{"id":195166,"date":"2025-05-23T06:44:00","date_gmt":"2025-05-23T05:44:00","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=195166"},"modified":"2025-06-05T15:42:15","modified_gmt":"2025-06-05T14:42:15","slug":"all-about-bayesian-optimization","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/all-about-bayesian-optimization","title":{"rendered":"Bayesian optimization: Definition and operation"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"195166\" class=\"elementor elementor-195166\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4266a6e e-flex e-con-boxed e-con\" data-id=\"4266a6e\" 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-e48e481 elementor-widget elementor-widget-text-editor\" data-id=\"e48e481\" 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<p><b>To define a predictive model, data scientists rely on multiple observations. However, while studying these observations leads to an optimal outcome, data experts often have limited time to analyze all the hypotheses. So how do you find the right model in the least amount of time? This is where Bayesian optimization comes in. What is it? How does it work? The answers are here.<\/b><\/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-006c889 e-flex e-con-boxed e-con\" data-id=\"006c889\" 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-9f4d15d elementor-widget elementor-widget-heading\" data-id=\"9f4d15d\" 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><h2 class=\"elementor-heading-title elementor-size-xl\">What is the Bayesian approach?<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3e9e677 elementor-widget elementor-widget-text-editor\" data-id=\"3e9e677\" 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><span style=\"font-weight: 400;\">Bayesian optimization directly stems from Bayes&#8217; theorem:<\/span><\/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-4ea2954 elementor-widget elementor-widget-image\" data-id=\"4ea2954\" 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=\"147\" height=\"73\" src=\"https:\/\/datascientest.com\/en\/files\/2025\/04\/image1-5.png\" class=\"attachment-full size-full wp-image-195172\" alt=\"\" \/>\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-40d0605 elementor-widget elementor-widget-text-editor\" data-id=\"40d0605\" 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><span style=\"font-weight: 400;\">Through this theorem, you have a value y that is a function of x. The idea is to <\/span><b>determine the value of x by optimizing the value of y<\/b><span style=\"font-weight: 400;\">. Here, x consists of a set of parameters (or observations).<\/span><\/p><p><span style=\"font-weight: 400;\">Concretely, this can be applied in a multitude of situations, such as setting an ideal price to maximize margins, configuring an application or a database to maximize its performance, managing parameters to optimize supervised learning, etc.<\/span><\/p><p><span style=\"font-weight: 400;\">In all these hypotheses, <\/span><a href=\"https:\/\/datascientest.com\/en\/data-scientist-jobs-and-others-better-understanding-their-differences\">data scientists<\/a><b> have a limited number of observations to achieve an optimal result<\/b><span style=\"font-weight: 400;\"> (whether due to time, financial, or material constraints).<\/span><\/p><p><span style=\"font-weight: 400;\">Indeed, to define the best model, it usually requires testing numerous hypotheses, performing several trainings and validations. But all these testing phases take time. It is not possible to study an unlimited number of hypotheses.<\/span><\/p><p><span style=\"font-weight: 400;\">To address these constraints, Bayesian optimization was implemented.<\/span><\/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-19b6a36 e-flex e-con-boxed e-con\" data-id=\"19b6a36\" 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-5c236b2 elementor-widget elementor-widget-heading\" data-id=\"5c236b2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-xl\">How does Bayesian optimization work?<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8d8baf4 elementor-widget elementor-widget-text-editor\" data-id=\"8d8baf4\" 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><span style=\"font-weight: 400;\">The central idea of Bayesian optimization is to <\/span><b>minimize the number of observations while quickly converging to the optimal solution<\/b><span style=\"font-weight: 400;\">. To do this, it is necessary to know three fundamental principles.<\/span><\/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-883aeea elementor-widget elementor-widget-heading\" data-id=\"883aeea\" 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\">The Gaussian process<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9e764cd elementor-widget elementor-widget-text-editor\" data-id=\"9e764cd\" 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><span style=\"font-weight: 400;\">The idea of the Bayesian approach is to <\/span><b>leverage known observations to infer probabilities of events<\/b><span style=\"font-weight: 400;\"> that have not been observed yet. To reach this conclusion, it is necessary to determine the probability distribution for each value X.<\/span><\/p><p><span style=\"font-weight: 400;\">For this, the most effective method is undoubtedly the Gaussian process. It allows identifying the most probable value (called <\/span><b>mean \u00b5<\/b><span style=\"font-weight: 400;\">) and the likely dispersion of the value around the mean (called <\/span><b>standard deviation \u03c3<\/b><span style=\"font-weight: 400;\">). This standard deviation \u03c3 decreases as you approach an already observed point.<\/span><\/p><p><span style=\"font-weight: 400;\">Ideally, you would calculate these values and distances for each observation point. But in practice, this exhaustive representation is not possible due to time constraints. Therefore, it is necessary to select the points to evaluate.<\/span><\/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-d4b43d8 elementor-widget elementor-widget-heading\" data-id=\"d4b43d8\" 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\">Exploration and exploitation<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dd8712d elementor-widget elementor-widget-text-editor\" data-id=\"dd8712d\" 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><span style=\"font-weight: 400;\">To design an efficient predictive model, data scientists must define the most relevant points. This happens in two phases:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Exploration<\/b><span style=\"font-weight: 400;\">: this is interesting when the standard deviation is particularly large. In other words, the unknown variable in the search space is significant. This allows for testing multiple models and improving the understanding of the function to be optimized.