0\/HTzhH3qDaaYNqg5FBTp\/yiphIxjVoqqETcIxlJSXR3xi0MiigJYZ7iOTH44xlJaTQkL5i5\/GBAwKF7TA4DO+Hlz2NpS\/NDnVhxgubroJ4I8\/aLkh3QhY+GfKcJiMTBq9EkUaERmgvCGEdQGDwqWkRFlaimzXXvfA4pOPTsbhpmNveWktK8peneBwhc8xR6zs1fxzQSRwjr07dzKWna12QMxk5890org48brKHvi5dEbrYKt9JHG4LS8XnT7jgQNqZ9DI5xKcqOm+CjzlVq5vwMdQsu+FgJbL5kFuHV6qOpXDFT7jawyJy63bCC2XlQEUHpXqww0+N98sn4mKs8ZMWG5IR4IW\/plqK4zMW0CxxhiEP+MSEi4pKDN1fMZVqGHD4jN3fJ8vNc2M5g3RQ3QKxR0RKadlS4Dc3Mj\/xaUjxdkXLxO+j58LOuQTEwafmJoaqJzwBVRXMujadkfC22u3NIOWOVmQc+EpvjldhdYnZteuyJ2pZ06nNXwi7OAodOyxyT9XXJxUVJjymUDBOHlycuHoo1MoAe76PKUAcuxNx+ikkBIoEXPvvQAjR7rSwRNEIHFZVCREr5QADBzo0rEShMMxlKaaROaA1hd0QNSCZvf27QGefBKgYcP0X27IgFlcRoHz0MWLAfr0ibRlbL\/nn+\/KtUVLDC4hiVxyCcDs2amPXiEIhKKTiMwBBQyGgMoGgU2bIgIGfWFwACCzt3uRK0RoahWJ13bBAnX0ykcfRVZY8RY6+ugQRa+kA1RUUxcSMURmQKG3ntVdUQYz0X8C38fPhZawDBouZ50Wr+2RR8YFzHvvAdx+e2T3ipDBa51QBZnwBiqqqQuJGCIzCFjl1TCjRK6IOSXQb0KctcciV8KKB4MGWjn0Bn3cbsty5XJZAeXaom+7Ilieegrg4ovj1xZvEXwOS\/RK6KHyKIaQY69HkGOvu469jn0wKIIilNk+U+J7o2SfRXGAP8iFSDVlmQatHNrzo5xHFAVTp1r4PR6WFcBjwiUjcfVVvLbk9+QjGVoepcrsGOpP2prMw+0q1mHGabK7igrG+veXV+tWkjPh+\/g5wl9KStR5zfC1W6TsuntQidmT5GJ6Ce1cqhzt5bUlTJLB1dgrqYo1kS5khA9GCJFFruBrtxw+U3LdParE7PoSnMOyAqm+toRJqBp7cnyTVRkGWWLirFunb4nBmaeZmbR2xoqzQtnMlvAHv66H79fdY+uG+HuUh63f4bCsgNljpHstheiVc8gQa0ylyTGUREyGihgUDjHTdX09YwsXRp4tCAuz39O3r1zEWF0ScG0AIEJVd8W36+7ToOF4mcbDWkVhqKmTMXgoVMMALScR5vN8CJEYbuf5QFM\/pmBRUKIz7CwJoEMh+rSJ4GtKupWauitaJ16l7orbkSu+XXcfKjG7skzjYaSd39eW0IFSQpiGopMyMDoJhQQKlchaPIOZtUdCfvlcKC8YBIOzv4FVq7J4ZzVrljthsitWbId9941EJxUWboN3322eUEjOzIDkRzQMEbyoIV+uuzbSR4sLkT\/i78DjlxVUNPV7PI60o2zM6VX\/KqxQ7aQUE2QRk9Chwu8wDobBMBgHq2Bv1wcIMcQaYBsAREKs7QoYRwMAESp8u+4eDxrqiUP8uLW\/z62JA+EeKRF1ekIVh2u0wnXvDtCkSVqnhCARk2KCLmKQ8tI6GNxrHayq6xbbVpS9Bmb+2gXyu7tXVktPxJgtJEcDQGbi63X3wbrhep4YwnMCd92UnDFGuWKYppZWSKE8MSkm6I69nLFjWQkMUDsZwgDXHcbEPDEA2yw7Z1KemMwk3a67ypleg5vO9IR7BMrRWXHoVr5Uz3F77Ni0cPyl6KQUE3gRU1vLyvIHsiL4TR31Ab+xsoJBrobvLV8eFzGFhdtshWzSAJCZ0HUnUk1gQs7NJGGsNSl0QgBFJxGGlL\/4KQwuHxvxgYHfoQQG8md8PbjsbSh\/abJrSwJojlVAsysuIWkTfyUrJIemWr0lA9xOJvj0LKxI151INWJkFvZXgwalwBfPbBLG8e7W0goDJGIykLWr62DwHX1iAmYmDIaBMI8\/x4TM7YfzzzkFnd46dIi\/VgYkCtnMUKgaLxFC0Z3fpR7G3ftL6tI7mMncW+dNtumgQyImA2m5bB7k1v0REzD5EDGD4LMiZPB9\/JxTcKb8ySfy97ADQKdMcmYMjuXDU6gab3oTpLbmsuguv+yfMOxvjVJThsGgxETlfU\/GJ5saobO2vjNUrvor7a0xFJ2UidFJNTVQOeELqK5k0LXtjoS3125pBi1zsiDnwlNcCd9zo4o14WE0g9\/HIr5O9TER6dnWXMwdVF5aC4NhZsRynb0Gxn3dBYZdme3fkpL2volSCa1gKEyFjbkHwsz5TSH\/+Hieo3Loyo85FzbC1MLrIWflEseVzf2GopNSTOAde0NUxZqwSZCc\/DK4Gm9GEKS25hZjx7Jy6BILfuBBD9CVO9T6Fp1kUGJCdWwdKiPHBsCfxWPGz4UxUokcewki0wmSk5\/L1Xgxf4eeMzhud6NkBhHStubiEk5LqObWjNjSe4M\/+Pb8znX++PQZlJjoCuvifoybWnHLy1wYELcaRY+5a4P1ab18S8tJmbic5DO0nJQCtGn0XUib79qxKNg8psAlIMt0gtTWPFjCwWWbamjJRYPq\/Usv9b4Mg4kkjOVLNsLgUWdy4aKg9XcMY4mCjFhO2rx5M7v44otZy5YtWU5ODrvqqqtYdXW14d\/s3LmT3Xjjjaxt27asefPm7JxzzmEbNmxQfSaemC3+GD9+vKVjo+WkOLScFKAKuKkwK7tcjTdQCciIYLU1t5fGXK4S7gm7drGSf3+tTlp635eR8688Jk7knwsTGZHsbujQoax3795s\/vz57JtvvmE9evRgF110keHfXH\/99Sw\/P599\/fXXbPHixax\/\/\/5s4MCBqs\/giRszZgxbv3597IHixwokYqyJGN+SmtXXM7ZwYeQ5XdFbR09F52uwpu\/kmFxLQJYJ7SFT2ppfojtgIq1MuBesZkMPMmkvYn7++Wf+AxctWhTb9uWXX7KsrCy2bt066d9UVFSwvfbai33wwQexbb\/88gvfz7x582Lb8PXHH3\/s6PhIxJgXMb6ml0+TlNx+Wj4cUVxsbkDAz6Wi886E9pApbc0JipjdvdvYChMwkVYWlGzCHpD2IuaNN95grVu3Vm2rra1lDRs2ZB999JH0b9D6gidl69atqu0FBQXsmWeeib3Gz+Tl5bF27dqxvn378u+qTzJT27VrFz\/ZyqO8vJxEjEkR49vyQDpGUPhk+bANmrDRlC2atrUPB6Zu7LRVZvQSC3+cCe0hk9qaG2Ls3nvNiW4H4tstC6Gr\/WZ98CySZkVMSL2uADZs2AC56L0nkJ2dDW3btuXv6f1No0aNoHXr1qrtHTt2VP3Nww8\/DMcddxw0a9YM\/ve\/\/8GNN97IHVJHjBihezwjR46Ehx56yPHvykQwiy86aCqVifEZ\/eYwmZSYi8FxpWJZBEU65LOQRTPooUQF4ef8cPLDPEPnn+\/JrtGJF9uICL42nbcjE9pDCNoaOmpXV8vvb1OOs06rNotJGLFN4GPnToBvv02M6MHv2rIl4lmOBzZgAHiWZC9Jzh38+tzoECi2eSUbuuLgbipyysT3BRYWMO666y6pY634wCWg\/\/znP6xXr14Jf9+hQwf28ssvS\/f97rvvskaNGiVsR2vLnXfeqXtM9913H+vatavhcZMlxrljr6dru0HJU+L1jMdNy0cAZ2eumdGD0h7CXDAT2xAGPHToEDmH+PzWW5bamitLyU6XBGWFFfXavh\/LjxYshBVuXO+AWiRDu5y0ceNGLlKMHjU1NZ4uJ2n57LPP+N+hUDEL+cTYi05ytDwQhgiKMPlgBPRYXTGjB6U9uIivvmVWKit7eS2dDsB6YnbMmMTf49dg7\/CcBv770l3EWHXsxQgjhWnTpply7J00aVJs2\/LlyxMce7U88sgjrE2bNpaOL51FjEr9a2YsMvWfcktMUCIoTHSCvs6kjTDZYafieB0P1kFpDy7je+i5S9YsR1Y1K1YUM3+vPBTrkvh7\/Bjs\/bYQ1gbXIpn2IkYJsT700EPZggUL2Jw5c1jPnj1VIdZr165l++yzD39fDLFGy8uMGTO4ABowYAB\/KEyePJm9\/vrrbOnSpWzlypV8aapZs2bs\/vvvt3Rs6SpiEgYQYbauN4CYETGeetkHJYIiSSeYkpm0zWNN9fE6Ek9BaQ9hj1Zx0ZplawJjxYpi5u+Vh\/Y17sevwd5vC+HY4FokM0LEYLI7FC0tWrRgrVq1YldeeaUq2V1paSk\/CcWCB7mS7A4tKyhOzj77bJ4HRgzTPuSQQ\/g+MRke5qEZPXo027Nnj6VjS1cRo57t1bOy\/IH8RVnBIP5aNttLaXRSUCIoTHSCgYk2MNlhhzLpXFDag971wn5G77qZvKa+5A1x25pVX89K\/vuzalf42vC3WrGiWPl72e9RhJGXg73fFsLaYFskM0LEBJl0FTEJgxT8xkpgQLzgmKSzTGmeGA\/zlHgx43FtJu3En8XC7Cx0eSqC0h70zvl11yWea0W8vP226WvqmW+Z9nj1HhbbXdmzk2J9SEx4YcHFUR86t6JY+Xu9Bwojrwd7vy2EY4NtkTQ7hlLtJI9I99pJ5aV1MLjXOlhV1y22DcvUz\/y1C+R3z7ZcO8lxmKWD2iM8DPiMMyLPAagdpNT\/wehUBSXM3FTosPJ9GP6Kf2ilho2NOkeOj9dPgtAejK4Xnlt8LV43pY5Phw4AmzYlvaaeXw+9NqJgsXaS2JdgHzLuf51g2EkbYq9lfYpY20gXo+PAk3HssaZ+Lg\/bNhom3QhLdvmcBu77bJARtZOCTDpbYjhjx3ILjGq2BwO4etc6\/m6bNStmiVmxYpt\/zqkBcZatGD2elUMX6WwHt1e8OsHdmbQTB0SbszPPZ\/4hJmn7Gz1e\/1zr1fHRuQ6+WMZctGbxJcncqrjlBbpyaxQ+x6y7uVXq82fVihI9V6rroElFUP7ch6ziin+Y258X1pgZM\/y1EBYH1CIpQJaYFJPWlpi6OigvOgYGl49NqJw6ueuN8LcuU2HjpqzIzG\/mONh+2WUQscOguN8GnTo1963CcKorHlduroOhXX6EjTU5CVVly6ErDIaZkNu4EqauOxhy2mU7n0k7qShsc3bm2czfaRKzAJC8\/THIXfcdTK05FnKgKvFc33cfwJVXmroOaLE85hh1gkj8PuV7Vq3KgqIiBrNmZTlLHOmiNSvh\/shaB9CwIcCePVDOukjvD0tWlOi5qly4Aoaelm3iOhwHOVAJlnFaIfrNNwGuvhrg+usBBg3y3kJYE0CLpAayxKSYdLbEiOvXWp+YAihlBe2qVY6\/21TJCrd57uwpzri0zqcYqIbvu+p8auBwWT5xrupc8ZkmOkKLM034jX\/OlZm0k2gDG7MzX6LKAhApYRdTzs94\/XUsdTEnVRPX1NC3LHrP9u+x0XdLqOF9OmoSq4BWCb+fWyij2\/FZ9VtlCR0VXyKdB1paHF0H5YFlCVwsmxHkZHOphhx7U0y6ipjy0lpWlL3acFAuaFjOCgqikUrwG5sO\/WIiprBwm6fOnrKOXOyosrMZO+AAxgoLXTSxGw22u3axspenxE3muVWs5L4vVa\/xffyca4m\/7DogWsz260tUmQsde6qXEw2FXvbq2D2U8DBaLtG5ptIcTtGihlwQFB4ciEGS36dH1Ed\/f77qtyl9SX+YGxEwydqvyYizslW1+tehe33kPjTZ9l1tUwFNNpdqSMSkiYixmljOayqmzOadiyhgZJ3PstfnxsQOWl8UEbN8mbcHrDewzp8fETCeJdJLMtiaCXt1HKWlRK+YnLk7Dcn2NKrMpY49KLl3pNcfBayegDH7MDov2oinAA2SUl8YmYVStIzoHbcFC6Ib4eeutqkAJ5tLNSRi0kDE2Eks5zm7drGKtz7i5lnZbIU7yL31EZYZFxx\/hRDr11\/3\/BCNZr6uO58aDLba2ZrW+XXatEQRUbG13t4MDzs9o6WHZJ2jzaUbt60cfH+l8o4dt1vdX5By2SQ4P3c+15mAMbqmorhG9R60QbK2li816y1LJ0ySjI7bogXRqRO6q20qaMnm6oNTL41ETBqIGDuJ5fxE10pUW8sWdD6TFcKqREtM1\/6+dKCyGZfrlhiDWZRWgMqOp3FjxpYtU3dmXATaEaXTp5uejer+DuWkpGiAi50ziYWCz9Bzq2yJ9iDkspFaACTWTFsP2TUNeA4QxXoiWl5MnReH0TJuJQJ0pU0FMdnc2OD4oZGISZPlJOVmaQ2b2dEwg70LF7JBMJsB1Kc0mZiRlWj+\/Z+zbNjNX6KQUfnEwI\/6CaxcRjvjcn0QM5hFiQK0oCDywP9jMfS99op\/FLfjWj12ZrxDz17NfQUsC5k33lAfw\/XXm3dA1P4OfJ2C2VjknNUbLzEU6VuqUp7F1sR3x9pf9+jv7FDJyi7\/V+R6KY\/TTzcnXtDJVHZN9cKyxUES3587N3UzbsF6gj5iKsvIWU9EzsPw4Yy9+aZrDrRui1nHbSpoQrM2GJMZBRIxaeTYi4PckCz1jT4064vI4Jciq0v5lO9iAw468S7rciI\/MLTAKAIGnxdAn8TopOzVkSWDFFhi0DdG+36CNcuMSdXELAq\/QxEv+MjLizzE4+Hf32YzP0+6eTG8XFeX\/a2yLJWC2ZhR5JthBlcTeJ7LRtJubC09WFwesZVOPyAWGb\/EpVfLirbbVBDLX4y14Ifmw7ITiZh0ik4aO5a9ADeyLlDOcmArb1\/nwfu+dUB6VhccUJRBujHsZNPghNgSEgqY+dCXvymKGLTE8KiDKbM9O16xY8IoJIxGigkGSQeWsERhxqRqchaFy0W4bCS+JVpmshvsYQfAj7HzxgfqgkHWOi8n6+pGv8PvTjTasWO0inSJIavA9jH5MlhK2o3MCVSZEMjanyU\/ItlAkswKo33gZ1M04\/Zzmc8LB2+7bYpff0ypILkesZByv5PN1VqcCPmw7EQiJl1EjMYB7iiYyZ9xScnyYOeBb05B\/p6Ee7EwazVbcF88XBGdeWMZe594N+L46ySvglFeFsmMCzsNzA8jm3ElDBrRm5nnqCgYKD2\/3MG028GmZ1HowKudreFxFRbWJw7U0SUU074xTtbVzWQ+lWU7lZxzV5zLhSgTaTZomx2754MltkNcmtExxYvnTjuYiufO8mAqG0isWGFSaI1JhcO1m23YbpuKXX9JSDdOCrnfF+bywSzeTvPPWLGeWJkI+bTsRCImXXxiNOb1R+Eu\/v++sMCxed2too95UJ444AiNP1kBSMsYzAIcz7jGjuUCJhZGrjm\/fB95O+I5LGyGdKKF5oAuW6QDNVocTPvGOFlXT\/a3KG6KiljFX7X+hCljhz1+PCtr2zvREtOhKnItLHbsvgyWsvOoc95dOx7ZQJJMlOL29u3VxQxT5EQalNB3Ozi5himNlhur029anQj5lNeGREw6RCdJEsu9Axfz131gQWS7D\/4lCjxZVCz3C4tn6AX1Nu2SiKsixsQswPaMK7rvctGRFJNxRX2PVB1Nx+pYmDnOmhJCzidOZGUrd8WWjbSztby8epYNtQnnDZfgTPvGOFlXt1B\/xlS2U5c6XkOfGKtWk\/p6VjFjCevfv967wRLPo5I50cx5d8syJBtIzOZLsSp2PSLVSQhTJcBSEi1Xa9BvmpkIaRIn+iGCScSkQ54YSWK5SXBObDkpltXSQ\/+SZEUf82CtfMARrBiuihgvZwHCvrUF6PQ6Gr0ODTvhmL+QEEqtdfYVnaDFZ1O+MU6KuJn926g1xjDbqUsdr3426HxW1LDUuliKXk8uMr0aLI0GAIO26chHR89\/Ae8tI4fgt95iLDc3WCG9IcWpAPM9Wm6sTr9pdiI0ZkzktV55Bw9EMImYdFhOkiSWm3IW+pcw1rfx9\/HEcm6um5r0zREfaImRhsNGrUSuiRgvs1tKbmZpDguJWJEN5qJDL4oW0QdHKcmAztBfwbEJ36FEdekKEDeiWLR\/m6T2jJhg0auOF6s5G2aDbrXReiZU2czTLXBW2rmzcedv8L22I1vsOnIHLaQ3w\/Gt8nutQb9pdjKjtHMxcaLHIphETJrWTvrq8SW83RzUZAXzE62ZHyORcBCOiJhS1aCjqn0yZbZaxFRX2w\/N8zK7pc6+ExxMS6yZh3keGG1pgb038nO2DPaTfscBbdZ649inhxlfCowN373bfsebLCQz5lCdo1uEr7xhN1axYae57\/Nj3T6Z8DP4XtuC0K4jdxBDep3iJMzXpRBhuxaZsjX1rKjLTs8mBKb7TTMTIczXY0bouHyPkYhJUxHzzUs\/8PbSc69VzC\/0zPw4CONgzLc3KGXlz8RvBtFKpBIxWHbAToP3Mrulzr7NWGIsD0qYzbfbwdzvRu87CrPLfM0BZHY2Vjb8cfuWmGQhmWZnhJjgLQj1aHbuZKxhQ+Nj1fleRz4RmgEpoQK0cH5Vg6iTpceg4iTM14UQYbu+Mfw9sSCsB0uzFYq4kvRtPIw7q7W5e8JsyL4H9xiJmDQVMYve\/ilWKdqvgpJmiz7q+eaoREy3bvG71Y1cKG7MAiQdvLYQHff3ydth2NGYslII3yX9DuV13g7\/sjEbzcbQj6JDh1g2YVsDr5mlHTwG7Yzv2mvVkTT4bCaviQOLnemZtRkrjEQYOIpO0QxIqig6vC81iRZVg6hyjZXjtpLROYg4WS50aanRzrVMyEod9Xtz00m+QhRXz07S768xutLpEqSHIphETJqKmKUf\/crbSm7WRv8KSpot+qjTAapEjB3hYcUUbsdMrBnEeTSOMFNSQnsx2kivozFtiYl+l\/Q7lFwRHatd6cxsoT1\/Y8fymZvo5Gw5OsnM0o5R5mArYsSBxc70zBqXtLSFuMQHfjceOwpAjTBwFNmiEduq6yI6Qr8\/V35dApZW3hFOlgtdXGq0alVTlpNVE8Lo97sVWl4uiiuMroR86aSpPCvf3hKk2L49FMEkYtJUxPz6v8jyTSuoCE1BSamIsWJ+NGkKR0tQ+ahJ0o7JShSK1YHGzvJAYPNkiGZ2wU8lNuPXREwlPVazSzt6Mz6rYsSBxc70zPrvIx3NSm1HtkgsZkqCNEVglvz763hdJm3b8im\/h+e4XWbDoaCz5N+kWU7Wfr9boeVl0XxWpiqEv\/KKtQR4PrUfEjFpKmLK5q\/j7acR7HI9aZ1XjmW6lhizN4IJ5zO0BPXvVxedeXRVdQx2RIHZgcbJ8kDg8mRoZ+pKWKXW98KKQDSztGMhZ41hu3HBeTWpIF0lyQsjm536uDRjahD1wk\/Ih\/o5vpXZcDggm3Z4l3w\/v7fQyu1yP1CGluOoVTfWLgSrr8pp12wCPDuTUJuQiElTEbPx502xdrSndo9rSevEpG5us62iQi5iXLwRuJhQZqTKTEMTFmzHypRMaKxZE1CLih20Hazoj2Lnmpld2rG67q53DC45rxqKgoCGKScdRL0YvH2on+NFmY2ECDjhb+2IBitO\/dpjj\/k1SfpfN\/qPEqN2YbS8GABHcBIxaSpiqtZFBmp87NxqMtzURNI6bakANxFrJyVYYtzqBDV5bLiVKe881TKZVSuT2SUfFDJOLSopt8poO9hkVhGnxSWVfdixwuh1oE6rPyfr\/AMwO7U1iHoR2Zcq\/xqHZTYSnKGFv+VLcxZFg6WlZMmxO\/Y3c9IujJYXXbyX7EIiJk1FTE11TazNbV1d4VrSOlvVk01+H0Yk6YoYFzp+LgCivjDSkOVCe8tkftU5CYR\/TLLQXbHjzcpnFYUHOysuqVz36dPNh1b71IHqdv7vz0357NTWIGolrbzZpaFU+Ne4UGZDVVJEdIaO1iuzck9b6h8Mjl3sszARpuwaul6gcpUPaQgcQiImTUVM\/Z56lgWRytHrf\/jT3do0XhSULC7mwsXQEuOg4+cC4Ih6lRd+QvK4\/U0UUrTUGSjWnXp30u2nsiicmdBdSYebtNyFWXM0lvhO8YzPdOcvqTycymM1127qWXn+AMOBHwVp+dPvS8WIdPD0Iw+Ph2U23EptYGXywYMO9CYF0IXNg76x5KEq4VxmfSJTbqZdYF022fEEyNnb7Biahf8A4TpVVVWQk5MDlZWV0KpVK1f33SxrB+yEZlD6zVooPLKr6b9bu7oOjum5DlbVdYMi+B1mwmDIh7VQDl1hMMyEVbA3FGWvgVkru0DXwmzHx1lZCVD9Vw20mTsRWlx2Gd+27fXXoXmTJrB2SzNo2aQWcprVAjRuDHDGGZFni6xdC3DM4dWwamNL\/pveg4vgYhjPf4tCdoN6KJnXAPr1s\/c7yssBBg8GWLUqvo2fv1E\/QP4\/zrG3U4PvKCoCGDcOYNiw+OuZMwHy88Eb8Mui1wdZC13gGJgVaQ\/4Oy99A\/KH7A\/lm5vB4EdPjJzrjttgVsle0HXvxvFrXQ3QVWmONTUAkyfzZ9W1FrF73bHLWrwYoE8fgKys5NuttKVjEs+59trMmiX8zhSC53zoUICNGxPbh3LMuU0qYerPBZADVfJ9QCsYClNhY8POMHPPUZBf1AhgxQqA7OzoPhjkNtsOU79pDjmts6TtJQZuv\/RSr36uqk3potemNH8rtmUFbNMz5+wF+T3Mt8eEdq9pTy2jux86pB42rt4BM+\/5H+S32xH7jHIcOc12w4aKZrC+omnsvZISgPyuDAYPrIFV65qYbnuVSdsFg9x138HUmuMgByrjf5fVGqrz94euv8\/i11\/2W3JyIHhjqBuKaffu3aysrIwtX76cbd682Y1dhh6vLDFIm6wtXDT\/8vnvlv7OadI6S98lzFKWL1fXTnJ1iUSzPKZbUNGh1STBRwJ9iFyeffpeFM5ktmK0cpXMUheATCil4OdymJ5DqUNH00As61kkqS\/Vn8a+DTxfUauNxg7xmFNEiZ7xMnN2mtYuMmMZwfIkWNlDPB58XdCuOsFfxnG7GDUpkuhO+DKV9VVjjU9V2\/d8Oamqqoq9\/PLL7Oijj2ZNmjRhDRo0YFlZWfy5oKCA\/e1vf2MLcY01Q\/FSxHRusJ63ve\/fX27tDx0mrbN74xYWxkUMChpXl0iiZmIsmKgIlpgAgN\/YfOirCiF3zUFO6PBDWRTOhInebNkFX5fD9BxKXXI09czBOlXhyE4d4rUpCwIanRX0CUOy+mpKZXv0icnrEPd7jBXYdctfsVYuQlUOxkKklG9L2n6LmKeffpq1bduW9e3blz388MNs6tSp7Mcff2QrV65kCxYsYG+88Qa74oorWOvWrdmQIUPYr7\/+yjINL0UM1tbBRjX\/v0sd78tOGQKzxG+AuIiJCBoXO4yoFz0WTDygy9ZEa4kyGHeotDWT0PoXlHQ+V+1D5KIzdEosMUmiEEru+9KUqHJUD8gKeg6lQU\/klopwZAvHJRWsOPsXLbaYAyeA0VlW8a2tGnxvTKAIAoZ\/97OTEnz68qA84r\/iRtspNjdpQd8gv85LSkTMhRdeyJYtW5b0c7t27WKvvPIKFzWZhpciZt9GkYY2c9R3jvYjms\/xcsay3Y4dy8qmfM8HbXz\/p58cJFwqU1tiUNB4cUNEvqdebi1p0ICVFwxkFX9Z61wTLAzROiQJ6bt1ElVZPX7xu9DfVdW5CecrQVx6NMu3Kqo8F2F6DqVYjDHIkRZBTfevOZ8JaRc6nRPPqYLntHNnVdQaLyQoLEvEXnsdneWgvafaiV5racX7PLaEuUoeOYoOv8vgAHfazi7jSYtY9sS3iZQOFJ2UxiLmkKa\/8MY19ZFFjvYj3tCNG9ezgoZr+QBd1ra3EPIXeThZD50+XS1i3F4iMcxCLKlRYstHQhOSqPIhShZubLFjRUGJ36udpeHnpOvTHszy7c5WPV0O01vK0CvGGBSrR1CtRMJxSVMTwCp2GCyO3UPcb6LjKm6hmX\/N6\/y5f4+N3AqqlD\/o3\/OviB+OHm4IbgftPZV+T3oin08gy+WRowVQamn5usKF5VDfl7R1IBGTxiKmf4sfeeP65J75rtxYykAZMV2ujd04WCkb12idzE68tsS4VuwsWaegk6gqNhN1MDBpO1bxN4kiEjs73fwTLs7y7c5WPbXEGBWjw2KMQXU0DWq6f+G4jEKOY47x8BtbAP1iuVTiDvOMLVhgwYrhVHBbbO+yQV3ZJhvUvUosmWxSsKAknkVdlb9G248VDNT9zRUuCLSULGn7LWLmz5\/PRowYwfr06cO6du3Kevbsyc444wy+bFQRJLf9NBYxg1t\/yxvX+ze7I5HRyoCCRbsOiw5lThqxHz4xsRu38w7jiCtFbNgxdfuQqVXb2WojF9DsLLWEeDDLt9MZGnXSmGwQBzoZpgcNq6UJgmL1CGq6\/6hvhG4lbGHwFIXMR3CmKvLvow\/0o9YScENwW2jv0nYcFYBla+rds7okEZVmJgWF7atUVi\/DfkznN5c7XCpLla+QryLm1FNPZddddx377LPP2B9\/\/MFqa2tZdXU1++6779ioUaPYCSecwD799FOnx54WeClihrRbxBvW29d8484OJWUInNZU8i06SREAT46P7PT66xMjrl6d4CwRWYrqiFhOJ49iCl\/PnevYP8bQLF1WzypmLFE5gOt1nkqtRDSWaIWMafO93dIEqbbGOAlH1hsY3bK8CQ7xuCQUKwx4zTUJg+ehsJgvLYk\/ISES0Mwg51RwW7RqSdsl+vvh71LqrLnRByURlcknBfWsf+MlbA3kGybE4wImyW8usylEUu0r5JuI2bp1K3\/esWNH0s9kOl6KmDM7zeeN6tVLZjnfmU4ZAqc1lXzLE+OH4yQ6jj76aKSz8jlTq+H6tJF1wksLhKbTTuikhQEYhQsKGMUiY6tzNCsifRKXftX5kX7GI8tbbGmyUyfp4DkNTlB97Wi4RvUaLYWeL6vZsGoZRhe6kXHbZN9jNW+LkzZdZmNJKIg5kjz1iTnssMMStv3yyy92dpW2eCliLsgv4Q3zuXNmOt6X6EyGvjDoE+NWjgLlxkXhIooY19eevXacTFF4rGFnJAwK2igR\/sD3vLBA6HTaqk5ac75QyCgWGVtmar38Rm++ydjw4az80rtZxTW3R16nsAyA23V+EgZGr9P9a++jqFVz2chPWePsOkNLTOPGEZ8t0\/u2eq86sGrp5nlyo8SK29Yl7QO3YzV5DG+30KZLbDjnprwIrR8iZvLkyeyxxx5jvXr14hl6RQ4++GB7R5qmeCliLt\/7G94wHz\/Z2QyzvDTuTIYCRvGBwWf0iYkLmVJHN7xMxLiG1x17isJjVevlhYwdcEDcoiEL91b5\/cg6VLfCsJN12jrny+rsUOxQZY7PSoca1Ey6jpYgzebCcVO069xH3F9OcPzvCOtVPjH4OtZPFOhcTzey\/DpMsocZp1WDetYg5\/ezG32PB0vVZQFyzg2ciFm1ahV76aWXeKK7Y489lhUVFbGjjjqK\/d\/\/\/R87\/PDDnR5zWuGliLluv1m8Yd5\/dLGjRHVKGQJRwCiOZfjA7UpRMhQ7KHoCJ2K87Nhl+7e7XwsiQrs+LUZ\/xIRM9mq2QMxGjJEL2vV00RrjhjXJTKdtcL7Mzg4dRWsFhST5OHRn1GZz4dgRAkboRN8pviOY\/l6c2DSEuCjIg7J4enzZdUgmQB56yPi+cOhYzwf1DpWJlhidkGXTFgk3+h677YSFwzk3sMtJs2bFfTHWrl3LSkpKPBmsw4yXImZE75m8UZ7WoljlsKbcQKZnp1Ez\/U\/XPCOtqYSd2DLYz3FNJc9EjNd1XNy08lgQEbL1abFzym64hx0AP8acLWURDaoO1S1rUrJOe\/fuSMEXyfmyMjuUORkmpALI008GmGocmeWt5sJxQ7Tr3EeY6A4dTou67+F+c8tg\/4RKy0oitmVdT+LpGBL6nNpaXkUb9yU9buU7cbnEA2uF4jirm0NKWCrH48bEnjLfELxuimjmv\/Gv4NWQKg+gc27gRAxGH73++uts48aNqu179uxhc+fOZTfccAMbM2aMvSNOM7wUMXf2K+YN8sRGxXEHtfyBvJXiTRm7ac02WI9rKjkRMY4c4pxaY9yy8tgQEbLfLRUCGFXy9MTIurleh4r3pN7xm7UQmRGMOgMtT4RmcXYom1GKIiaZEHIVC1a0iACtZ0VddvIwXpGkkwuruXD0Bk6rS4cGlhKeoXf4Y7HXWgdffK0UDyzouDPBL6bs\/bn6y53io3Nn\/fvCprVCNagb5V7B\/i06cUgoAyAIaPT7ifWrSnZzr\/oeG1QE0Dk3cCIGByAMpe7Xrx8rLCxkhx56KNt33335\/y+\/\/HKeQ4bwXsTgMhLeJ3\/bZ6bqJlXNMmx27l7UUkoqYnQ6XcObclXEn0e3c3Q6I3LTyuOi47F0SSaZuV4UONrjN2shSvYdWFpEWesSHuU4YChJvCzODmWiTVvp15dsohasaHzgVMJ3hcrDpmbDdnPhaC0RVpYOzYSvo1PW+PGxrLxaEb3gwS9iqeoTrnH36IQqtypxkqQVvS4P\/Lz\/OKKeFTUoNc69UnhwxD9QWpBR3ea4348me7frfY\/kdyS0l2ifWY7pDiqC65wb6Iy9NTU1PFfMli1b7O4irfFSxDx6UkTEXNVzdmwwdyO3S4JosLNEZUfE6HS6hubRvB3xmZRObgVVx24Vt6r1urgkJV+SiVrhjKIb9I7frIXIjE9Cy5bS95RZujiga38Pb1Nb5UJWK9q0IsZzS4xVK5q2KjSG9ZrxS7ATpSKzRFg9XpNLNdyiYmBNw\/mrJWub1w75USo+KU6eeyXaT2gTTGrbWsxx2ezy1owZjp3pdSdyQr6b\/hb7ZEdCx8dq7L6VHaiqqnK6i7TESxHz9BkREXNJ4Rxpojq7uV3UosHhEpVZEZOk0zV0VOtYHYmacjt3i5kBxWlUhcXrY3gejHxijGaKRstMLuZp4UUEddKlxzpNiZCViTZlMPHNYVF7\/ZI5oRpVhTY6TreiVKxa\/bRLNSiSRMsdhvC36839YrS\/QdsmRQf0pL\/Z4L5wMsgm\/C1aCGWiRQwjF\/oJvTansvqZXd5SvtuBhUk6kZMI5fJyn5acfEw34ZuI6d27N1u\/fr3T3aQdXoqYly6IOPaemzdXmqhO67BmBVXH5NISlaGIMdHp+h4y6NaA4tKSlKFFSmKuxyys\/P8SHxVVR260zCSSrNM+\/XRn50siZI1mxcqMONkSjWPTuvb6JXNC1VaFzhokHwS9ilLxKKEct6ZhVl8TA5+pCDSD+wKXdvgSkI1BNmGAltSHUi0\/65wf7W+w1ecYTc4sWjMSJjD3fal2Th71oen9OnL+9TndhG8i5oorrmAFBQUJye6wFMHJJ5\/MMhUvRcwbV8zm7Whoi9m6hducJHNyc4nKUMRY6HR9rawqGVAqrviH2iw9fHhsQNEdEF1akpLNnpQBWtux4wNzURYWJi4zqTvyHPeclpVMdnqPNm0Ye+89\/QFYc55QgMmretdz51Gxo9Ub2FxxctS7frm58g48SVVoN4W3VKBFvz\/B4uBCQjnFb0SG0v5NTzYM7gsxrNvqIJswQL8\/N+FaSJefBXGtjYKzHQlnNDmzYc3QTdiXVRDvM03u13YYts\/V2H2tYn3\/\/fezdu3asW+++YatWLGCnX\/++axBgwbstNNOY5mKlyLm3Rvn8DZ0OCwy9ry3m9vFxSUqQxFjcqkl1cmbMJySh5oq51kSOiwLLXXT+Y8PWmWRmRb6j+glf1Ol+YdV+hEZMj8BE8eUMHgK11BqrhfN9jIkQlY2G+ffO2qS1A9ArxqxtmPGz6gqLnfZGTmnsn0ku35aa0yyqtAdEgdmKyRN\/hcN+cUq7iqLg5sJ5QyW0kwPjCbuC+3ytZWlQ9VxdK9nJf\/+Wu1orV1+1iwl6YXxa6OWDJdvjCZnDqwZCRM57JNBaI8W9mu5T\/XJhyllIgb5z3\/+w5o0acL22msvNnToULZAr2xthuCliPnwjnm8HR0C3yavemo1t4tOLSUnS1RSEWNyqcW4c6xnZVO+99zJDAdPaaVfTeiwqmPzomjk2LF8YFr40BfSTl1M75+dHV9m4uZnsSO\/5G7jY9IRq5bN9eIDlRUmbJP8Jtkx8CUx8XwKnT\/61\/BB20nWYzwP0WRnUiGabEDXWmMEK4i0rbQ7xLZfmankf3tvjOV0kgrVZBMQM35gMvFmdYnChiOxqUFW57qb\/VvxN2AotWzJUky0aMuCh9fApjVDzHej6pMhOqnCpWGL+7Vk3fY6qWgqRcyGDRvYiBEjWNOmTXlNpWbNmrEJEyawTMdLEfPZAwt5+zm80Q+u53YRaym5tUQlFTEmllpMdY7RPA+eUaue4cbOS9YgaeiwV5k48Tgquh0cifTJXs3mz4mHhOLzRx+pCy2K0SKqjtxBeKhtc72eNcaKz5Cjzl+rp+rZ\/M5n6Tutmwk7Fgd04fOxaCzZ5OLpieaWsewk\/2u4PiHrtplrall0S\/K5WFq6s3BfOFlCtvq34m\/A5UtRZIq\/AZPh6UXSJW3TuB1vTovWDJWQgtLEPhm6Rq2gOc7qSVmNnPPYGuObiEHxcsghh7DPPvuMv\/7yyy9Zq1at2BNPPMEyGS9FzPQnlvA2dGDjX13dr1hLyc0lqgQRY3KphS\/jmMkTU3hw8hvJbmhgMj8HSeiwJ4wdq57l51ZJhQoKGcUIKu3IHVqIDM31PB9Hvv4+tdYYsz5DeqZszBAcvaZGTrwff5y4a5nTemzwkpwj6VKZMqBrPs8TxMmEXOfO\/N6xk6vDdPI\/o0g1I6ufkbgwkc\/F7fwkUsuDyarTdpefLZcbkAlpO7l+DAS5ykIEuyIFeaNlYcTCvV1hNTsUFkt9obTn37JPjFvpJoIqYsaPH5+wbcmSJaxz587sxhtvZJmKlyJmzss\/8LbTY69SV\/er1FJye4kqQcRYGEh1O5booB67ac0ma7Nyw0nEVoKvUPszIoOpl+j5WxTVs9Gj1acMLTKGHflK5xYi6b7zdvDljKQ5Oe69V\/fc6s7ykqTix6UnPbGLQk+bg09bgRnF8LLvBcEsnqPrrkteZFMmAPTKBDjo8E0l\/7vvS2\/TDfjgC+EkQtK206pZjHxazFrw9Nq5hFgm4Y47dOvbNYqWgsB2vQD6qPbLJ3uCJcxydJLLvn2B9onRUlpayrP5ZipeipjF437m7adrw3Xu7tij8gMJIkZv1qd0\/JrcDY47VrvOdBqxJbXEYIcy\/HHmKZpBXHYcolBJlnhMay63M2vWWnmmTalh\/Xv+JS2DoBIB3aJWM7NCdvp041T8UR8ZcUlI6ZhFAYPPaJHRZpzlAz8MSIiIkubj0C6V6bU7k+Z3O9YL35P\/+ewLoRpkMSIyatnDKBxx+dZUdJLD2kGmIsDE8+Akn5LB+eTH8dsuVvbylLjVs0MVK2l9ChcxojBPsKALkV5Km7IUteeFb19YRAySydl8vRQxyz5ZydtN+6xNLAyYqp1kRWhY7VjthgYKYktMuc6dZf\/5OV8+cRp+nhSdAfEjOFv1k9Aio3TUMedVnY5cdFy0E3osswioojcUp1k9fxk964VRwrAkD62TNQoWUcDwiii1tdwXJsESE3VaV2atMfH3QiQiTTs4JO3ATZjf7YSA+578z6iWk0ez79h5EdpQ7BobZKi1VLzRhEiXXh+Nf1zCUrZem9YmEHRgzdALtZ6vqWivtl6pl+EsiWe3ffuCImLWrFlj6fNY6TrT8FLErJwemZG0hMr0ETFmhYZVJzMXzOHSGZ6S9lvwUfGkOqxkQESTccJAHLXAxKOT4r4xCrJCdlZnq0bm+oiQMagYrAlPT4pZ87zGdC6+FRMwGqd1PH8JlcBHfSgfJGShuXoduEnzu1irx8x1cCP5n2VS5AuBvnBY+Vp2j8si0yw55eokydOeK\/Gex3tKes+LotwIl60ZJbNqpaHWZXqWYnTADyGeipjc3Fx27bXXsoXoVKdDRUUFe+2119gBBxzAnnvuOeYFmzdvZhdffDFr2bIly8nJYVdddRWrrq42\/JtXX32VHXPMMfxv8ARt3brVlf36KWLKF\/7BG+heUMPSQsRYERpWO1YXzOGmQosbLzEV9msJyYCI36cMvDgQf9TxOtVSiiJkDj1U3mGLs1KZEDGaxZsx12MyOsXErepItVYMMx22VfP8uHEJyy1okZE5raMQxOUAmdN6gkM0+pmYxcKAZdZ\/Q3ve48n\/EnOXmE7k52fpDatYvMedLCMZWcTE5UhMHlnS+Vx7otxFawb\/TdoinBA9luuv521V1Xb\/\/bUnVpLQi5grr7yS3XrrrXyA79ixIzvllFPY3\/72NzZ8+HB2ySWX8OrWjRo1Yv3792eff\/458wrMR4NlD7B6Niba69GjB7vooosM\/+bZZ59lI0eO5A89EWNnv36KmE3L\/4o10rqaOhZ0TBeATCY0rDqZuRgaqJqtaTPMytbH3UAzIIrRSShkFCc+bXE+nFskG8DsRHCYWgI5Yg\/76LZvEkWAxq8K1\/iTDrKyzl\/PNK9Jkqb9TUZO6+iQjMIL31\/25vyE81KYXRZbLkxqiv9T7RQc8\/EySLCW7DpYydjsWrVil6wHuuervp6VT\/kuEq4sYtOR1K5DrxkBpHUMl4pyj7PXxo9J39I5P+9s3fYfRjwVMZjQDvPDbN++neeFufrqq9lZZ53FhgwZwkXMU089xZYuXcq85Oef0bkV2KJFi2LbMLw7KyuLrVuX3OG1uLhYKmKc7tcPEVO9PlL2Hh\/bN21nXqLqhDRhymY7S1MFIM0IDasdqxfmcD9zJmgGcR6FgzVslOUN\/H2PPsrDlu3MwO3k4Ug2iM+bF1+u0lvuQCsRWotsWQt0rqk2aqvkvz+rnX1Xyp3WlXNa0K6affWvYlUtqo\/gzNiyXWH76pgFxJQfiwUfLzPXwe0QZkttTy\/SSii9YVn0Rpf28Nyrjt2BeDIrzK2GHH\/0gXz5xtN730hs6aS\/yFace72Iyko3EdOtWzc2depU\/n8c3P\/880\/mN2+88QZr3bq1alttbS1r2LAh+0iJM7UhYuzud9euXfxkK4\/y8nLPREztzvhNtfk375ynEzqhaMZYHAiUWUH\/A6tjsym9ztRIxFSMHm8clvuqkDjRSlSTV6GBKfITMLQI6eSD8CKXRrJ9irlLGjaUp3AXHY8t+W3oXFNV\/hx0sn7q\/eQZlSWDQ\/y4IsnwtIMDr91UYHLZwqSPlxfXwVUciHZdK4dQmy0h75TDpRetINR22VacppXlWUwfoNqu5+TtcoROQqkJLMURjdgS00ssEHzkRKuh6z5S6SRinn\/+eW6NOfLII3mNpGeeeYb7x+zYsYP5BZY56NWrV8L2Dh06sJdfftm2iLG73wceeCA2UIsPL0QM0gDqeOP847sNzCvUnVA9W9blRG5yL8heq3LgjIsa+exaT8Qk1CSSzKyNfE34TV4qn\/GWT9RJf++k40lhzgTdYzEx0\/cjl4YsFb4oDJSHLHLKNDqzdG2W3IqOvSLCWCdPhrZ94nGIDtEfjShWm+mjkR9oNTDlT2TSx8vznCZu4FC0S3+jEuWn3PcuCX95dmbBsTvJoC4TQLHPd6xOLN8hOnu7HKEjXUKcMpu3a23eogpoxQ6DxfFaaZqClq74SKUAz0Osf\/jhB\/bII49wS8zee+\/NLRXZ2dk8N8wFF1zAfU6++OILy\/u96667pGJAfGDF7KCJGD8tMUgzQGHA2KpZ3vZ02pTXebA2dpMXNCyPJF2SpW43IWJQaEjrzGgjAN4vMR+KqdTC6V7P85ZwS46FGZ2h2d4LYWQ3q7DNsHG3c2nodbp64cCOBmiDWTqvtYT+NtfcrvZ9iZavEKssyzp0UcjIZtzlWfmxcNqk1hMTPl5eXQdXcUm064UFW45WM7hHtOdNLMPBhakoSAyWA\/UEtxL1hM9aZ2qlfbm5rCdtH7s0uWIwIvKSu2JCngt3yRKfJ8uNPuBbnhh0et20aRO3wqAj7OjRo9n111\/PnXpbtGhheX8bN27kIsXoUVNTE7jlJD99YpC2WZt5Q\/55ym\/Ma0Tzr\/jADJJmsmlqRYyS0yEhgVNuFfv45mKW3zYi0Apa\/BXp6N58M+GmxL8XndyUDjGZoDIiqeOqTWFkGrNZhR2EjdvJT2IWrQDUzmzt1MCxRG0kNFcljKNFS82IA8MqwRohouvHYiHRnVfXwTVcDA1Oem6TtPlY25LcI6hpFAEqnk9ZtuZkAkaxFomWOcy3iNcCtx12mLoQpGKZc+TnpUNSS522DloDby3BfvtlBSLZXb2H1YUVB9zFixfHtk2bNs01x167+\/VLxOQ1iIRZf\/veL57sX8XYsQnp9kWLTLKEb6KIWbduG+vTR79SrPLIgj2sa4O1EXEi3JhiB7\/s0U8NEjxFOyth5pbsJowIoxTNjr1M9ieC52HGElZeVm+qM7LbcXliiUlG9LxoLXl8GSDJMo0Y+SGzxCTLRyP6jRkO+MI18t1Z1youhQYbWmJMDL5xwVfPMyiL94hiQcP5ciyfiwDOO40EtJFFTBEysuVRfP3VVzJ\/Knf7B0Orn4\/ZlCtSILoDIWK8BkOhMZx7wYIFbM6cOaxnz56qUGhMsrfPPvvw9xXWr1\/PvvvuO\/b666\/zEzR79mz+GnPDmN1vEERM9+w1vL3OffVHTyKKYmhSr8dFTHnizErn5hFFzIoV21TOn4qQ0XY2DSHivCwuC6jFRD2fdYvVpaWCKnqjG9XXUQkjmzlUdDErokZNkhZvcz06ykINKbsdlyw8VfvsupDRnBdp4i9DAcOMk\/RFd8L3G3X0TGwf0UE2CD5TAUF1bjHTtcG51WuTupE5guM2Cg5t2jK74evJ+gXf2nQUqdXPSj9Qb7P4rUAqlj8zQsSg8EBxgctWWDkb89eISemwfhOeBLS6JHPAHTNmjOn9BkHE7Nco0hEUP\/td0ogipYOwo5jFLKdKB69NZqY13SdbTtJGsXTsqI5kUUSSWPCsJO88dcjss5P0izJGBVUs86ekvg7qWtFPQrwJ7UaMGNVa+emxT1nfviYqcqOQcTPZnwNnYDsdlzzaR13PyZNZq+S8JLSLkiS\/sXs9X96UlZlAfxteX6ljtfH50NZX8qnOTBDRBgYoAk+a9TaJwFNFNGF\/kDVIVUvJzBKR3mTErEUsFdZF3b5I6P9Ysn7ATvHbJMfiygQvCRkhYoKM1yLm0KaRIpBf\/juez0a348BZiw1fEW2W03jl1NUasVGqSt2uRebYqxUyMUHTYGNs\/7hf8btka8F6qbaXdT2J9d\/7T92ZGw6kBxwgX0u3k0PFuNZKV+4E3bhxYpFC3jEI0RqqAdBksr+YU59kIFBZ3mw4A1vtuJTzoPgPyAZ71\/0HdDIbJ1pi6lnZGvWs1Iq1KeU+UyFDdb4w9b1wMXQrg+sJPE3K\/9g1Rcf+Mv+sBn76eRnee0JxTKZ9iP2AgyjGZMfktYAjEZPmImZAix95A\/r47mj8oFnzuIUGp81yKubjQHERy3IK+yWkbjcTnYQp4RM6Axig6qwSlq1mxSsgJ\/g+CL+TC6AGkb\/lx59VwH\/8\/Dm1SZ397NyoZuorYUI1MbIh0ilpnJNlHZGBo6U2vFgcCFSD8F\/2nQCtng8xUkNWk8btSA6jauMJ7V+JZtP6ppTJTe5u+QhlKrHzJfGv4dFkouDTE3iCSE2wruWdl9CGvfLf8MsSg8eFTVEmxNCCXNhphzmrX3Gx\/eK3BktRdpJk2oFETJqLmGNbf8sb0PibSkxHFFmutrxLneW04taHEkSNMotSzaymzDZliekqyReF4ihu8SlljWFn4sxr5S5W\/soUac4GcRkgYskpVQ9mmroj2pvQiclU67OTUGtFUyk59puMKiSLnY7OQKA6D7gcgqGY2lnnKB3zs8lOzY2OyzMBIJyXhPOhtAuMguu+J975FwxUD34umdwJ99BGJOkWOJRYf91ua375eZmyZB6yhxV2qI5kO35Vx+qH9wP2tU6jlzT3BVliMggvRIx4Yw5tv5A3oDFXzZbfmJKIIiPnWzuiRvtQ6uJoZ1NmfGLy2mxTCRlMMJYgQIS08oYp4AUfE9FKpDyys+X1RdwwQyeNxJAUKSyBaMSFC3k4TIViOti\/3Y7Lr+gGU6nulSUM5V5w2eROGGNGYGgjkkQHfrTO4kOZ4CiTM68sYX76eWmrZysxKdp73Ex9NOY0eklzX4gTMPKJyQDcFjHazvms1jN44xk94K3EQUAnosjI+datY5RFRRlHJ9Wzso8X8+MVHYZjdUD0kuAVRXPNyDqMsWNVViKtmNO7CS3VxjEAl7wSxKNRkUIjS4xJR1BboZgmOjW3nPl0BeKaelbUZaerjr7SQTLaIZdjRl+t87RTkzvhupgV0x2IvnGNYFe8DIRgaeXV06O5W9wWMn77eblyz9W6UONNuC+4K4Fi4aTopMzAbRGjddg9r+GH\/P+PNn0owWFXFlGkWtaQmF+dYhQVtXx5XMT88osmT4zgZa8sITWCnaw5VMfTaCs34L33smVPf8kK8uulnQWfiWl8P2QmaOwE0TdGdhPqCiOTZmjRUVcrUrQirKS4Jh7tok1jbsMR1FIopolOzW0HSWnnLC79eJl8Wk\/IYVVsA5M7+cAYY\/X8WGlTirM0bmucXcc65uxg2Q0iS4L4PP+BL\/g9U9B+W9xpvstO3RxIbvxOv\/y8HFs\/x9qfuKjKuUTvi4qs1rwEDE46cbInO1bKE5NmeLGcJDbswfA1fx4Kn6sauBhRhCIAi4MlWDGyV7OFc2tdbXBGUVGFhdUqS0wsY69Y9yg3lw8ouCSF4chrRkVCWsXBvOLPXfxGQfGjeyPtX5Hgp6OciwNgadzCk7cjoQN1ehNG9lOv72ishIwLvkluzWR0Oz1NVIgVa48XS0C6y20eWggNZ6UdOuh28uLvV9LO61kN\/BIzQRJVbuQRSmZpkLUXcekG\/zbmLK912nYhP0oqse2HVmt\/4qJbzgWAL81jcILuBDIdM\/ZmMl459ir+HkfBLN62joFi1aCoRBThoI1FwWTLMYdisbBOO1xXzvpRUTpVrC2a8U3N4rrXc6dfmYMnOsEtePALVa4PZUBwehPqJuQShBSu4aOYcbtIm+GgIOQ+sRP268WgqZuC3qtlnGSzUh2TO58QRM+jXoZpMQW91wIiaKUKnFjqrFgajAozxv82MZtvYJy1jcSUiVpQli0xxfbLRUSuaWLEpNqKXO9LTS8SMekanRR12EXxgg0KxYzKYTfqfLvwoS\/ig3iHKlbWtjdvjAtan8Q9253O\/PWQRUUVNvxZZYmRzRbEAnuG+zc5i\/Oqw9cb1HE7rpcXdksUDUrEVJ\/um7iVSRQNyv70TO\/Jji8UhQTNWGKiIfCuW2OSzUqNHtEEkaIPV15e\/LWYjt72ObZgLQjitbbkv6H5rWYsDXqDeUI5gfu+lC8TiqImVRiJKcl7jn1idjkrF2HGHcEPiyCJmHQUMYLDrmKJ6Qfzdc3xbuWLsYQkKmo69IuJmMLCSHSSODtWhWdjyGASzM5S3L7RkgkjdOxDB781a8ytm7shtII2OzfCVAp6t2fNZmelBiZ3rZDRihlH95JFa4FbjtZuYtpqIMkebvQ30vYSnZgl5HoSk7\/Jlgm9sMaYEaBGkW+S99wWqhWaPlB8re0DRZ9CaTmX6GQDJ5v9j6j3vM8hEZOOPjGCQj4RvuTP+8EylUL2JF9MEmI3hk5UVAE\/RqXEwzbjFOTa\/B06+JVwScRMByOLYNC7wd3qsILkJ+E4Bb3J628avVnpvfdaMrnrZWp1JBxshnanSsQ7uh+F36rNHi4TYno+dvPzzo6lSEAhgwkzxYzXKj8Or6s7mxGgRkvmkvfcnJRUaPYlvlbCw5V9yXwKpSk6lEgloX6YVxZBEjHpFp2kKQEwDY7n\/+8I6w2z5XqSL0ZAdWPc\/7lqQPoIzow60m5TWWJ0zZRCLhWv85bYnWklmwljXgcrwiSIM2svUHWomrovCSno\/fBhsGByl7U3V8Szg9DuZKLBTwudqfsx+lvFrN9G9wc6S2vbi\/i3KGC41XNVLVvQ+czEWkzRz5sqqmoHMwJUu5QpKwcgec8t8Vlert83ic7Rqj4r6lMoJg2NXVMlgnLiRJ5w1Ot+i0RMuuWJ0ZQA+BM6RCYbsIf9Dt3k2XJ9yBejSgQl5HbBZHXK9zaErTERM3PaX4mWIVHAJCsE5+egrzPTStZpWz1G30RZipGFbiqP2IATsErPWideXEYSr5Pi7GsZowHOwjHptRe\/\/GdMtfXob62AHPYT7BvpxzTWYDwOpVK0WKtKbC+xEhvZq9mCklq+bNt\/742q\/kYRwgnC2O12ZUaAGiWbc5qIzub1+egjdaZh0UlauV5m+y+v+y0SMem2nKTJlrtnzNtsL6jhDWfN\/f+VZsv1K18M9weJ1vNAIYMWGPF7iuGwmIhZ9+AzumZKc57z3nfMZmZayWbCVm\/wVCyPpQQHkRN+I7Y30YlXK2ZsCRmDQcxoJs5r5xRaD092W\/Dr1ffB7ZMnq48RS16gkMBoSYyaxFBdbi3RpLKXhqtrzlOs2ClmCNdYpzGdhChgtJYZ10SCGQFqFNaP2\/EEOUlEZ4EygzB1bd9ktY\/1st8iEZPmtZOQbg0jBQ5LRv9oqgK1LF9MwvKTTcqWb2eFWRoLS4NSVvb0RLbt9ddjImb5ovWxEOfY57SJ3nQ85311YjWYaZkVKGZv8EyxxLgROeEnSnvTRiEps1XchqHXlsWzwQBn5DSJAkYZfHAMlA4wmmRvisO5XtvSOpqbWcbQy2CrROiJFeLxt1R0O5gtgL4xSy1PYhmNRtOmsld9f7Kss9OnGxf7NFNU1Q5mrCjJwvqNHh4sp5Zo+qLRo+V9k5U+liwxaY4fImZgyx94w5l4y9yky09iSzMq1mgbA98bsexAzCfG5szQF2dFg5mW26bWVPrEBM0hOGjHgyiJGWUdu2wJxBQGA1xCevc1Eb8sfFbECIoEpaaOqh3lViVE+OExoaCQDVjioMSXZkwOXnr1fUSRhc9TpjBWMXq8SmiIS85itJG0rScTAm++GfHPkPlvGJXycGLlM5PO30lYvwfWmDILlhiz96Ef\/RaJmAwQMf+XX8IbzbNnzXStWGOyOkjSASWJ7822igpNdJLHS0FO0ek8eQI9E6ZWrXOv3g2eyrwfQQvNDtrxeCawTGRTVUXvaEKLRdGg3W95\/oCI\/4cwCIrCQhywxOKF+CxbGrLrkB53Gk2s5C76ysWPpz5x0LOYdTbB6ol5Y7yw8plJ5283rN8toeXQJyYZfvVbJGIyQMTcclgk4d3tfYp9q4MkG1CS+d4sf\/zdxDwxQR2kJJ0ndzrNam0qP4JSCM7MDZ7KgTtoidOCdjyeYXKAw3IRCYVCZYO9wfKneO7EgUstNNx3SBcFkswykmCxfWGJ7fOEn\/NtOdassMKs5HpLpmg9Gj488sD\/e7icWm4nOslkSgc\/+i0SMRkgYp46LSJiLixw1wvUqA6SttikGd8bacZeyXemUsCYDf9FU73RjDxulq9nZVO+l4Zn8xt8a8S6hc+pWkIJWnh30I7HE0uNBZ8gtCYkWBdMLn9ivh3xXpUJC91lKRcc0vUsI9KlHyyNUaY5h5rzxC3HuEymOU9+hPqG0Snddp4YCzloKGNvmuOHiJkwIrKcdFSr770dUAyy\/ZrxvenLi1VKaicFBJVoEzJ\/JkQ5ZOWbWq\/mN\/ioSVInvdgNHpC6LlYcP\/0oqBdGJ2dPCmVaSVIpWeLg4cg9NqqOSSss0FdGdkxOHdJxgJS1KVFI4fui4LCSJDJl1rsQOaXbztgbgMSYCiRiMkDEfPPSD7HOzQtMdaQmfG\/WvfpeXMRUV7Mgwjs+JQtlsiiHZDOtZImwbGZq9QKzjp+GwsuiuEnWsU6bpj4efB1k3B5MFSddaVvESL4y85FOSvShTHCIEU6q73bokN6wodznQlzKwmVXrYOomSUubbsJsh8V4QwSMWksYpROf9Wsslh15Pq6Pe6raZey\/YrRSRhuHVS4adpm+LelRFgOMrW6jVnHz1jSMZnwsmBVSmbiFsOWlQe+xiigIOPWUpjlKsImHE3tRNQZfU5PtBm1JZllRuskrPUnM3MOHS9raAW4y9ZGSwEShAoSMWkqYsROf+WyXbFOYdMTb7o7+3Ax268YnbQNe6mAZGOVYTt5k9JB7d5tnAjLQaZWt7Hk+KknvCxalYycDZUZPD66dLGQUM6HZS6\/lsL4\/R3NQqubGqHHxsj9bcLRVOsboydYrEQn6VlAZHlilL9Di4xyfWUWIFnort1zaOVcJyz7KuUR0Aenwt8ACUINiZg0FTFap9sO8Cf\/\/\/R2\/5fgdOsEN7P9isnutqXY8mCEow5U6aCuu053Rqz6nN77PoEJ0TAxmszykuD4aSS8bFiVZGGfooDp2FGdHVdMNCdt1wHxL5KJYCxQKEN3Fo61c7odzMp1cpygXxYuE\/Fzb8LRlPvG7F+RdMnFSp4YIwuIkslXT5DIBEwqsldzgYGRhtwHrmvkQHfujFZw7sq380R9Ff4ESPhKfTBEfzJIxKTxcpLYOewLGPnD2DFQzI6EWax7YWIYplWTpqvZfmtr2bZu3eIiBgfCFPuByDph8ZzioIl+GKaXA0RrBI78eomwop2kX+nGjcAkZNwhW\/Cx0HX81BNeb73lav0f7UM574az1hT5F8kGcdlvwuaAAlH2OenvsRIBY9LRtOLPXaYz8bodcWJVkGBSP0Vce2mJ4QJDW\/36uuvUfVxulbu1pQwCJHxlrDPR71dSShIxae7YqzjdHgHz1DO\/+5Y4Nmm6mu137FhufVFZYlI8a9aeE1mNHHxfycaadMZkNsW4npXG73MSK8jXii83aDMRq2bN6MStJ7w6dHD0O7QD3LPP6g94up1jCvyLZMsp2qW5Xr3US3OKkEnq7BvCCBi3LJsqh2ZM8udluLRmuZwLjIZHqa3NLhXJtRRp5jW1zkS\/n87UJGLSPTop6nRbCL+zo6GY5cMa3i7\/e+QY5yZNh9l+tTdMgohJcaVirV8GihVZjRz8XNIbU+wUjB4oAmRWmlRYYzQDP8\/doefQiZYavfTtyu+y8Tv0rBaWZuAp8i8ym0QMCyGKQgaXljwblAOGSqxlr45YIBTrruS3Jzg0RwWEZ+HS0XtAtLzE2p04eXNDFLsUIOEKY52Jfj\/D2knEpLOIkTjd4lISPt\/d+OmETjxlJs3oDSO1xKTYGqO96XD5SFvkz5SJ1EmhN58SZanMv5qBfyH0ZYXZZTqdUr28ErCZh8G1dS0Vegr9i8TfgBYrXHqThQijBcayOAs5qoFOEMFcMAi1khLCpbUOzZIq117URpMKDLdEsUGAxLKuJ+kuyXsSuVTrjuj3KykliZh09omRON0OgS\/46+NgutTp1neTpnDDSEVMiq0xiONICKPokJYtIz4jYrrxW27RTzXu0TKB7nJidFDBisItoIoVtq9ONA9j6nshW7FpAWNwbV1LhW6mEF9A2g9aYIz8QoJY+NKdNhe1\/AqDpmIBThAkWodmzXV0O3WEeA8YWmIcimKjAAlMjVHQTnLfeRW5NNY90e9HFBmJmHSNTtJxun0ObuLb+sBCudOt3yZNwUFR1xLjkeXBCo4iIZJZYVDEpBjpcmJWlrosBKxiC\/POTBz4d+1i5a9MSUz3fu+9tq1KoqjCZTyxQrSYCh23G1aINlOILwDtJ1lnn64J21Thy5qHNHzZL6uaIH61GbmlCS4diGKjAIkCKI39xIKCeDCGZ8tnte6Lfq+jyEjEpGueGB2n26lwEv9vL1ie6HTrYs4X0wgOiqoQa0x2FxAHRUsp97Uky9GBD3R8TXE2XtGvR+yslU7U1vq\/cm0VR+Xrr7dkVcLjEsULihUxY68oXvBzuhFJKfYvSiZQzJjd\/fQx8NXiY2XQ9NOqFp1c4fKoLCN3QqkRZRnVxmQrWYAE3oNojTFqH64x1rroN2ovaCk16jvdgERMui4n6TjdLh3xGm9IbWFzgtOtmzlf7KDK2BuQ2kmigJH5YWgLpCVgNhR2+nRHx8k7kjJ5XgejgUc7w5ctJ2IHugz2szdgOIxycDR4B6AQXzKBol0OM\/p9fvgYyCw+WpErtnXHosbKoOmnVS0qwNG6yGtLdahkZZf\/KyLEow98jdt5UkG0QtqdbJkIkFj29Je8AKaXYoDZEP1GFkLRzwv96ZI5bduFREwG1E4S2boas+JGGtb2Tdu9yfmSJiJGHEBFPwwx4Zu4XTqQakNh9cKn0QfGJrGORHGOFDrzZEsNCSLh\/bkJy4l5UJ7osGt24HchtNn24G0nDNnFBF9mBJjVgoZOfQySWVnQouVaRJ6bg2YKrWpB8UXyPLlfsXXRb6a0RHaDPWwB9EnqtG0XEjEZJmLq99Sz5hCp+\/Pr\/0q9yfmSJiJGVpJeFiljJruoJ+bw6IDLs+o6CDtVJfDLr2d5bSIFLpUHdyq0WhdK9nsdDDS+pZl3MauvWT8WzIJrZZC0O5iZPR4x7xEKF1lZB1eWsawMmgGwqqUSX9r\/Lnu5h2STjLj1up7N73yWOadtj8fQLPwHCNepqqqCnJwcqKyshFatWvnynfs0KoVfa7tD8bPfw+CbD4lsrKmByglfQHUlg65tdyT8zdotzaBlThbkXHgKQOPGnhzX9u3boUWLFvz\/27Ztg+bNm0OqqawEqK4G6NoVoLyMweCBNbBqXZPY+4WFALNnA+Tnm9jZuHEAl11m\/P6ll5o\/OGV\/48ZB+V9NYfAth8Aq2BuK4HcYd99KGPbuEFi1KguKihjMnJlleIzl5QBHHglQVhbflpcHkJ0d2VZUBDBzpsnfqT0+p78zyty5AIMGxV+XlAAMHAjuUVcH0KsXQGlp5AevWBE5AS61Hy1r1wK0bAmQk2N+f3idBg8GWLUqvs3stcHvO+aYyN+KfyPuE7fPmhUZJrXfgxQUAIwfDzBsWOJ+LFNTAzB5cuRZD+xrzjgj8n+zn\/Wof0oV2uuDt48r599FZO0S+8b3L\/8C+j10asLn1z73IbS8\/BxLbd\/xGOpcLxFBsMQgx7VZEplsXj+HBYmgWWISkEVulZg0RUusMLhEEwtJduJrgtOevDxWBvlyp2wTvkx4jOKMW\/lttmfcLludfJmJBqhquAw3fGKs7ENr8dG2D08sYYQKpw7dfi6FlWgthLP8ccSm5aQMFDGXFX3D29JjQ4sDVRY+aCJGm\/xNGrll0JGrzPfvz9VfohNzq9j1NYk+pOHxEmc8bceGSwiNG8sHKVu+Dy46YfqSNCtAVcNluBmdZEYQyj4jE7mEtzgJrfczLL9M1qaSZfF2aZJAIiYDRcw9A4p5Gxp+0MxAlYUPkohJiNoRIrcKYDXLa7MtNujrDaSqgad7PSt7eUrkPGL6fqH2Sywqwa6viUYYJVhiBGffZPV8sEo0ZpVV1rSVz1kSry46YdodvC3PQANSNVwPtwckI78amWhUnHrJEuM\/dq0pfoXll0knGYKPnkzIuDhJIBGTQSJGuRleumAmb0dntZudYGFJZVn4IIkYdbHHelbQcG1MwCi5U\/h2TcSGL1YEyYCbNCFX1NnXtUy4RrjohGln8Lb8NwHI6quLYAl1a2nAyBIjG\/jwIYoYtMjold4ggoXXVsxyPaEUzeKdtByJC47YJGIyRMSIHfvY4fN5++kLC6QWllTVUAqSiEHE84C5UvJgrTr526gPTc2CXfXn0PGtMZWQCy0+Fur52La8uVxh2ergbXkG6kP+EdsCRBIt5UTMJBvUlJBq1yq3E4b44bPipT9Zhd6EYdcubnlGS3Msj45H5VNIxGSIiBE7o6M7\/MSfO8M6XQtLKsrCB03E6J4HFApZBbFZupnOxrUcD5IBF31qTIXHFx4csyqY7djCWJPH0gzUh\/wjtpeCJIkCtfsSB0HtvrTXzqy4w1wxyj613yfu0+3l5aDkY\/ELP31WSoz6H4e5kVJ93UjEZNByknJjtIeNvCFnwR62D\/zEGsJu1rNwN\/t9+W62e3v08doYNhsG8veUB77e\/fpb8c+4\/Ni6cWtMxOD\/zfzNnl27Gdu925XkZFL0aklZmKW7NhMyGHBRyOiZbFVRUMLxep48K8WYOu8+5B+x7ZsgiZYS9yUmytPmMVKWA8VB0O6g6ccgla61oYxIhc8KyO4DF3MjpQISMRnm2MstCw1Wsb2gxlTf7e8jbomJ\/D\/536CPymZow9jBB0tNk446YKNaUiaLvrm6Jm12wNV7CMfrW\/K4FJNUqBksfaEJnC\/BSczeVgdvy+3AIFpK3FcsK6pORmntIJjqWbMeftaGyiSflaT7X+WsLEgQIBGTadFJUcvCETAvLUQMPqbBiZH\/fPutq7M7rXOatHqtwSzd9Y5ZGXCx6jUWjTQqKmnw4L\/L65DlAOBEqLliGdCY6S0t4Y0eL79+0dmybF+y2l5hupa+hNIHEK8mFKb6n9wqtQU3hNYYEjGZJGJUloV61gq28seB8D1bmncC2\/LrJrZs9iZ2YINl8e2wH9sCrfkzvubbGyzjn9uyaqurj\/Jla2MiBv+f7PNHDdjN77v3ut8buQEnTZKk47cnIngHEC24xvMdRNPuJ4RHvzLFsAqzJyZysxaZe+9NLCb3ypT47wrDjNfmer3TAdEVASox02stQyg6Eo+7nvVvvIRVQI76wxrLn3Zfbg+CqSBTLIRavFjaTd7\/1KvbWRCi8WxAIiaTfGJMVKlOZQ0lq469550XObQXDh8T+c+TT0bekOS2sTqYuSVAPDHfO4j+CZ3vgY31ercsYI6EkMQpV896gss\/Cd9nFJaqadeyR5j9m9LdV8vv6CHd\/mfUJHWizZBaY0jEZEp0ktkq1Su2Jy0Lj++7ERrnVMQoBaEfPGp65D833GB68DDTSQTVf8ApofldkmtpBjeFmu0BRuOUyy14OgVEE5aBMAoQ8uXqRCigJ9tX2K0XGWWJqa9nZVO+V11L35bQagOcG8kiJGIyJU9MAKpUuy1icLUEf8Lw45ZF\/jNkiG79m0yb3aUFDmoZuSnULLcdzQBRnpUfn0AIAxNaYBLER94Ow1TtqpxAGidemZNvmAb\/TPOJQUuILP+WL0u7Y73PjeQXVMU6U6pYB6BKtdtVrJ99FuDWWwEuOu5PeG9Gp0gF4tpagNWrI7digwa8lGr59BUw+IRsW5V\/CW+rMietKK25lm5UlraCrarRmurdldAKhsJU2Jh7IMxc3FL1dx9\/DHDOOfHXJcW7YeCmT3WrNVfu2AuGPnUCbKxrC+MnZMFFF8WrGb\/3HsDFF0fO\/9atkVOnVKWWXa8gYaXCdtB\/iynq6qCyx+EwdM1o2JidBzN\/7QL53ePtWvndubkAU6e6dE\/p3VtaUnSv2YWqWGdg7aSgYtUS8\/bbkUnDSUftUE9BtVYmxRE3A2Z3XuKrP00AahnZsgzomOkrslqz8oKBKjO902VO8XpgBl3cpmwXrwcmrwvMEqEOofPVcql9x\/I7Sdq1Z0u7xd7nRvITWk5KMSRi7IuYzz6L3GuHHVovFTBq03t98CNxAo5vuTwCsF5vJ7utVnypkgxqRJhbSyc4yOExyAQAHpdSHiAMAsALX61A+n+lumL6LnfLgqQaEjEphkSMfRGD\/gDYB3TrxhjLzTVOx48h0uk+u0sXv4UArNebCU\/ts18169u3Pv4ZYXBS+ZkpQiY6WHEnexfFYKYmigutdScAVsZ0gkRMiiERY1\/ErFwZufdbtKhnrEkTacfAzbVZ+dKZTqAicUKEpxEkPtQycis89SfYV7VUiUkEY0uYBhV8uZO9y4NrpjnFhlbcBcDKmG6QiEkxJGLsi5gtW+J9wC5olDZrvGHAs2ivMKzXC6HfqnDn7vWs5N9fq5IhKkkStWZ6L5Y5Mio8OazizoSVMZBLYAGGopMyJTopBFiNTqqvB2jUCGDPHoB1Z94IeZ++EnmjQweAJ58EaNgw\/mGMuDrjjJRFXqUTtiJ2zIJROZMn60bnBOJaaqKPykd9CIOfPycQ0W9z5wIMGhR\/XVICMHAgZDSetleXo4IqCw6EoR2\/h42bshKOz9OIpRBD0Ukphiwx9i0xCJYQwtb544X\/ofXlTJzZmsS12a2OU2bJrFpvLFMWIEuMPoHIE2XCysiDEfJ2BGsJLEpQLUQZYYnZsmUL3HTTTTBlyhRo0KABnHvuufDcc8\/FZv0yXnvtNXjvvffg22+\/herqati6dSu0bt1a9ZnCwkJYs2aNatvIkSPh7rvvNn1sZImxb4lB9tsPYPlygBntzodjN0+Kv4F\/e9ppAFlZXh5yRrFjB8DXXwNs2w7QojnAcccDNG8GsH0HwAxh+\/HHAzRrBoFhd21k1l2zK37MCsqxN24SmeU22ivJznAWPX++atN2aAozGp8C22rifyyeH8u0awfwyCMAmv7GCG0+FTQWDRuWmHclEwmMJcaklbH80DNg8JDGgbqWlZUAQ4cCbNwIgbMQZYQlZujQoax3795s\/vz57JtvvmE9evRgF110keHfPPvss2zkyJH8gT9\/69atCZ\/p1q0be\/jhh9n69etjD7MWBAWyxDizxAwaFJmdfADnmvOloAc9wvB46aVwO7AGhLBaDoNmVSsPcBszO4YGP22fDr\/88gtMnToVFi1aBH369OHbXnjhBTjllFPgqaeegry8POnf3Xzzzfx5JspOA1q2bAmdOnXy4MgJM7RvV4+LybAZ2qvfQAtM27YA\/\/yn2jeGcMTOnZGJpMxIUFERcVNp2hQCB2awfeEFgL82Y5sBuHQYwDvj4q9vugmgTZskO1m0COCdd2IvKyAHnocR8Be0h\/bwF9x09jpoM7h3wneNGGHBqPL55wD\/+18kW6pJMEsyzoIRcZaMz\/hamSXj5zIJzAIsWqeUc6OcE9yOz0HMAozHiRYY0b8JX6fKmta1a+J5k1mIgnYeVbCQ8sYbb7DWrVurttXW1rKGDRuyj7ByWhKKi4sNLTEdO3Zkbdu2ZYcccgh74okn+L6N2LVrF1eMyqO8vJwsMQ4sMVcdvZLPAv4D98hntOQbk1Hr457NbiWhsao8RFkFqhBZ23lIXn01sv9TT0376+E22nMg5olZsEB9DoKeJypolpggH5dZS0wDCCkbNmyAXGWaEiU7Oxvatm3L33PCiBEjYMKECVBcXAzXXXcdPProo3DnnXca\/g36zOD6nfLIz9SFajeoq4N2P3zN\/4uzYWkNkAceiEQFEK6vj2OtG1wPF8HXuB3fx88FcXYrYnp2O2cOQGlppN+OkgNVMBWGwiw4BvJZWWRKip+LfhfO8C37CPToEXn+7TcLfxT5Dr1ZMG5P90gWWZvE34znf\/x44DWmxDYpvT54bdHaJlzjVKD1b8IIM3xWLCDaey4091CKCdxyEjrPPv7440mXkrzkVqw+GOXggw+GRo0acTGDQqWxTvjnPffco\/o7dEoiIWOTOXOgfeXv\/L+boZ08BlsZWPDuJ1wBC0Cig5\/SqcqK9SmfC9LgiceH5m8RfG3KUXLAAICJExOcMvHnxX4i3vP4uSi2TOuKiMGTiLkDaCnUUZusqooIGFmbTLg+uFSIofM4Kl96KaSCoC+BlTu5h1JM4ETMbbfdBldccYXhZ4qKiri\/ykZs3QJ1dXU8YsltX5YjjjiC73v16tWwzz77SD+D4kZP4BAWGTAA2l3fHGA0wOZDjge4TTNFkAwsRGaujxtF74iDni7Yjs4\/3\/sDxZOG34ViCQ8aqwmnO2j5WLwYAH0WbUYTOm6TaK1Fqy2CzxdemJIKzoH0b2KR61PesQ8MPjbL\/j2UalhI+fnnn\/l62eLFi2Pbpk2bxrKysti6desc+cRoeeedd1iDBg3YFkwlaxKKTrLnE6Osf3\/8cWRd9ogjMs8HINUEcX08bJEVUvbdN3JQX33FMgIli60L\/mu226Q2k24KfekC5980dmwkf41YYiNA91Da+8Tst99+MHToULjmmmtg4cKFUFJSAsOHD4cLL7wwFpm0bt062Hffffn7Cugv8\/3338Nv0bXppUuX8tdowUHmzZsHo0aNgh9++AFWrVoF7777Ltxyyy1w6aWXQpukYQ6EW+vfaHFHNm8Ovk9GuhGW9XFldqvNsaHMbnF7oKJ3bPrFhBKtBcSh\/5qtNqkcg2IF8sGXDvsmXDqSgUteem3Rd\/+musi5aQnVkFu5EoqKWDjuIRksxGzevJnnhWnRogVr1aoVu\/LKK1l1dXXs\/dLSUq7k0Oqi8MADD8SsAuJjzJgx\/P0lS5awI444guXk5LAmTZqw\/fbbjz366KM8+sgKZImxbokRZ9Zdu0ae27QJxqwgkwiLJSaQs1sjbr45cjJvu42lPS5bQGy1yegx8GKxYrFO4VjcbCOBra6d5Prw8\/Pch6HN2BtqERNkSMTYW06SdVaFhZFnjIT9\/XfGdu8O1iOdCtSGNYlYKHjxxciJPPpoxurrWSDA41i40N3j0SnhYPdGsdUmo8dQATnxcHnoqjoWt4VFaJY3a929Pl5BIibFkIixnycGb\/poMeFQPLKzGfvvf1noCU0nHFamTg2Eb4ZXfisJ+3Qht5PtNhk9Bu7zAb9FPqcIGaxSPupDT9p0KCYBY927Pl5CIibFkIhxluxOW9gt6I8hQ1joCZU5PIwsXx5vMKjSUz3zVWbkygjrxvFIkgc6me3bapOaY0DhIgqZkqxBrCh7tWfCItDLsbXuXh8vSfuyA0T6IstZ0K0bwGefBSu8F5k7F+DUU9PDV1NJIoYOiNrzrCQRQwe\/IOWICRXz5sX\/jwn2Hnss0nhSRXFx5DgQjKedMMF5HhXMQKfsU5bbyeJ32GqTSgJD5XOwFmbCYBgMM2EV7A2D2ByAOoCivJ0wc2ZT1x3Wg1ZawMvrEwRCXcU6yFAVa3tVrMNWtfePPwC6dInkLsP6Q3slq5acQjByQjYYIBhRQQLF42iQXr3kA0hQwAaAeVQwiscOOBDiIIiNzKvvMAOGNmJVcjwegQ0VTeCTb+Odx1mn74FOee4nHdy2LVLUuko4Da1aApxxBkC0G0wN9R5fn3POATjpJPB7DCUR4xEkYqyLGBxIMYxaK1i0wiZIhd3w7sGftmNHpLYfjlNBDl\/H\/JBaIaicXwyltJxOnzAHqnHMGqsF0zakorImKm6saEkQbvHEEwB33OH7GErLSURgCGRWyyRgCgpM\/\/Hjj5ElpaCKmLCWFEgLxHwl4pwRZ7soYlD9+plFVrEKaUUMHh+W5f7HP+zNxHG\/y5fHkzzJQJPlvvv6+ntRwL\/5JsCWrQBt2wCcey7Ahx\/GX191lTttXvs9yn71tvtOncfXR1w\/8xOffHQyDnLsdZaxNxR5P6Kce27EN27UKBZoQhE5kY7oRYOkKiokaMeTJhF35BjvLmmfsZdIT8JYtTcsiVjFLJxoecGJU1B9jdIGbdbYVFdkD9rxpFFWZ8UJGZe7tfeS7ernRFJIxBCEQ3r2jDyvXOn\/dxulOcft2hINYSkpkDYokTJ6rodiRfZMPB6P8VtYhHESFnbIJ4YgHEb7KJYYUcT4Ee1jx1lXFr6Or8kS4xFYaX3ixEj1aj38rMgetOPxAWz7evdhUAIECPuQiCEIhwICoxYRjOrcvRvgzz\/9ifax6qxrFL4u\/j3hIigIzj8fAkPQjocgHELLSQThUEBccEEkShYt8ZjPTBEK+L5RSgan4CxS9HHB78Xke6JQwffxc2gZ0m4fODDx7\/WWpgiCIIIIWWJSyJ49e6C2thbSnZqaGuiGKXej\/2+IYXwhYK+99tI9VkVAKMKgUaPIdswTtWGDWkB4iRh+rjjrIlpHxjCGrxME4Q6VaZzokpLdeYRRoh485Rs2bICKigrIBOrr66Ec1zL4oJkPDbzM1ukyrVu3hk6dOkGWTjSHdukGway9hYX+Zu\/FZHu4nKWA39+smfozaCnChywFBAaj4GUJ0aUhHIJt5IMPEtsJkV5UhjTRJSW7CzCKgMnNzYVmzZrpDpDpZHHaiRlCecdZGApLDArNHTt2wEa88wGgc+fOpuukoHEtFZFKIqKgIQgZP\/8MUFICcOKJqT6S8BNkS0d1mie6JBGTggFdETDt2rWDTPnNCk2aNAmFiEGaRtPBo5DB6yU7blm0D+qdUaPiyzdegp3TzTcDrF8f+d577wV49NH4a7+OgwgXI0YALF2Ks91UH0n4Cbqlo6tm6RufZTXpwhqpRSLGZxQfGLTAEMFHuU543bQixija5557vI\/2wRne1VdHBIvoA3PmmfHjwuMIUq0pIhhg0VIUMV46nmcKYbB05Jv0nQsjtAKeItJ9CSndr1MQon38zEZKpBdKmyAR4xwrUYKpJD9NE12SJYYgbBCEaB8lG6lsLV7JRhrmqAPCO0jEZJ6lozxNE12SJYYIjUXkk08+gaAQlDoplOacsAOJmMyydJRrlr7RoVu0HEWDR0MJiRjCNFdccQUXE\/jAHCrdu3eHO++8E3bt2gWZCAkIIqyQiPHP0pFqgbA2AEvfXkIiJuxgmp9Fi\/QLurnM0KFDYf369bBq1Sp49tln4dVXX4UHsOotQRChoUWLyPO2bak+kvQgyJaOlg5956wWmfUbEjFh5513APr1A3j3XV++rnHjxjz5GyatO+uss+CEE06Ar776ir+3efNmuOiii6BLly48queggw6C8ePHq\/7+uOOOgxEjRnALTtu2bfm+HnzwQdVnVq5cCUcffTQPx95\/\/\/1j+xdZunQp3xeGQWOo+rXXXgvbhB4ZrUZ4fI8++ih07NiRJ617+OGHoa6uDu644w7+3V27doUxY8Z4dq4IIqiQJSZzLB05Dpa+lfDxY45JFGL4Grfj+6kUMiRiwgymWVWsIPiMr31k2bJlMHfuXGgUzbmPy0qHH344fP755\/w9FBbDhg2DhQsXqv7u7bffhubNm8OCBQvgiSee4OJCESqY3fecc87h+8T3R48eDXfddZfq77dv3w5DhgyBNm3awKJFi+CDDz6A6dOnw\/Dhw1WfmzFjBvzxxx8we\/ZseOaZZ7jF6LTTTuN\/h\/u+\/vrr4brrroO1YbWjEoRNSMRkVpRgjs2lb234uCJkRMuT1zXikoJlBwj3qaysxPUd\/iyyc+dO9vPPP\/Nnx4wdi4tI8ce4ccxLLr\/8ctawYUPWvHlz1rhxY\/77GjRowCZNmqT7N6eeeiq75ZZb2KJFi\/jj6KOPZkceeaTqM3379mV33XUX\/\/+0adNYdnY2W7duXez9L7\/8kn\/Xxx9\/zF+\/9tprrE2bNmzbtm2xz3z++ef8WDZs2BA71m7durE9e\/bEPrPPPvuwo446Kva6rq6O\/5bx48frHr+r14sgAgLeSthl9O+f6iNJDyoqGCsvl7+H2\/H9sFJWxlhRUaS94HNJifo1vu\/nGKqFQqzDboXBPCbYnrDoDb7GCoSy4jguceyxx8Irr7zCrSHoE5OdnQ3nnntuLDMvLt9MnDgR1q1bB7t37+YFH5XMtwoHH3yw6jWm9FfS+\/\/yyy98qSovLy\/2\/oABA1Sfx8\/07t2bW3MUBg0axK04K1as4MtHyAEHHKCq04TbDzzwwNhrTF6HS1HKdxNEpkCWGHdBS4aeNSPV+WHSPXyclpPCCvqalJbGHXqxsh+2sAkTPP1aFA49evTgIuLNN9\/kyzJvvPEGf+\/JJ5+E5557ji\/\/FBcXw\/fff8+XfVDMiGBkkwhGO6EAcRvZ9\/j13QQRZEjEEOkSPk4iJuxWGBHFGuOTbwxaOe69917417\/+xQs8lpSUwJlnngmXXnopFzlFRUXw66+\/WtrnfvvtxyteYwSUwvz58xM+88MPP3BrkAJ+Nx7PPvvs48IvI4j0hkQMkQ7h4wiJmHSwwij4ZI0ROf\/88\/myzEsvvQQ9e\/bkDrro7ItLPug0++eff1raH0Y79erVCy6\/\/HIuVL755hv45z\/\/qfrMJZdcwiOX8DPoQIxWn5tuuok7EStLSQRBmBMxPmVnIEJKeYDDxxESMelihUmRNQZ9YjAqCKOMbrvtNjjssMP4EtLgwYN5+DSGOVsBrSkff\/wxt+z069cP\/va3v8F\/\/vMf1WcwfHvatGmwZcsW6Nu3L5x33nlw\/PHHw4svvujyryOI9M4Tg92EZrWXIEITPo5koXdv6r4+famqqoKcnByorKyEVq1axbZjGHJpaSnPdovWBMtg6zn22OSfKy6OtK4AgA6\/3333Hf\/\/oYcemlANOsg4vl4EEUBQvCjuYZs2AbRvn+ojIoJIZTRPDMY+aJ14FQsNho97UWJFbwzVQtFJYQMjdSZOBKip0f9M48aRzxEEQUjAAEYMGty5M7KkRCKGCGuRWRIxYQMFyvnnp\/ooCIIIOTj4KCKGIMIaPk4+MQRBEBkIRSgR6QCJGIIgiAyERAyRDpCIIQiCyEBIxBDpAIkYgiCIDBYxQvF3gggdJGIIgiAyOFcMWWKIMEMihiAIIgOh5SQiHSARQxAEkYGQiCHSARIxBEEQGQiJGCIdIBFDmOaKK66ArKys2KNdu3YwdOhQ+PHHH1UlBp599lk46KCDeJr+Nm3awKmnnsqLOWrZvXs3r7mEFa+xHlL79u1h0KBBMGbMGKitreWf2bRpE9xwww1QUFAAjRs35vWYsDYTVq0mCMI+JGKIdIBETEjrWegV3MLt+L5XoGhZv349f3z99de8AORpp53G38MyXBdeeCE8\/PDD8I9\/\/INXsp45cybk5+fzitb4f1HAoBh57LHH4Nprr+WVrxcuXAh\/\/\/vf4YUXXoCffvqJf+7cc8\/ldZfefvtt+PXXX2Hy5Mm8uOTmzZu9+5EEkQGQiCHSASo7EDJSWZALUawhCD7ffffdcNRRR3GLyYwZM2DSpElcaJx++umxvxk9ejT8\/vvv8Mgjj3DBgsW8Ro0aBbNnz4bFixfzopAKRUVFcP7553ORU1FRAd988w0XP8cccwx\/v1u3bry6NUEQziARQ6QDZIkJGdjhoIBRSqCjcBEFDG7H9\/3omLZt2wbvvPMO9OjRgy8tvffee9CrVy+VgFG45JJLeDXS6dOn89fvvvsunHDCCSoBo7DXXntB8+bNoUWLFvzxySefQI1RwUuCIGyHWFOeGCLMkIgJGVhwCy0wRUVxITN3blzA4HZ836vCXJ999llMXLRs2ZJbXd5\/\/31o0KABX+7Zb7\/9pH\/XvXt3\/oyfQVauXAn77ruv4XfhUtVbb73Fl5Jat27N\/WXuvfdelQ8OQRD2IEsMkQ6QiAkhuIQkCplBg9QCRlxicptjjz0Wvv\/+e\/5AHxb0azn55JNhzZo1Mb8YM5j9HPrE\/PHHH1wsoT8OLi0ddthhXNwQBGEfEjFEOkAiJqSgUBk3Tr0NX3spYBBc5sHlI3z07dsX\/vvf\/8L27dvh9ddf50tJ6Mwro7S0lD\/jZ5Tn5cuXm\/pOjHI68cQT4b777uMOwBgl9cADD7j4qwgi8wIDZCLG68AAgnAbEjEhBX1ghg1Tb8PXio+MX2CoNS4l7dy5k0cm4TLRlClTEj6HPjA5OTncDwa5+OKLuX8MRh5pwfBqFEZ67L\/\/\/obvEwRhHBiAfvKKeMFnNIxi34Hb8X0SMkRYIBETQkQnXlxCwpQpoo+Ml0IGHWw3bNjAH2h1uemmm7iDLzrzoog5++yz4fLLL4c33ngDVq9ezf1XMM8LRiL961\/\/4pYc5Oabb+Y+Lscffzy89NJLPI\/MqlWrYOLEidC\/f38uhjCM+rjjjuPOw7gftOZ88MEHPLfMmWee6d2PJIgMCAz4v\/+LbNuzB+C33\/wPDCAIN6AQ65CB5l6tE6\/iI6Nsx+dZs7xx7p06dSp07tyZ\/x8de9E5F4UF5m5BUIRg+DQmvLvxxhv5UhCKkldffZUntRNDtb\/66iv+OXzv9ttv5wnv0DF4xIgRcOCBB\/LEeUcccQT\/DIZoo4UGc85cc8013MGXIAh7gQFKX6GAfnWbNgF07Ahw110ACxdGHgRhlgMPRDcB8J0sZtbDkrBEVVUVXz7BsGLMi6Kwa9cublHAaB0c4MOWJ8YOKEaUZSMMqW7YsCGEBafXiyCCbs0lCDd44gmAO+4Az8dQLWSJCRkoTFCgoLlXa2lBQYMWGHTYC4qAQVC09OnTJ9WHQRCEJjAALTAKBx8cd\/YlCKt06QIpgURMCEGBoidSvMoPQxBEegcGYNK7zz7zPsKRINwk1I69W7Zs4Zlg0dSEydCuvvpq7mRq9Hl0RN1nn32gadOmvKgg+l+guUqkrKyMFy1EH43c3Fy44447oK6uzodfRBAEkb6BAQThNqEWMShgsFAgOohiJlmMgMHaPHpg0jR8PPXUU7Bs2TKeMA0dVVH8iP4bKGCwdg\/mJMFssfi5+++\/36dfRRAE4V9gwMCBiVnA9QrMEkTQCK1jL4b3Yr6QRYsWxfwtUJCccsopsHbtWsjLyzO1H4ysufTSS3neEUxz\/+WXX\/KqzCh2OqKrfrSA4V133cWLHDZq1MgVx97CwkJuDSKCDea\/wVBxcuwl0oEwBgYQmUmVScfe0Fpi5s2bx5eQRIdRTKSGidcWLFhgej\/KCUIBo+z3oIMOigkYBFPr4wlFq49R\/hT8jPiQgcUNkR07dpg+RiJ1KNdJuW4EkQ6BARgAoPV9UQIDSMAQYSK0jr2YbA39VURQiLRt25a\/Z4a\/\/voL\/v3vf6uWoPBvRQGDKK+N9jty5Eh46KGHTEXqoPjaiFMhAO53g1lviWCBBkoUMHid8HqFKSycIIygwAAinQiciLn77rvh8ccfN\/yMXn0eK6ClBH1fcEnqwQcfdLy\/e+65B2699VbV\/jExm4xOnTrxZ0XIEMEFBYxyvQiCIIhgETgRc9ttt\/ECf0YUFRXxgUUrAjCCCCOQkg061dXVvCIyZpz9+OOPVUsF+LdYnVnkzz\/\/jL2nB2agxYcZ0PKCWW\/RkoRZaIlggu2CLDAEQRDBJXAipkOHDvyRjAEDBkBFRQUsWbIEDj\/8cL5txowZUF9fz1PV64EWEvRxQcExefLkBGdN3O9\/\/vMfLpCU5SqMfkK\/GbTauAkOkDRIEgRBEIQ9QuvYizV20JqCdXTQclJSUgLDhw\/nRQiVyKR169bx2j6KZQUFzEknncQjkbBAIb5WihliaDWC76NYGTZsGC9KOG3aNF648O9\/\/7tpSwtBEARBEBloibHCu+++y4ULVkLGqKRzzz0Xnn\/++dj7uFSzYsWKWITJt99+G4tc6tGjh2pfStgzWkYw5wxWXkarDFZdxqrMDz\/8sM+\/jiAIgiCItMwTky4x7gRBEARBqKECkClG0YZ6+WIIgiAIgpCjjJ3J7CwkYjwCI6AQvTBrgiAIgiCSj6VokdGDlpM8AqOksHQBhnG7lcxOyT1TXl5OS1Q+Quc9NdB5Tx107lMDnfc4KE1QwGCgDvq86kGWGI\/Ak97Vo\/SX2LgzvYGnAjrvqYHOe+qgc58a6LxHMLLAhD7EmiAIgiCIzIZEDEEQBEEQoYRETIjAZHsPPPAAJd3zGTrvqYHOe+qgc58a6Lxbhxx7CYIgCIIIJWSJIQiCIAgilJCIIQiCIAgilJCIIQiCIAgilJCIIQiCIAgilJCICQkvvfQSr7LdpEkTOOKII2DhwoWpPqS04sEHH+SZlcXHvvvuG3t\/165d8Pe\/\/x3atWsHLVq04BXT\/\/zzz5Qec1iZPXs2nH766TwTJ57nTz75RPU+xhrcf\/\/90LlzZ2jatCmccMIJsHLlStVntmzZApdccglPCNa6dWu4+uqrYdu2bT7\/kvQ671dccUXCPTB06FDVZ+i8W2fkyJHQt29fnr09NzcXzjrrLFixYoXqM2b6l7KyMjj11FOhWbNmfD933HEH1NXVQaZDIiYEvP\/++3Drrbfy0Ltvv\/0WevfuDUOGDIGNGzem+tDSigMOOADWr18fe8yZMyf23i233AJTpkyBDz74AGbNmsVLSpxzzjkpPd6wsn37dt6GUZjLeOKJJ+D555+H0aNHw4IFC6B58+a8vWNHr4AD6U8\/\/QRfffUVfPbZZ3yAvvbaa338Fel33hEULeI9MH78eNX7dN6tg\/0FCpT58+fz81ZbWwsnnXQSvx5m+5c9e\/ZwAbN7926YO3cuvP322\/DWW29xsZ\/xYIg1EWz69evH\/v73v8de79mzh+Xl5bGRI0em9LjSiQceeID17t1b+l5FRQXba6+92AcffBDb9ssvv2BqAjZv3jwfjzL9wHP48ccfx17X19ezTp06sSeffFJ1\/hs3bszGjx\/PX\/\/888\/87xYtWhT7zJdffsmysrLYunXrfP4F6XHekcsvv5ydeeaZun9D590dNm7cyM\/jrFmzTPcvX3zxBWvQoAHbsGFD7DOvvPIKa9WqFaupqWGZDFliAg4q7yVLlnCTuliXCV\/PmzcvpceWbuCSBZrai4qK+IwTzbcInn+cPYnXAJeaCgoK6Bq4TGlpKWzYsEF1rrF+Ci6hKucan3Epo0+fPrHP4OfxvkDLDWGfmTNn8qWKffbZB2644QbYvHlz7D067+5QWVnJn9u2bWu6f8Hngw46CDp27Bj7DFonq6qquGUskyERE3D++usvbkoUGy+Cr7GzJ9wBB0k0z06dOhVeeeUVPpgeddRRvIoqnudGjRrxDlyEroH7KOfTqL3jMw60ItnZ2XxQoOthH1xKGjt2LHz99dfw+OOP82WNk08+mfc\/CJ1359TX18PNN98MgwYNggMPPJBvM9O\/4LPsnkAy\/dxTFWuCAOCdtcLBBx\/MRU23bt1g4sSJ3LmUINKdCy+8MPZ\/nPXjfbD33ntz68zxxx+f0mNLF9A3ZtmyZSp\/O8IZZIkJOO3bt4eGDRsmeKrj606dOqXsuNIdnBX16tULfvvtN36ecVmvoqJC9Rm6Bu6jnE+j9o7PWqd2jNLAyBm6Hu6By6rY\/+A9gNB5d8bw4cO5M3RxcTF07do1tt1M\/4LPsnsCyfRzTyIm4KCZ8fDDD+cmXtEkia8HDBiQ0mNLZzBs9Pfff+dhvnj+99prL9U1wBBJ9Jmha+Au3bt3552yeK5x3R99LpRzjc\/Y4aMvgcKMGTP4fYEWNMId1q5dy31i8B5A6LzbA\/2oUcB8\/PHH\/HxhGxcx07\/g89KlS1UiEiOdWrVqBfvvvz9kNKn2LCaSM2HCBB6d8dZbb\/EIgWuvvZa1bt1a5alOOOO2225jM2fOZKWlpaykpISdcMIJrH379jySALn++utZQUEBmzFjBlu8eDEbMGAAfxDWqa6uZt999x1\/YBf0zDPP8P+vWbOGv\/\/YY4\/x9v3pp5+yH3\/8kUfMdO\/ene3cuTO2j6FDh7JDDz2ULViwgM2ZM4f17NmTXXTRRSn8VeE+7\/je7bffzqNh8B6YPn06O+yww\/h53bVrV2wfdN6tc8MNN7CcnBzev6xfvz722LFjR+wzyfqXuro6duCBB7KTTjqJff\/992zq1KmsQ4cO7J577mGZDomYkPDCCy\/wRt6oUSMecj1\/\/vxUH1JaccEFF7DOnTvz89ulSxf++rfffou9jwPojTfeyNq0acOaNWvGzj77bN4REdYpLi7mg6j2gSG+Spj1fffdxzp27MjF+\/HHH89WrFih2sfmzZv54NmiRQseZnrllVfygZiwd95xQMUBEgdGDPft1q0bu+aaaxImSnTerSM75