{"id":177091,"date":"2024-01-20T15:57:55","date_gmt":"2024-01-20T14:57:55","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=177091"},"modified":"2024-01-20T15:59:34","modified_gmt":"2024-01-20T14:59:34","slug":"bayesian-optimization-definition-and-operation","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/bayesian-optimization-definition-and-operation","title":{"rendered":"Bayesian optimization: Definition and operation"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"177091\" class=\"elementor elementor-177091\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5a3a573 e-flex e-con-boxed e-con\" data-id=\"5a3a573\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3f0676e elementor-widget elementor-widget-text-editor\" data-id=\"3f0676e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<h2>To define a predictive model, data scientists call on multiple observations. But while the study of these observations leads to an optimal result, data scientists often have little time to analyze all the hypotheses.<br \/>So how do you find the right model in the shortest possible time? This is where Bayesian optimization comes in. What is it? How does it work? You&#8217;ll find the answers here.<\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5ad59df e-flex e-con-boxed e-con\" data-id=\"5ad59df\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d8a9570 elementor-widget elementor-widget-heading\" data-id=\"d8a9570\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h3 class=\"elementor-heading-title elementor-size-default\">What is the Bayesian approach?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b2f8484 elementor-widget elementor-widget-text-editor\" data-id=\"b2f8484\" data-element_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<p>Bayesian optimization follows directly from Bay\u00e8s&#8217; theorem:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-16988ef elementor-widget elementor-widget-image\" data-id=\"16988ef\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"585\" src=\"https:\/\/datascientest.com\/en\/files\/2024\/04\/ki-dev.jpg\" class=\"attachment-full size-full wp-image-184172\" alt=\"Exploring the Role of an AI Developer: Responsibilities, Skills, and Key Attributes\" srcset=\"https:\/\/datascientest.com\/en\/files\/2024\/04\/ki-dev.jpg 1024w, https:\/\/datascientest.com\/en\/files\/2024\/04\/ki-dev-300x171.jpg 300w, https:\/\/datascientest.com\/en\/files\/2024\/04\/ki-dev-768x439.jpg 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9f23d07 elementor-widget elementor-widget-text-editor\" data-id=\"9f23d07\" data-element_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<p>Through this theorem, you <strong>have a value y that is a function of x.<\/strong> The idea is then to determine the value of x by optimizing the value of y. Here, x is made up of a set of parameters (or observations).<\/p><p>In practical terms, this can be applied in a multitude of situations, such as setting an ideal price to maximize margins, configuring an application or database to maximize its performance, managing parameters to optimize supervised learning, etc.<\/p><p>In all these cases, <a href=\"https:\/\/datascientest.com\/en\/how-to-become-a-data-scientist-the-the-best-kept-secrets\">Data Scientists only have a limited number of observations<\/a> at their disposal to achieve an optimal result (whether due to time, financial or hardware constraints).<\/p><p>Indeed, to define the best model, it is generally necessary to test numerous hypotheses, carry out several training sessions and validations. But all these testing phases take time. It is therefore not possible to study an unlimited number of hypotheses.<\/p><p>To cope with these constraints, <strong>Bayesian optimization<\/strong> was introduced.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-38cddd6 elementor-widget elementor-widget-image\" data-id=\"38cddd6\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/12\/coding-g7ba6522fd_640.jpg\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-f77c605 e-flex e-con-boxed e-con\" data-id=\"f77c605\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-bcfe73f elementor-widget elementor-widget-heading\" data-id=\"bcfe73f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">How does Bayesian optimization work?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-66fd86f elementor-widget elementor-widget-text-editor\" data-id=\"66fd86f\" data-element_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<p>The central idea of <strong>Bayesian optimization<\/strong> is to minimize the number of observations while converging rapidly to the optimal solution. To achieve this, we need to be aware of three fundamental principles.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4d62392 elementor-widget elementor-widget-heading\" data-id=\"4d62392\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The Gaussian process<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6b0e168 elementor-widget elementor-widget-text-editor\" data-id=\"6b0e168\" data-element_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<p>The idea of the <strong>Bayesian approach<\/strong> is to use known observations to deduce probabilities of events that have not yet been observed. To reach this conclusion, we need to determine the probability distribution for each X value.<\/p><p>The most efficient method is undoubtedly the<strong> Gaussian process.<\/strong> This identifies the most probable value (called the mean \u00b5) and the probable dispersion of the value around the mean (called the standard deviation \u03c3). This standard deviation \u03c3 weakens the closer you get to a previously observed point.<\/p><p>Ideally, these values and distances should be calculated for each observation point. In practice, however, this <strong>exhaustive representation<\/strong> is not possible due to time constraints. So you need to select the points you want to evaluate.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b758c32 elementor-widget elementor-widget-heading\" data-id=\"b758c32\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Exploration and exploitation<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1385899 elementor-widget elementor-widget-text-editor\" data-id=\"1385899\" data-element_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<p>To design a <strong>high-performance predictive model,<\/strong><a href=\"https:\/\/datascientest.com\/en\/synergies-unveiled-the-dynamic-intersection-of-data-science-and-finance\"> Data Scientists<\/a> need to define the most relevant points. This is a two-stage process:<\/p><ul><li><strong>Exploration:<\/strong> this is of interest when the standard deviation is particularly large. In other words, the unknown variable in the search space is high. This allows us to test several models and improve our knowledge of the function to be optimized.