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Exploitation<\/b><span style=\"font-weight: 400;\">: at this stage, it is about refining the models previously tested. The idea is to find the maximum or optimal point. To do this, data scientists exploit the mean \u00b5. If it is situated at the extremes, it is easier to identify the right model.<\/span><\/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-149b4bd elementor-widget elementor-widget-image\" data-id=\"149b4bd\" 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\" width=\"640\" height=\"424\" src=\"https:\/\/datascientest.com\/en\/files\/2025\/04\/pexels-lukas-577210.jpg\" class=\"attachment-full size-full wp-image-195176\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2025\/04\/pexels-lukas-577210.jpg 640w, https:\/\/datascientest.com\/en\/files\/2025\/04\/pexels-lukas-577210-300x199.jpg 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/>\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-c5aecdd elementor-widget elementor-widget-text-editor\" data-id=\"c5aecdd\" 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><span style=\"font-weight: 400;\">Be careful, it is important to find the right balance between exploration and exploitation. Indeed, if you favor exploration, you risk overlooking other potentially more efficient models. Conversely, if you favor exploitation, you might miss necessary improvements.<\/span><\/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-49d723b elementor-widget elementor-widget-heading\" data-id=\"49d723b\" 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\">The acquisition function<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3d0ffbc elementor-widget elementor-widget-text-editor\" data-id=\"3d0ffbc\" 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><span style=\"font-weight: 400;\">The acquisition function allows finding the right compromise between these two variables. Indeed, for each point in the search space, the function identifies a potential for optimization. Among all these points, the function identifies a maximum. This is the next point to test. You just need to repeat the calculation as many times as necessary until you achieve a convergence between the maximum and the minimum. This pair of parameters is the one that should allow reaching the best performance.<\/span><\/p><p><b><span style=\"text-decoration: underline;\">Good to know<\/span>:<\/b><span style=\"font-weight: 400;\"> Noise can alter the data and make learning more difficult. To avoid this situation, it is crucial to ensure that the environment is stable enough and the observations are reproducible before using Bayesian optimization.<\/span><\/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-37f5496 e-flex e-con-boxed e-con\" data-id=\"37f5496\" 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-000d9f5 elementor-widget elementor-widget-heading\" data-id=\"000d9f5\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-xl\">How to put Bayesian optimization into practice?<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8418178 elementor-widget elementor-widget-text-editor\" data-id=\"8418178\" 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><span style=\"font-weight: 400;\">To simplify Bayesian optimization calculations, it is easiest to <\/span><b>use good tools<\/b><span style=\"font-weight: 400;\">, such as the Python package scikit-optimize or bayesian-optimization. You just need to define a search space, and the tool will then find the high-potential points, notably thanks to the Gaussian process. Again, you will need to relaunch <\/span><a href=\"https:\/\/datascientest.com\/en\/python-the-most-popular-programming-language\"><span style=\"font-weight: 400;\">Python<\/span><\/a><span style=\"font-weight: 400;\"> until a satisfactory result is obtained.<\/span><\/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-e652a60 elementor-align-center button-principal elementor-widget elementor-widget-button\" data-id=\"e652a60\" 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\" 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 how to master Bayesian optimisation<\/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-6dbeda3 e-flex e-con-boxed e-con\" data-id=\"6dbeda3\" 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-8793cea elementor-widget elementor-widget-html\" data-id=\"8793cea\" 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\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"FAQPage\",\r\n  \"mainEntity\": [{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"What is the Bayesian approach?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"In practice, 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 performance, managing parameters to optimize supervised learning, etc. In all these scenarios, data scientists only have a limited number of observations to achieve an optimal result (due to time, financial, or material constraints).\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"How does Bayesian optimization work?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The idea behind Bayesian optimization is to use known observations to deduce the probabilities of events that have not yet been observed. To reach this conclusion, it is necessary to determine the probability distribution for each value X. The most effective method for this is undoubtedly the Gaussian process. It allows for identifying 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 as you approach an already observed point.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"How to implement Bayesian optimization?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"To simplify Bayesian optimization calculations, the best approach is to use good tools, such as the Python package scikit-optimize or bayesian-optimization. You just need to define a search space, and the tool will then find the high-potential points, notably using the Gaussian process. Again, you will need to run Python until you obtain a satisfactory result.\"\r\n    }\r\n  }]\r\n}\r\n<\/script>\r\n\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 rely on multiple observations. However, while studying these observations leads to an optimal outcome, data experts often have limited time to analyze all the hypotheses. So how do you find the right model in the least amount of time? This is where Bayesian optimization comes in. What is [&hellip;]<\/p>\n","protected":false},"author":45,"featured_media":195167,"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=\"To find the right predictive model in minimal time, Data Scientists use Bayesian optimization. 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