{"id":2497,"date":"2023-07-22T00:42:48","date_gmt":"2023-07-22T00:42:48","guid":{"rendered":"https:\/\/statorials.org\/tr\/kl-diverjans-pitonu\/"},"modified":"2023-07-22T00:42:48","modified_gmt":"2023-07-22T00:42:48","slug":"kl-diverjans-pitonu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/kl-diverjans-pitonu\/","title":{"rendered":"Python&#39;da kl diverjans\u0131 nas\u0131l hesaplan\u0131r (\u00f6rnekle)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistikte <strong>Kullback-Leibler (KL) farkl\u0131l\u0131\u011f\u0131,<\/strong> iki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 aras\u0131ndaki fark\u0131 \u00f6l\u00e7en bir mesafe \u00f6l\u00e7\u00fcs\u00fcd\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">P ve Q olmak \u00fczere iki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131m\u0131z varsa, genellikle KL \u0131raksamas\u0131n\u0131 &#8220;P&#8217;nin Q&#8217;dan \u0131raksamas\u0131&#8221; anlam\u0131na gelen KL(P || Q) g\u00f6sterimini kullanarak yazar\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak hesapl\u0131yoruz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">KL(P || Q) = \u03a3P(x) <em>ln<\/em> (P(x) \/ Q(x))<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki da\u011f\u0131l\u0131m aras\u0131ndaki KL fark\u0131n\u0131n s\u0131f\u0131r olmas\u0131, da\u011f\u0131l\u0131mlar\u0131n ayn\u0131 oldu\u011funu g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Python&#8217;da iki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 aras\u0131ndaki KL farkl\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in <a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.special.rel_entr.html\" target=\"_blank\" rel=\"noopener\">scipy.special.rel_entr()<\/a> fonksiyonunu kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekte bu fonksiyonun pratikte nas\u0131l kullan\u0131laca\u011f\u0131 g\u00f6sterilmektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Python&#8217;da KL farkl\u0131l\u0131\u011f\u0131n\u0131n hesaplanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Python&#8217;da a\u015fa\u011f\u0131daki iki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131na sahip oldu\u011fumuzu varsayal\u0131m:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not<\/strong> : Her da\u011f\u0131l\u0131m\u0131n olas\u0131l\u0131k toplam\u0131n\u0131n bir olmas\u0131 \u00f6nemlidir.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define two probability distributions\n<span style=\"color: #000000;\">P = [.05, .1, .2, .05, .15, .25, .08, .12]\nQ = [.3, .1, .2, .1, .1, .02, .08, .1]\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0130ki da\u011f\u0131l\u0131m aras\u0131ndaki KL fark\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">special<\/span> <span style=\"color: #008000;\">import<\/span> rel_entr\n\n<span style=\"color: #008080;\">#calculate (P || Q)\n<\/span>sum(rel_entr(P, Q))\n\n0.589885181619163<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">P da\u011f\u0131l\u0131m\u0131n\u0131n Q da\u011f\u0131l\u0131m\u0131ndan KL sapmas\u0131 yakla\u015f\u0131k <strong>0,589&#8217;dur<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu hesaplamada kullan\u0131lan birimlerin, <em>do\u011fal bilgi biriminin<\/em> k\u0131saltmas\u0131 olan <a href=\"https:\/\/en.wikipedia.org\/wiki\/Nat_(unit)\" target=\"_blank\" rel=\"noopener\">nats<\/a> olarak bilindi\u011fini unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani KL diverjans\u0131n\u0131n <strong>0,589 nat<\/strong> oldu\u011funu s\u00f6yleyebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ayr\u0131ca KL \u0131raksamas\u0131n\u0131n simetrik bir metrik olmad\u0131\u011f\u0131n\u0131 unutmay\u0131n. Bu, Q da\u011f\u0131l\u0131m\u0131n\u0131n P da\u011f\u0131l\u0131m\u0131ndan KL sapmas\u0131n\u0131 hesaplarsak muhtemelen farkl\u0131 bir de\u011fer elde edece\u011fimiz anlam\u0131na gelir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">special<\/span> <span style=\"color: #008000;\">import<\/span> rel_entr\n\n<span style=\"color: #008080;\">#calculate (Q || P)\n<\/span>sum(rel_entr(Q, P))\n\n0.497549319448034<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Q da\u011f\u0131l\u0131m\u0131n\u0131n P da\u011f\u0131l\u0131m\u0131ndan KL sapmas\u0131 yakla\u015f\u0131k <strong>0,497 nat&#8217;t\u0131r<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not<\/strong> : Baz\u0131 form\u00fcller KL sapmas\u0131n\u0131 hesaplamak i\u00e7in log taban\u0131-2&#8217;yi kullan\u0131r. Bu durumda nat&#8217;lardan ziyade <a href=\"https:\/\/en.wikipedia.org\/wiki\/Bit\" target=\"_blank\" rel=\"noopener\">bitler<\/a> cinsinden farkl\u0131l\u0131ktan bahsediyoruz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde Python&#8217;da di\u011fer yayg\u0131n i\u015flemlerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/piton-korelasyon-matrisi\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da Korelasyon Matrisi Nas\u0131l Olu\u015fturulur<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/piton-kovaryans-matrisi\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da Kovaryans Matrisi Nas\u0131l Olu\u015fturulur<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistikte Kullback-Leibler (KL) farkl\u0131l\u0131\u011f\u0131, iki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 aras\u0131ndaki fark\u0131 \u00f6l\u00e7en bir mesafe \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. P ve Q olmak \u00fczere iki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131m\u0131z varsa, genellikle KL \u0131raksamas\u0131n\u0131 &#8220;P&#8217;nin Q&#8217;dan \u0131raksamas\u0131&#8221; anlam\u0131na gelen KL(P || Q) g\u00f6sterimini kullanarak yazar\u0131z. A\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak hesapl\u0131yoruz: KL(P || Q) = \u03a3P(x) ln (P(x) \/ Q(x)) \u0130ki da\u011f\u0131l\u0131m aras\u0131ndaki KL fark\u0131n\u0131n s\u0131f\u0131r [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-2497","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python&#039;da KL Diverjans\u0131 Nas\u0131l Hesaplan\u0131r (\u00d6rnekle) - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde Python&#039;da iki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 aras\u0131ndaki KL farkl\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131 bir \u00f6rnekle a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/kl-diverjans-pitonu\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python&#039;da KL Diverjans\u0131 Nas\u0131l Hesaplan\u0131r (\u00d6rnekle) - 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