<\/li><li><strong>Exploitation:<\/strong> at this stage, the aim is to refine the models tested upstream. The idea is to find the maximum point. To do this, Data Scientists use the average \u00b5. If it lies within the extremes, it&#8217;s easier to identify the right model.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6f3dd19 elementor-widget elementor-widget-image\" data-id=\"6f3dd19\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"585\" src=\"https:\/\/datascientest.com\/en\/files\/2024\/04\/nightshade.png\" class=\"attachment-full size-full wp-image-184177\" alt=\"Nightshade: Safeguarding Artists from Generative AI Intrusion\" srcset=\"https:\/\/datascientest.com\/en\/files\/2024\/04\/nightshade.png 1024w, https:\/\/datascientest.com\/en\/files\/2024\/04\/nightshade-300x171.png 300w, https:\/\/datascientest.com\/en\/files\/2024\/04\/nightshade-768x439.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0c7f34e elementor-widget elementor-widget-text-editor\" data-id=\"0c7f34e\" data-element_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<p>It&#8217;s important to strike the right balance between exploration and exploitation. If you favour exploration, you run the risk of overlooking other, potentially more efficient, models. Conversely, if you <strong>favor exploitation, you could overlook necessary improvements.<\/strong><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-372e5ca elementor-widget elementor-widget-heading\" data-id=\"372e5ca\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The acquisition function<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ea6e5fa elementor-widget elementor-widget-text-editor\" data-id=\"ea6e5fa\" data-element_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<p>The<strong> acquisition function<\/strong> helps to find the right compromise between these two variables. For each point in the search space, the function identifies an optimization potential. Among all these points, the function identifies a maximum. This is the next point to be tested. Simply repeat the calculation as many times as necessary until convergence between the maximum and minimum is achieved. This is the pair of parameters that should deliver the best performance.<\/p><p>Good to know: Noise can alter data and make learning more difficult. To avoid this, it is essential to check that the environment is sufficiently stable and the observations reproducible before using <strong>Bayesian optimization.<\/strong><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c05953f e-flex e-con-boxed e-con\" data-id=\"c05953f\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9582d73 elementor-widget elementor-widget-heading\" data-id=\"9582d73\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">How can Bayesian optimization be put into practice?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-19bd10d elementor-widget elementor-widget-text-editor\" data-id=\"19bd10d\" data-element_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<p>The easiest way to simplify <strong>Bayesian optimization<\/strong> calculations is to use the right tools. Like the Python package scikit-optimize or bayesian-optimization. All you have to do is define a search space, and the tool will then take care of finding points with high potential, thanks in particular to the Gaussian process. Here again, you&#8217;ll need to restart Python until you get a satisfactory result.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2699b95 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"2699b95\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Learn to master Bayesian optimization<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-087abd5 e-flex e-con-boxed e-con\" data-id=\"087abd5\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-674f974 elementor-widget elementor-widget-html\" data-id=\"674f974\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"What is the Bayesian approach?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In practical terms, this can be applied in a multitude of situations, such as setting an ideal price to maximize margins, configuring an application or database to maximize its performance, managing parameters to optimize supervised learning, etc. In all these hypotheses, Data Scientists only have a limited number of observations at their disposal to achieve an optimal result (whether due to time, financial or hardware constraints).\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"How does Bayesian optimization work?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The idea of the Bayesian approach is to exploit known observations to deduce event probabilities that have not yet been observed. To reach this conclusion, we need to determine the probability distribution for each X value. The most efficient method is undoubtedly the Gaussian process. This identifies the most probable value (called the mean \u00b5) and the probable dispersion of the value around the mean (called the standard deviation \u03c3). This standard deviation \u03c3 weakens the closer you get to a previously observed point.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"How do you put Bayesian optimization into practice?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"To simplify Bayesian optimization calculations, the easiest way is to use good tools. Like the Python package scikit-optimize or bayesian-optimization. All you have to do is define a search space, and the tool will then take care of finding points with high potential, thanks in particular to the Gaussian process. Here again, you'll need to restart Python until you get a satisfactory result.\"\n    }\n  }]\n}\n<\/script>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>To define a predictive model, data scientists call on multiple observations. But while the study of these observations leads to an optimal result, data scientists often have little time to analyze all the hypotheses.So how do you find the right model in the shortest possible time? This is where Bayesian optimization comes in. What is [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":177092,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Bayesian optimization: Definition and operation<\/title>\n<meta name=\"description\" content=\"Discover the power of Bayesian optimization and how it operates. 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