{"id":172317,"date":"2023-10-29T11:00:15","date_gmt":"2023-10-29T10:00:15","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=172317"},"modified":"2023-10-29T11:04:02","modified_gmt":"2023-10-29T10:04:02","slug":"markov-models-get-ready","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/markov-models-get-ready","title":{"rendered":"Markov models: Get ready"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"172317\" class=\"elementor elementor-172317\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7bcaed1a e-flex e-con-boxed e-con\" data-id=\"7bcaed1a\" 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-49b81f55 elementor-widget elementor-widget-heading\" data-id=\"49b81f55\" 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-default\"><p>A model is said to possess the Markov property if its state at an instant T depends uniquely on its state at instant T-1.<\/p>\n<p>If we can observe the states the model is in at each instant, we speak of an observable Markov model. Otherwise, we speak of a hidden Markov model.<\/p>\n<p>In this article, we'll illustrate these models to understand how they work and how useful they are.<\/p><\/h2>\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-3ab98e0b e-flex e-con-boxed e-con\" data-id=\"3ab98e0b\" 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-1c4c8a1c elementor-widget elementor-widget-heading\" data-id=\"1c4c8a1c\" 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\">Observable Markov model<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1e0ec4ec elementor-widget elementor-widget-text-editor\" data-id=\"1e0ec4ec\" 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>Consider the following situation:<br \/>You&#8217;re cooped up at home on a rainy day, and you&#8217;d like to determine the weather for the next five days.<\/p><ul><li>Since you&#8217;re not a meteorologist, you simplify the task by assuming that the weather follows a Markov model: the weather on day D depends solely on the weather on day D-1.<\/li><li>To make things even simpler, you assume that there are only three possible types of weather: sunny, cloudy or rainy.<\/li><li>Based on observations over the last few months, you draw up the following transition diagram:<\/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-6f1cc8d4 elementor-widget elementor-widget-image\" data-id=\"6f1cc8d4\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"512\" height=\"472\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image1_markdown.png\" class=\"attachment-full size-full wp-image-172321\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image1_markdown.png 512w, https:\/\/datascientest.com\/en\/files\/2023\/10\/image1_markdown-300x277.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/>\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-2e670b4d elementor-widget elementor-widget-text-editor\" data-id=\"2e670b4d\" 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 associated transition matrix is<\/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-34c9d59b elementor-widget elementor-widget-image\" data-id=\"34c9d59b\" 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=\"512\" height=\"225\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image2_markdown.png\" class=\"attachment-full size-full wp-image-172322\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image2_markdown.png 512w, https:\/\/datascientest.com\/en\/files\/2023\/10\/image2_markdown-300x132.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/>\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-38fc05c elementor-widget elementor-widget-text-editor\" data-id=\"38fc05c\" 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>As a reminder, this matrix reads as follows:<\/p><p>The probability that it will be sunny tomorrow knowing that it&#8217;s raining today is 35%.<br \/>The probability that there will be clouds tomorrow knowing that there are already clouds today is 25%.<\/p><p>Let&#8217;s calculate the probability that the weather over the next five days will be &#8220;sunny, sunny, rainy, cloudy, sunny&#8221;.<\/p><p>Since the weather on any given day depends solely on the weather on the previous day, all we have to do is multiply the probabilities (as a reminder, it&#8217;s raining today):<\/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-7659a637 elementor-widget elementor-widget-image\" data-id=\"7659a637\" 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=\"512\" height=\"60\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image3_markdown.png\" class=\"attachment-full size-full wp-image-172323\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image3_markdown.png 512w, https:\/\/datascientest.com\/en\/files\/2023\/10\/image3_markdown-300x35.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/>\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-1dec8287 elementor-widget elementor-widget-text-editor\" data-id=\"1dec8287\" 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>We can calculate this probability for all possible combinations, and select the combination with the highest probability to answer the problem.<\/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-4d7b7602 elementor-widget elementor-widget-text-editor\" data-id=\"4d7b7602\" 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;\">In our case, here are the 5 most likely combinations:<\/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-7f411ba7 elementor-widget elementor-widget-image\" data-id=\"7f411ba7\" 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=\"439\" height=\"184\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image4_markdown.png\" class=\"attachment-full size-full wp-image-172324\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image4_markdown.png 439w, https:\/\/datascientest.com\/en\/files\/2023\/10\/image4_markdown-300x126.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/>\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-eb5d6d6 elementor-widget elementor-widget-shortcode\" data-id=\"eb5d6d6\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\"https:\/\/gist.github.com\/MaximeRighini\/6632773a82550e7d1f7428db4031ebca.js\"><\/script><\/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-433a035e e-flex e-con-boxed e-con\" data-id=\"433a035e\" 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-10b1dc1c elementor-widget elementor-widget-heading\" data-id=\"10b1dc1c\" 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\">Hidden Markov model<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-55ddaf3b elementor-widget elementor-widget-text-editor\" data-id=\"55ddaf3b\" 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 same assumptions apply as in the previous section.