{"id":7870,"date":"2020-03-17T21:56:27","date_gmt":"2020-03-17T20:56:27","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=7870"},"modified":"2022-12-03T23:03:47","modified_gmt":"2022-12-03T22:03:47","slug":"algorithme-doptimisation-bayesienne","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/probabilistic-algorithms-2\/bayesian-optimization-algorithm-2\/","title":{"rendered":"Bayesian optimization algorithm"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"7870\" class=\"elementor elementor-7870\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8a3882e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8a3882e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6ae7f4b\" data-id=\"6ae7f4b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c5b944b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"c5b944b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/probabilistic-algorithms-2\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Probabilistic algorithms<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4817f13\" data-id=\"4817f13\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5c9f972 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"5c9f972\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Home page<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4e6fe54\" data-id=\"4e6fe54\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f5f145b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"f5f145b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/en.wikipedia.org\/wiki\/Bayesian_optimization\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6dd796dc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6dd796dc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-55fedde1\" data-id=\"55fedde1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5b24f1ce elementor-widget elementor-widget-text-editor\" data-id=\"5b24f1ce\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">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\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/probabilistic-algorithms-2\/bayesian-optimization-algorithm-2\/#Algorithme-doptimisation-bayesienne\" >Bayesian optimization algorithm<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Algorithme-doptimisation-bayesienne\"><\/span>Bayesian optimization algorithm<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-text-align-justify\">In a <a href=\"https:\/\/complex-systems-ai.com\/en\/algorithmic\/\">algorithm<\/a> In Bayesian optimization, the information processing goal is to build a probabilistic model that describes the relationships between the components of the fitting solutions in the problem space. This is achieved by repeating the process of building and sampling from a Bayesian network that contains conditional dependencies, independences, and conditional probabilities between components of a solution.<\/p>\n<p class=\"has-text-align-justify\">The network is built from the relative frequencies of the components within a population of candidate high fitness solutions. Once the network is built, the candidate solutions are rejected and a new population of candidate solutions is generated from the model. The process is repeated until the model converges to a suitable prototype solution.<\/p>\n\n<p class=\"has-text-align-justify\">The following algorithm provides a <a href=\"https:\/\/complex-systems-ai.com\/en\/algorithmic\/pseudo-language-and-flowchart\/\">pseudocode<\/a> of the Bayesian optimization algorithm to minimize a cost function. The Bayesian network is built at each iteration using a greedy algorithm. The network is evaluated based on its match to the information in the population of candidate solutions using either a Bayesian Dirichlet (BD) metric or a Bayesian Information Criterion (BIC).<\/p>\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-7866 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/boa.png\" alt=\"bayesian optimization algorithm\" width=\"686\" height=\"522\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/boa.png 686w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/boa-300x228.png 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/figure>\n\n<p class=\"has-text-align-justify\">The Bayesian optimization algorithm was designed and studied on basic binary string problems, most often representing binary function optimization problems.<\/p>\n\n<p class=\"has-text-align-justify\">Bayesian networks are typically built (expanded) from scratch with each iteration using an iterative process of adding, removing, and reversing links. In addition, earlier networks can be used as a basis for the next generation.<\/p>\n\n<p class=\"has-text-align-justify\">A greedy escalation algorithm is used at each algorithm iteration to optimize a Bayesian network to represent a population of candidate solutions.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Probabilistic Algorithms Wiki Home Page Bayesian Optimization Algorithm In a Bayesian optimization algorithm, the information processing goal is to construct a probabilistic model that \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":7129,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7870","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/7870","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=7870"}],"version-history":[{"count":5,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/7870\/revisions"}],"predecessor-version":[{"id":18887,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/7870\/revisions\/18887"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/7129"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=7870"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}