\/gYM2aMpf5l9erV7OSTT2ZNmzblEyyceNXW1rJMJwv\/SbU1iCAIgiAIwirkE0MQBEEQRCghEUMQBEEQRCghEUMQBEEQRCghEUMQBEEQRCghEUMQBEEQRCghEUMQBEEQRCghEUMQBEEQRCghEUMQBEEQRCghEUMQBEEQRCghEUMQhO8MHjwYbr75ZggSQTwmgiCMobIDBEH4zpYtW3jl3pYtW3LxcMghh8CoUaN8+37Zd4rH5DW33HILrFmzBj766CPPv4sg0hmyxBAE4Ttt27Z1XSzs3r07cMekx8KFC6FPnz6+fBdBpDMkYgiCSNnSzRVXXAGzZs2C5557DrKysvhj9erV\/DP19fUwcuRI6N69OzRt2hR69+4NkyZNUu1j+PDhfD\/t27eHIUOG8O1Tp06FI488Elq3bg3t2rWD0047DX7\/\/ffY3+l9p3Y5qaamBkaMGAG5ubnQpEkTvs9Fixapvh\/fv\/POO7kA6tSpEzz44INJhRZae+bOnQv\/\/Oc\/+Xf379\/f1XNLEJkEiRiCIFIGCokBAwbANddcA+vXr+eP\/Px8\/h4KmLFjx8Lo0aPhp59+4kswl156KRcgCm+\/\/TY0atQISkpK+OeQ7du3w6233gqLFy+Gr7\/+Gho0aABnn302F0XJvlMExcmHH37Iv+Pbb7+FHj16cKGEy07i9zdv3hwWLFgATzzxBDz88MPw1Vdf6f7e7OxsfqzI999\/z78bRRdBEPbItvl3BEEQjsnJyeEipFmzZtySIVpBHn30UZg+fToXHEhRURHMmTMHXn31VTjmmGP4tp49e3LxIHLuueeqXr\/55pvQoUMH+Pnnn+HAAw\/U\/U4RFEKvvPIKvPXWW3DyySfzba+\/\/joXKG+88QbccccdfNvBBx8MDzzwQOxYXnzxRS6cTjzxROl+UVD98ccf3EKEliWCIJxBIoYgiMDx22+\/wY4dOxLEAC7HHHroobHXhx9+eMLfrly5Eu6\/\/35uHfnrr79iFpiysjIuYsyAy0+1tbUwaNCg2DZcBurXrx\/88ssvsW0oYkQ6d+4MGzduNNz3d999RwKGIFyCRAxBEIFj27Zt\/Pnzzz+HLl26qN5r3Lhx7P+4lKPl9NNPh27dunHLSV5eHhcxKF6cOv7KQGEjgj4uimjSA5eRSMQQhDuQiCEIIqXg0s6ePXtU2\/bff38uVtB6oiwdmWHz5s2wYsUKLmCOOuoovg2XoMx8p8jee+8d87VBQYSgZQYde53mklm6dGnCkhdBEPYgEUMQREopLCzkSz8YIdSiRYtYqPPtt9\/OnXnRsoGRQZWVlVxUtGrVCi6\/\/HLpvtq0acP9TV577TW+tIMi6O677zb1nSJo4bnhhhu47wu+V1BQwH1vcInr6quvdvR78feg0ELfGPwe9NEhCMIeFJ1EEERKQbHSsGFDbn1BB1wUHsi\/\/\/1vuO+++3iU0n777QdDhw7ly0sYcq0HOs5OmDABlixZwpeQUAQ9+eSTpr9T5LHHHuMWk2HDhsFhhx3G\/XSmTZvGhZITHnnkEe4wjMtk+H+CIOxDGXsJgiAIggglZIkhCIIgCCKUkIghCIIgCCKUkIghCIIgCCKUkIghCIIgCCKUkIghCIIgCCKUkIghCIIgCCKUkIghCIIgCCKUkIghCIIgCCKUkIghCIIgCCKUkIghCIIgCCKUkIghCIIgCALCyP8DRp2fpeQSRWUAAAAASUVORK5CYII=\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=20475fdb-5ae5-4e01-b00d-8c0023a053d5\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Random\u3068\u6bd4\u3079\u308c\u3070\u6bd4\u8f03\u7684\u76ee\u7684\u95a2\u6570\u5024\u306e\u4f4e\u3044\u9818\u57df\u3092\u63a2\u7d22\u3067\u304d\u3066\u306f\u3044\u307e\u3059\u304c\u3001\u5148\u7a0b\u307e\u3067\u306e\u554f\u984c\u306e\u3088\u3046\u306b\u975e\u5e38\u306b\u6027\u80fd\u304c\u3088\u3044\u3068\u3044\u3046\u308f\u3051\u3067\u306f\u306a\u3044\u3088\u3046\u3067\u3059\u3002BOCS\u304c\u4f7f\u3063\u3066\u3044\u308b\u4ee3\u7406\u30e2\u30c7\u30eb\u306f2\u6b21\u306e\u9805\u307e\u3067\u3057\u304b\u30e2\u30c7\u30eb\u5316\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u76ee\u7684\u95a2\u6570\u304c\u8907\u96d1\u306a\u69cb\u9020\u3092\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u8457\u3057\u304f\u6027\u80fd\u304c\u60aa\u3044\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=e8aad7db-c2f4-4401-a7f2-d938a0d102e9\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E8%A3%9C%E8%B6%B3_%E7%B8%AE%E5%B0%8F%E4%BF%82%E6%95%B0%E3%82%92%E8%80%83%E6%85%AE%E3%81%97%E3%81%9F%E4%BA%8B%E5%89%8D%E5%88%86%E5%B8%83%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6\"><\/span>\u88dc\u8db3: \u7e2e\u5c0f\u4fc2\u6570\u3092\u8003\u616e\u3057\u305f\u4e8b\u524d\u5206\u5e03\u306b\u3064\u3044\u3066<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f19acc87-4f0a-478c-b6ad-7f2d8e04ff49\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u7bc0\u3067\u306f\u3001\u672c\u8a18\u4e8b\u306e\u9014\u4e2d\u3067\u51fa\u3066\u304d\u305f\u99ac\u8e44\u5206\u5e03\u3092\u3082\u3046\u5c11\u3057\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=ce63a06c-cf51-4372-882f-e0f0b65563d0\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E3%82%B9%E3%83%91%E3%83%BC%E3%82%B9%E6%80%A7%E3%81%AE%E4%BB%AE%E5%AE%9A\"><\/span>\u30b9\u30d1\u30fc\u30b9\u6027\u306e\u4eee\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=305feaf0-cd04-4fab-93c7-7fda0bdeed2d\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7dda\u5f62\u56de\u5e30\u306b\u304a\u3044\u3066\u3001\u5165\u529b $x^{(t)} \\in \\mathbb R^p$ \u304c\u9ad8\u6b21\u5143\u306a\u5834\u5408\u3001\u3064\u307e\u308a\u8aac\u660e\u5909\u6570\u304c\u591a\u3044\u5834\u5408\u306f\u3001\u7279\u5fb4\u91cf $x_i^{(t)}$ \u306e\u3046\u3061\u306e\u307b\u3068\u3093\u3069\u306f\u51fa\u529b $y^{(t)}$ \u306b\u5bc4\u4e0e\u305b\u305a\u3001\u3054\u304f\u4e00\u90e8\u306e\u6210\u5206\u304c\u51fa\u529b\u5024\u306b\u5927\u304d\u304f\u5f71\u97ff\u3059\u308b\u50be\u5411\u306b\u3042\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3088\u3063\u3066\u3001<strong>\u30b9\u30d1\u30fc\u30b9\u6027<\/strong> \u3092\u4eee\u5b9a\u3059\u308b\u3001\u3059\u306a\u308f\u3061\u4fc2\u6570 $\\bm \\beta \\in \\mathbb R^p$ \u306e\u3046\u3061 <strong>\u3054\u304f\u4e00\u90e8\u306e\u6210\u5206\u304c\u5927\u304d\u304f\u3001\u305d\u308c\u4ee5\u5916\u306f\u975e\u5e38\u306b\u5c0f\u3055\u3044<\/strong> \u3088\u3046\u306a\u63a8\u5b9a\u3092\u3059\u308b\u3068\u3001\u30c7\u30fc\u30bf\u306e\u500b\u6570 $N$ \u304c\u5c11\u306a\u3044\u5834\u5408\u306b\u3082\u3042\u308b\u7a0b\u5ea6\u3046\u307e\u304f $\\bm \\beta$ \u3092\u63a8\u5b9a\u3067\u304d\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u77e5\u8b58\u3092\u4e0a\u624b\u304f\u53d6\u308a\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u308b $\\bm \\beta$ \u306e\u4e8b\u524d\u5206\u5e03\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f62\u306e\u5206\u5e03\u306e\u5b9a\u5f0f\u5316\u304c\u3088\u304f\u884c\u308f\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=71498e65-478a-4617-97bc-fe6a56002095\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\bm \\beta \\mid \\sigma, \\tau \\bm \\lambda \\sim \\mathcal N_p(\\bm 0, \\sigma^2 \\tau^2 \\operatorname{diag}(\\bm \\lambda^2)).<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=ee78b92a-e208-4094-be24-417448830bb4\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u305f\u3060\u3057 $\\bm \\lambda \\in \\mathbb R_+^p, \\tau \\in \\mathbb R_+$ \u3067\u3059\u3002\u3053\u3053\u3067\u3001$\\sigma, \\tau, \\bm \\lambda$ \u304c\u6240\u4e0e\u306e\u3082\u3068\u3067\u3001\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u3092\u7528\u3044\u3066 $\\theta$ \u306e\u4e8b\u5f8c\u5206\u5e03\u3092\u8a08\u7b97\u3059\u308b\u3068<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f3b35d35-aa0b-44fa-bbe5-217e666b2217\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\np(\\bm \\beta \\mid \\bm X, \\bm y, \\sigma, \\tau, \\bm \\lambda)<br \/>\n&amp;\\propto p(\\bm y \\mid \\bm X, \\bm \\beta, \\sigma, \\tau, \\bm \\lambda) p(\\bm \\beta \\mid \\sigma, \\tau, \\bm \\lambda) \\\\<br \/>\n&amp;= \\prod_{t=1}^N p(y^{(t)} \\mid \\bm x^{(t)}, \\bm \\beta, \\sigma, \\tau, \\bm \\lambda) \\times p(\\bm \\beta \\mid \\sigma, \\tau, \\bm \\lambda) \\\\<br \/>\n&amp;\\propto \\exp \\left( -\\frac{1}{2\\sigma^2} \\sum_{t=1}^N (y^{(t)} &#8211; \\bm x^{(t) \\top} \\bm \\beta)^2 \\right) \\times\\exp \\left( &#8211; \\sum_{i=1}^p \\frac{1}{2\\sigma^2\\tau^2\\lambda_i^2} \\beta_i^2 \\right) \\\\<br \/>\n&amp;= \\exp\\left(<br \/>\n-\\frac{1}{2\\sigma^2} \\left(<br \/>\n\\left\\| \\bm y &#8211; \\bm X \\bm \\beta \\right\\|_2^2 + \\bm \\beta^\\top \\mathop{\\rm diag}\\left\\{ \\frac{1}{\\tau^2 \\lambda_i^2} \\right\\} \\bm \\beta<br \/>\n\\right)<br \/>\n\\right) \\\\<br \/>\n&amp;= \\exp\\left(<br \/>\n-\\frac{1}{2} \\left(<br \/>\n\\bm \\beta^\\top \\frac{X^\\top X}{\\sigma^2} \\bm \\beta + \\bm \\beta^\\top \\mathop{\\rm diag}\\left\\{ \\frac{1}{\\sigma^2\\tau^2\\lambda_i^2} \\right\\} \\bm \\beta &#8211; 2 \\bm \\beta^\\top \\frac{1}{\\sigma^2} X^\\top y + \\mathrm{const.}<br \/>\n\\right)<br \/>\n\\right) \\\\<br \/>\n&amp;\\propto \\exp\\left(<br \/>\n-\\frac{1}{2} \\left(<br \/>\n(\\bm \\beta &#8211; \\bm \\mu_N)^\\top \\bm \\Sigma_N (\\bm \\beta &#8211; \\bm \\mu_n)<br \/>\n\\right)<br \/>\n\\right)<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3c10b389-7cc6-44e2-a37a-d5e783d5fb84\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3068\u306a\u308a\u3001\u4e8b\u5f8c\u5206\u5e03\u306f\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03\u3068\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=48d7401e-1370-4cc8-9cc3-a7bcc0c51bc1\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\bm \\beta \\mid \\cdot \\sim \\mathcal N_p(\\bm \\mu_N, \\bm \\Sigma_N)<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3d201f56-84bf-4ce8-9d3e-ad7d57dea0c0\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u305f\u3060\u3057 $\\bm X = [x_i^{(t)}]_{t,i} \\in \\mathbb R^{N \\times p}$ \u306f\u89b3\u6e2c\u884c\u5217 (\u5165\u529b\u3092\u4e26\u3079\u305f\u884c\u5217)\u3001$\\bm y = [y^{(t)}]_i \\in \\mathbb R^{N}$ \u306f\u5fdc\u7b54\u30d9\u30af\u30c8\u30eb (\u51fa\u529b\u3092\u4e26\u3079\u305f\u30d9\u30af\u30c8\u30eb) \u3067\u3042\u308a\u3001<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=11245863-d84d-4d1e-8a4c-a629daa62eb3\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\bm \\mu_N<br \/>\n&amp;= \\sigma^2 \\bm A^{-1}, \\\\<br \/>\n\\bm \\Sigma_N<br \/>\n&amp;= \\bm A^{-1} \\bm X^\\top \\bm y, \\\\<br \/>\n\\bm A &amp;= \\bm X^\\top \\bm X + \\mathop{\\rm diag}\\left\\{ \\frac{1}{\\tau^2\\lambda_i^2} \\right\\}<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=4f516ff4-2a15-44c1-bb03-5d2b828d6ba2\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=5827a6e9-de83-423e-8d8d-502320d234bb\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E7%B8%AE%E5%B0%8F%E4%BF%82%E6%95%B0\"><\/span>\u7e2e\u5c0f\u4fc2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=1d7f6231-7320-40e1-ac60-63ed967c4444\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u3053\u307e\u3067 $y^{(i)} = \\bm x^{(i) ~ \\top} \\bm \\beta + \\varepsilon$\u3001\u3064\u307e\u308a<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=b70f754d-4492-489b-968b-9691d4b66858\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\ny^{(1)} &amp;= \\sum_i x^{(1)}_i \\beta_i + \\varepsilon \\\\<br \/>\ny^{(2)} &amp;= \\sum_i x^{(2)}_i \\beta_i + \\varepsilon \\\\<br \/>\n&amp; \\vdots \\\\<br \/>\ny^{(N)} &amp;= \\sum_i x^{(N)}_i \\beta_i + \\varepsilon \\\\<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=fc36ba01-e371-4721-943d-c128c557e12b\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3092\u8003\u3048\u3066\u304d\u307e\u3057\u305f\u304c\u3001\u3053\u3053\u304b\u3089\u66f4\u306b\u6761\u4ef6\u3092\u8ffd\u52a0\u3057\u3066 $N=p$ \u3068\u3057\u3001$t$ \u756a\u76ee\u306e\u89b3\u6e2c\u3067\u5165\u529b\u30d9\u30af\u30c8\u30eb\u306e $t$ \u756a\u76ee\u306e\u8981\u7d20 $x_t^{(t)}$ \u306e\u307f\u304c $1$\u3001\u305d\u308c\u4ee5\u5916\u304c\u3059\u3079\u3066 $0$ \u3067\u3042\u308b\u3088\u3046\u306a\u5165\u529b $\\bm X=\\bm I_p$ \u3092\u4e0e\u3048\u305f\u3068\u3057\u3066\u3001<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=b4525195-9dd8-458e-946f-b33bfd86522d\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\ny^{(i)} = \\beta_i + \\varepsilon \\quad (t=1,\\dots,p)<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=e1f1ada5-f075-4717-8f7e-e663dcc0de0e\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3068\u3044\u3046\u72b6\u6cc1\u3092\u8003\u3048\u307e\u3059\u3002\u4e8b\u5f8c\u5e73\u5747 $\\bm \\mu_N$ \u306f<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=773d6a9f-d6b0-44c1-b23d-7fd9d131f230\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\bm \\mu_N<br \/>\n&amp;= \\left( \\bm X^\\top \\bm X + \\mathop{\\rm diag}\\left\\{ \\frac{1}{\\tau^2 \\lambda_i^2} \\right\\} \\right)^{-1} \\bm X^\\top \\bm y \\\\<br \/>\n&amp;= \\left( \\bm I_p + \\mathop{\\rm diag}\\left\\{ \\frac{1}{\\tau^2 \\lambda_i^2} \\right\\} \\right)^{-1} \\bm y<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=ac22cc1e-b8fd-41a2-b72d-26eb592f4b8e\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3068\u306a\u308a\u3001\u305d\u306e\u7b2c $i$ \u6210\u5206 $\\mu_{N,i}$ \u306f<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=8865a21a-6c01-4d22-92c6-29d10c7f4a58\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\mu_{N,i} &amp;= \\dfrac{1}{1 + \\dfrac{1}{\\tau^2 \\lambda_i^2}} y^{(i)} = \\left( 1 &#8211; \\dfrac{1}{1 + \\tau^2 \\lambda_i^2} \\right) y^{(i)}<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=65543d26-3ac0-4903-bb59-f0ab269789b0\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=4768c929-b207-44cb-b0ed-d1f351e0967f\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\kappa_i = \\frac{1}{1 + \\tau^2 \\lambda_i^2}<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=133660ff-c034-4924-9d4a-ba6fdc342095\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3068\u3059\u308c\u3070<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f7e65e28-81b7-4068-9033-1f02cfdb8f61\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\mu_{N,i} = (1 &#8211; \\kappa_i) y_i<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=6f9e8ccf-04ce-468b-9e5f-0e3e8c9ec2b9\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u65b0\u305f\u306b\u767b\u5834\u3057\u305f $\\kappa_i = \\dfrac{1}{1 + \\tau^2 \\lambda_i^2}$ \u3092\u7e2e\u5c0f\u4fc2\u6570 (shrinkage coefficient) \u3068\u3044\u3044\u307e\u3059\u3002\u4eca $0 \\lt \\tau^2 \\lambda_i^2$ \u306a\u306e\u3067\u3001\u7e2e\u5c0f\u4fc2\u6570\u306e\u53d6\u308a\u3046\u308b\u7bc4\u56f2\u306f $0 \\lt \\kappa_i \\lt 1$ \u3068\u306a\u308a\u307e\u3059\u3002\u5f53\u7136\u306a\u304c\u3089 $0 \\lt 1-\\kappa_i \\lt 1$ \u3067\u3059\u3002<\/p>\n<p>\u4e0a\u306e\u5f0f\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b\u3001\u56de\u5e30\u4fc2\u6570 $\\bm \\beta$ \u306e\u4e8b\u5f8c\u5e73\u5747 $\\bm \\mu_N$ \u306e\u7b2c $i$ \u6210\u5206 $\\mu_{N, i}$ \u306f\u3001$\\bm y$ \u306e\u7b2c $i$ \u6210\u5206 $y_i$ \u3092 $1 &#8211; \\kappa_i$ \u500d\u306b\u7e2e\u5c0f\u3057\u305f\u683c\u597d\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u3059\u306a\u308f\u3061 <strong>\u7e2e\u5c0f\u4fc2\u6570 $\\kappa_i$ \u306f\u89b3\u6e2c\u3055\u308c\u305f\u5024 $y_i$ \u3092\u3069\u308c\u307b\u3069 $0$ \u306b\u5727\u7e2e\u3059\u308b\u304b\u306b\u5bc4\u4e0e\u3057\u307e\u3059<\/strong>\u3002$\\kappa_i \\approx 0$ \u306e\u5834\u5408\u306b\u306f $y_i$ \u304c\u307b\u3068\u3093\u3069\u305d\u306e\u307e\u307e $\\mu_{N, i}$ \u3068\u306a\u308b\u4e00\u65b9\u3001$\\kappa_i \\approx 1$ \u306e\u5834\u5408\u306b\u306f $\\mu_{N, i} \\approx 0$ \u306b\u5727\u7e2e\u3057\u307e\u3059\u3002\u305d\u3057\u3066 $\\kappa_i$ \u304c $1$ \u306b\u8fd1\u3044\u304b $0$ \u306b\u8fd1\u3044\u304b\u306f $\\tau^2 \\lambda_i^2$ \u306e\u5024\u306b\u3088\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=4dc30660-91cf-4166-8ab9-14d72be113f8\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0a\u3092\u307e\u3068\u3081\u308b\u3068\u3001<\/p>\n<ul>\n<li>$\\tau^2 \\lambda_i^2$ \u304c $0$ \u306b\u8fd1\u3044\u307b\u3069 $\\kappa_i$ \u306f $1$ \u306b\u8fd1\u3065\u304d\u3001$\\mu_{N, i}$ \u306f $0$ \u306b\u5727\u7e2e\u3055\u308c\u308b<\/li>\n<li>$\\tau^2 \\lambda_i^2$ \u304c $1$ \u306b\u8fd1\u3044\u307b\u3069 $\\kappa_i$ \u306f $0$ \u306b\u8fd1\u3065\u304d\u3001$\\mu_{N, i}$ \u306f\u5727\u7e2e\u3055\u308c\u306a\u3044<\/li>\n<\/ul>\n<p>\u3068\u3044\u3046\u7279\u5fb4\u304c\u3042\u308b\u3068\u3044\u3048\u307e\u3059\u3002\u66f4\u306b $\\lambda_i^2$ \u306f\u5404 $\\kappa_i$ \u306e\u5024\u306b\u5f71\u97ff\u3057\u3001$\\tau^2$ \u306f\u3059\u3079\u3066\u306e $\\kappa_1, \\kappa_2, \\dots, \\kappa_p$ \u306b\u5f71\u97ff\u3057\u307e\u3059\u3002\u3088\u3063\u3066<\/p>\n<ul>\n<li>$\\lambda_i$ \u306f\u5404\u4fc2\u6570\u306e\u63a8\u5b9a\u5024 $\\mu_{N, i}$ \u304c $0$ \u306b\u5727\u7e2e\u3055\u308c\u308b\u304b\u306b\u5bc4\u4e0e\u3059\u308b<\/li>\n<li>$\\tau$ \u306f\u4fc2\u6570\u306e\u63a8\u5b9a\u5024\u5168\u4f53 $\\bm \\mu_N$ \u304c $0$ \u306b\u5727\u7e2e\u3055\u308c\u308b\u304b\u306b\u5bc4\u4e0e\u3059\u308b<\/li>\n<\/ul>\n<p>\u3068\u3044\u3048\u307e\u3059\u3002\u305d\u3053\u3067 $\\lambda_i$ \u3092 <strong>\u5c40\u6240\u7e2e\u5c0f\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong> (local shrinkage parameter)\u3001$\\tau$ \u3092 <strong>\u5927\u57df\u7e2e\u5c0f\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong> (global shrinkage parameter) \u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=c032efe8-77ef-4583-990b-73d31aaf0b55\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E9%A6%AC%E8%B9%84%E5%88%86%E5%B8%83\"><\/span>\u99ac\u8e44\u5206\u5e03<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=ed0d30ca-23bd-4063-b12c-c555a3de7fbf\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0a\u306e\u8b70\u8ad6\u306b\u3088\u308c\u3070\u3001\u7e2e\u5c0f\u4fc2\u6570 $\\kappa_i$ \u304c\u63a8\u5b9a\u5024 $\\mu_{N, i}$ \u306b\u5f37\u304f\u5f71\u97ff\u3059\u308b\u306e\u3067\u3001\u7e2e\u5c0f\u4fc2\u6570 $\\kappa_i$ \u304c\u3069\u306e\u3088\u3046\u306a\u5206\u5e03\u306b\u5f93\u3046\u306e\u304b\u304c\u6c17\u306b\u306a\u308a\u307e\u3059\u3002\u7e2e\u5c0f\u4fc2\u6570\u306f $\\lambda_i$ \u3068 $\\tau$ \u306b\u5f71\u97ff\u3092\u53d7\u3051\u307e\u3059\u3002\u3053\u3053\u3067\u7c21\u5358\u306e\u305f\u3081\u306b $\\tau=1$ \u3068\u56fa\u5b9a\u3059\u308b\u5834\u5408\u3001$p(\\kappa_i)$ \u306f $\\lambda_i$ \u306e\u5206\u5e03 $p(\\lambda_i)$ \u3092\u5909\u6570\u5909\u63db\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=2343b54b-969d-4284-af15-69d1609d52dc\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u69d8\u3005\u306a $p(\\lambda_i)$ \u306b\u5bfe\u5fdc\u3059\u308b $p(\\kappa_i)$ \u306e\u5206\u5e03\u306e\u5177\u4f53\u7684\u306a\u5f62\u72b6\u306f\u6587\u732e [Carvalho+ (2009)] \u306b\u307e\u3068\u3081\u3089\u308c\u3066\u3044\u307e\u3059\u304c\u3001\u7279\u306b $\\lambda_i \\sim \\mathrm{HalfCauchy}(0,1)$ \u3092\u8a2d\u5b9a\u3057\u305f\u5834\u5408\u3001$\\kappa_i$ \u306f\u6b21\u306e\u3088\u3046\u306a\u30d9\u30fc\u30bf\u5206\u5e03 $\\mathop{\\rm Beta}(0.5, 0.5)$ \u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=806f8214-259c-4ab7-bfcd-2c956138c6fb\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$<br \/>\n\\begin{aligned}<br \/>\np(\\kappa_i) = \\frac{1}{\\pi}(1-\\kappa_i)^{-1\/2}\\kappa_i^{-1\/2}<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=d7576360-e327-4764-a03e-e9969d13c8b0\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3055\u3066\u3001\u30d9\u30fc\u30bf\u5206\u5e03 $\\mathop{\\rm Beta}(0.5, 0.5)$ \u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u99ac\u306e\u8e44 (\u3072\u3065\u3081) \u306e\u3088\u3046\u306a\u5f62\u72b6\u304c\u73fe\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\" id=\"cell-id=a60a7bf7-749b-42b6-9bae-187be4c36a16\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"kn\">from<\/span><span class=\"w\"> <\/span><span class=\"nn\">scipy.special<\/span><span class=\"w\"> <\/span><span class=\"kn\">import<\/span> <span class=\"n\">beta<\/span>\n\n\n<span class=\"k\">def<\/span><span class=\"w\"> <\/span><span class=\"nf\">_beta_pdf<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">beta<\/span><span class=\"p\">(<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"p\">(<\/span><span class=\"mf\">1.0<\/span> <span class=\"o\">-<\/span> <span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">**<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"n\">x<\/span> <span class=\"o\">**<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">return<\/span> <span class=\"n\">p<\/span>\n\n\n<span class=\"n\">x_plot<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mf\">1e-3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.0<\/span> <span class=\"o\">-<\/span> <span class=\"mf\">1e-3<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1000<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">y_plot<\/span> <span class=\"o\">=<\/span> <span class=\"n\">_beta_pdf<\/span><span class=\"p\">(<\/span><span class=\"n\">x_plot<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">fig<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">figure<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">fig<\/span><span class=\"o\">.<\/span><span class=\"n\">add_subplot<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">x_plot<\/span><span class=\"p\">,<\/span> <span class=\"n\">y_plot<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$\\kappa$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$p(\\kappa)$\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.0<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">()<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea\"><img decoding=\"async\" alt=\"No description has been provided for this image\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=8c5795bc-5f72-4ac5-b307-235ecc5b9cec\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u3053\u3068\u304b\u3089\u3001\u7279\u306b $\\lambda_i \\sim \\mathrm{HalfCauchy}(0, 1)$ \u3092\u4eee\u5b9a\u3059\u308b\u5834\u5408\u3001\u3053\u306e $\\theta$ \u306e\u4e8b\u524d\u5206\u5e03\u306f\u99ac\u8e44\u5206\u5e03 (horseshoe distribution) \u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=432aa874-272c-4810-b43a-cc366280d99b\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u5f62\u72b6\u3092\u898b\u308b\u3068\u660e\u3089\u304b\u306a\u3088\u3046\u306b\u3001\u99ac\u8e44\u5206\u5e03\u306f $\\kappa_i \\approx 0$ \u307e\u305f\u306f $\\kappa_i \\approx 1$ \u306e\u5024\u3092\u53d6\u308a\u3084\u3059\u3044\u3068\u3044\u3046\u6027\u8cea\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u6027\u8cea\u304b\u3089\u3001\u99ac\u8e44\u5206\u5e03\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u63a8\u5b9a\u5024\u306e\u3046\u3061\u4e00\u90e8\u306f $0$ \u306b\u3001\u6b8b\u308a\u306f $0$ \u306b\u5727\u7e2e\u3055\u308c\u305f\u63a8\u5b9a\u5024\u3092\u88dc\u3046\u3088\u3046\u306a\u5927\u304d\u306a\u5024\u306b\u306a\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=de1c72e0-951f-4dc2-959a-994c1d659337\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u306a\u304a\u99ac\u8e44\u5206\u5e03\u306e\u7531\u6765\u306f\u7e2e\u5c0f\u4fc2\u6570 $\\kappa_i$ \u304c\u30d9\u30fc\u30bf\u5206\u5e03 $\\mathop{\\rm Beta}(0.5,0.5)$ \u306b\u5f93\u3046\u3053\u3068\u306b\u3042\u308a\u307e\u3059\u304c\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u305d\u306e\u3082\u306e\u3092\u99ac\u8e44\u5206\u5e03\u3068\u547c\u3076\u306e\u3067\u306f\u306a\u304f\u3001\u3042\u304f\u307e\u3067 $\\theta$ \u306e\u4e8b\u524d\u5206\u5e03\u3092\u99ac\u8e44\u5206\u5e03\u3068\u547c\u3076\u3068\u3044\u3046\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=fe258752-cbd1-4b77-a761-adf85c1ae6b1\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=ed1cc37c-3add-4381-b170-05582e5b410b\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u672c\u8a18\u4e8b\u3067\u306fBOCS\u306e\u6700\u3082\u57fa\u672c\u7684\u306a\u5b9f\u88c5\u3092\u884c\u3044\u307e\u3057\u305f\u3002\u81ea\u5206\u306e\u624b\u3067\u5b9f\u88c5\u3059\u308b\u3053\u3068\u3067Thompson\u62bd\u51fa\u306b\u3088\u308b\u30d9\u30a4\u30ba\u6700\u9069\u5316\u306e\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u306b\u3064\u3044\u3066\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u3055\u3089\u306b\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3078\u306e\u9069\u7528\u306b\u95a2\u3059\u308b\u96e3\u3057\u3055\u3082\u77e5\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=f6e5ec28-464f-4d0e-ad45-470902f9de8e\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u307e\u305fBOCS\u306b\u304a\u3051\u308b\u8ab2\u984c\u3068\u3057\u3066<\/p>\n<ul>\n<li>\u5236\u7d04\u6761\u4ef6\u4ed8\u304d\u306e\u554f\u984c\u306f\u3069\u3046\u3059\u308b\u306e\u304b<\/li>\n<li>\u30c7\u30fc\u30bf\u306e\u6570 $N$ \u3084\u5165\u529b\u6b21\u5143 $d$ \u304c\u5927\u304d\u304f\u306a\u308b\u3068\u8a08\u7b97\u30b3\u30b9\u30c8\u304c\u5927\u304d\u304f\u306a\u308b\u554f\u984c\u306f\u3069\u3046\u3059\u308b\u306e\u304b<\/li>\n<\/ul>\n<p>\u306a\u3069\u306e\u70b9\u304c\u6c17\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u4eca\u5f8c\u306f\u3053\u306e\u3088\u3046\u306a\u8ab2\u984c\u304c\u3069\u306e\u3088\u3046\u306b\u6271\u308f\u308c\u3066\u3044\u308b\u306e\u304b\u3092\u8abf\u3079\u305f\u308a\u3001\u89e3\u6c7a\u7b56\u3092\u63a2\u3057\u305f\u308a\u3057\u3066\u3001BOCS\u306e\u6539\u5584\u7b56\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u3044\u304d\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=7bbe7374-ba19-4f45-80eb-c80fee833a56\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><\/span>\u53c2\u8003\u6587\u732e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=84186547-ad13-481c-bcbb-86edc1ccc9e3\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<ul>\n<li>[Carvalho+ (2009)] C. M. Carvalho, N. G. Polson, and J. G. Scott, Handling Sparsity via the Horseshoe, in Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics (PMLR, 2009), pp. 73\u201380.<\/li>\n<li>[Wand+ (2011)] M. P. Wand, J. T. Ormerod, S. A. Padoan, and R. Fr\u00fchwirth, Mean Field Variational Bayes for Elaborate Distributions, Bayesian Analysis <strong>6<\/strong>, 847 (2011).<\/li>\n<li>[Bhattacharya+ (2016)] A. Bhattacharya, A. Chakraborty, and B. K. Mallick, Fast Sampling with Gaussian Scale Mixture Priors in High-Dimensional Regression, Biometrika <strong>103<\/strong>, 985 (2016).<\/li>\n<li>[Makalic &amp; Schmidt (2016)] E. Makalic and D. F. Schmidt, A Simple Sampler for the Horseshoe Estimator, IEEE Signal Processing Letters <strong>23<\/strong>, 179 (2016).<\/li>\n<li>[Baptista &amp; Poloczek (2018)] R. Baptista and M. Poloczek, Bayesian Optimization of Combinatorial Structures, in Proceedings of the 35th International Conference on Machine Learning, edited by J. Dy and A. Krause, Vol. 80 (PMLR, 2018), pp. 462\u2013471.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=3358555c-8e58-4d6b-bf7a-118d6350e163\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\"><\/span>\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\" id=\"cell-id=7cd88f78-07ae-41de-89ca-6e572e7ed8d1\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u68ee\u7530\u572d\u7950<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001\u30b7\u30df\u30e5\u30ec\u30fc\u30c6\u30c3\u30c9\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3068QUBO\u30e2\u30c7\u30eb\u3092\u7528\u3044\u305f\u30d9\u30a4\u30ba\u6700\u9069\u5316\u624b\u6cd5\u3067\u3042\u308bBOCS-SA\u3092Python\u3067\u3044\u3061\u304b\u3089\u5b9f\u88c5\u3057\u3001\u7c21\u5358\u306a\u30d9\u30f3\u30c1\u30de\u30fc\u30af\u554f\u984c\u306e\u6700\u9069\u5316\u3092\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"author":1,"featured_media":8185,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[47,56,63,104,112],"class_list":["post-7235","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hands-on","tag-47","tag-56","tag-63","tag-104","tag-112"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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