<\/p><p>Now let&#8217;s suppose that a weather psychopath has locked you in a windowless room with only a computer and a lamp. Every day, the lamp lights up in a certain color according to the weather. Your kidnapper provides you with the following observation matrix:<\/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-34c7e331 elementor-widget elementor-widget-image\" data-id=\"34c7e331\" 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=\"512\" height=\"252\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image5_markdown.png\" class=\"attachment-large size-large wp-image-172325\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image5_markdown.png 512w, https:\/\/datascientest.com\/en\/files\/2023\/10\/image5_markdown-300x148.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/>\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-f855755 elementor-widget elementor-widget-text-editor\" data-id=\"f855755\" 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>For example, if it&#8217;s raining, the lamp has a 70% chance of being green and a 30% chance of being blue.<\/p><p>You&#8217;ll be able to go home if you determine the weather for the next five days based solely on the color of the lamp. You then build a hidden Markov model.<\/p><p>You stay indoors for 5 days and find the following colors:<\/p><p>blue, blue, red, green, red.<\/p><p>You remember that it was raining the day before you were locked in.<\/p><p>You can then write a <a href=\"https:\/\/datascientest.com\/en\/mastering-nltk-your-ultimate-guide-to-pythons-nlp-toolkit\">python code<\/a> that returns the combination that has the highest probability of being realized:<\/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-f43f3ae elementor-widget elementor-widget-shortcode\" data-id=\"f43f3ae\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\"https:\/\/gist.github.com\/MaximeRighini\/04208ab8412a1dd41fd5eebfeee906d2.js\"><\/script><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1e7bd719 elementor-widget elementor-widget-image\" data-id=\"1e7bd719\" 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=\"422\" height=\"183\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image6_markdown.png\" class=\"attachment-full size-full wp-image-172326\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/image6_markdown.png 422w, https:\/\/datascientest.com\/en\/files\/2023\/10\/image6_markdown-300x130.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/>\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-4c47c727 elementor-widget elementor-widget-text-editor\" data-id=\"4c47c727\" 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><strong>NB:<\/strong> We could also have implemented the Viterbi algorithm, which would have returned the most likely combination, i.e. [&#8216;Clouds&#8217;, &#8216;Clouds&#8217;, &#8216;Sun&#8217;, &#8216;Rain&#8217;, &#8216;Sun&#8217;].<\/p><p>This <strong>approach to prediction<\/strong> is interesting, but very basic. If you&#8217;d like to learn how to make more impressive predictions, using machine learning algorithms for example, contact us directly online to find out more about our data science training courses or discover other articles about machine learning:<\/p><table dir=\"ltr\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\"><colgroup><col width=\"656\" \/><\/colgroup><tbody><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Image Processing&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/image-processing-fundamental-principles-and-practical-uses\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/image-processing-fundamental-principles-and-practical-uses\" target=\"_blank\" rel=\"noopener\">Image Processing<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Deep Learning - All you need to know&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/all-about-deep-learning\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/all-about-deep-learning\" target=\"_blank\" rel=\"noopener\">Deep Learning &#8211; All you need to know<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Mushroom Recognition&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/mushroom-recognition\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/mushroom-recognition\" target=\"_blank\" rel=\"noopener\">Mushroom Recognition<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Tensor Flow - Google's ML&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/tensor-flow-all-about-googles-machine-learning-framework\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/tensor-flow-all-about-googles-machine-learning-framework\" target=\"_blank\" rel=\"noopener\">Tensor Flow &#8211; Google&#8217;s ML<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Dive into ML&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/unlock-your-future-dive-into-machine-learning-engineer-training\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/unlock-your-future-dive-into-machine-learning-engineer-training\" target=\"_blank\" rel=\"noopener\">Dive into ML<\/a><\/td><\/tr><\/tbody><\/table>\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\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>A model is said to possess the Markov property if its state at an instant T depends uniquely on its state at instant T-1. If we can observe the states the model is in at each instant, we speak of an observable Markov model. Otherwise, we speak of a hidden Markov model. In this article, [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":172320,"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>Markov models: Get ready<\/title>\n<meta name=\"description\" content=\"&quot;Prepare to dive into the world of Markov models, a powerful tool for understanding and predicting sequential data. Explore the fundamentals, applications, and intricacies of Markov models in this informative and engaging journey\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/en\/markov-models-get-ready\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Markov models: Get ready\" \/>\n<meta property=\"og:description\" content=\"A model is said to possess the Markov property if its state at an instant T depends uniquely on its state at instant T-1. 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