{"id":1196,"date":"2023-07-27T08:09:52","date_gmt":"2023-07-27T08:09:52","guid":{"rendered":"https:\/\/statorials.org\/tr\/kement-regresyonu\/"},"modified":"2023-07-27T08:09:52","modified_gmt":"2023-07-27T08:09:52","slug":"kement-regresyonu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/kement-regresyonu\/","title":{"rendered":"Kement regresyonuna giri\u015f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">S\u0131radan <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00e7oklu do\u011frusal regresyonda<\/a> , formun bir modeline uyacak \u015fekilde bir dizi <em>p<\/em> tahmin de\u011fi\u015fkeni ve bir <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">yan\u0131t de\u011fi\u015fkeni<\/a> kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> X <sub>1<\/sub> <sub>+<\/sub> \u03b2 <sub>2<\/sub> X <sub>2<\/sub> + \u2026 + \u03b2 <sub>p<\/sub><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Y<\/strong> : Yan\u0131t de\u011fi\u015fkeni<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>j<\/sub><\/strong> : <sup>j&#8217;inci<\/sup> tahmin de\u011fi\u015fkeni<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>\u03b2j<\/sub><\/strong> : Di\u011fer t\u00fcm belirleyicileri sabit tutarak, <sub>Xj&#8217;deki<\/sub> bir birimlik art\u0131\u015f\u0131n Y \u00fczerindeki ortalama etkisi<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03b5<\/strong> : Hata terimi<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u03b2 <sub>0<\/sub> , \u03b2 <sub>1<\/sub> , B <sub>2<\/sub> , \u2026, \u03b2 <sub>p<\/sub> de\u011ferleri, art\u0131klar\u0131n karelerinin toplam\u0131n\u0131 (RSS) en aza indiren <strong>en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi<\/strong> kullan\u0131larak se\u00e7ilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS = \u03a3(y <sub>ben<\/sub> \u2013 \u0177 <sub>ben<\/sub> ) <sup>2<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : <em>Toplam<\/em> anlam\u0131na gelen bir Yunan sembol\u00fc<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y <sub>i<\/sub><\/strong> : <sup>i&#8217;inci<\/sup> g\u00f6zlem i\u00e7in ger\u00e7ek yan\u0131t de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0177 <sub>i<\/sub><\/strong> : \u00c7oklu do\u011frusal regresyon modeline dayal\u0131 olarak tahmin edilen yan\u0131t de\u011feri<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ancak yorday\u0131c\u0131 de\u011fi\u015fkenler y\u00fcksek d\u00fczeyde korelasyona sahip oldu\u011funda <a href=\"https:\/\/statorials.org\/tr\/coklu-baglanti-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00e7oklu do\u011frusall\u0131k<\/a> bir sorun haline gelebilir. Bu, model katsay\u0131 tahminlerini g\u00fcvenilmez hale getirebilir ve y\u00fcksek varyans sergileyebilir. Yani model daha \u00f6nce hi\u00e7 g\u00f6rmedi\u011fi yeni bir veri setine uyguland\u0131\u011f\u0131nda muhtemelen d\u00fc\u015f\u00fck performans g\u00f6sterecektir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu sorunu a\u015fman\u0131n bir yolu, <strong>kement regresyonu<\/strong> olarak bilinen ve bunun yerine a\u015fa\u011f\u0131dakileri en aza indirmeyi ama\u00e7layan bir y\u00f6ntem kullanmakt\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS + \u03bb\u03a3|\u03b2 <sub>j<\/sub> |<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">burada <em>j<\/em> 1&#8217;den <em>p&#8217;ye<\/em> gider ve \u03bb \u2265 0&#8217;d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Denklemdeki bu ikinci terim <em>\u00e7ekilme cezas\u0131<\/em> olarak bilinir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bb = 0 oldu\u011funda, bu ceza teriminin hi\u00e7bir etkisi yoktur ve kement regresyonu, en k\u00fc\u00e7\u00fck kareler ile ayn\u0131 katsay\u0131 tahminlerini \u00fcretir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak \u03bb sonsuza yakla\u015ft\u0131k\u00e7a \u00e7\u0131karma cezas\u0131 daha etkili hale gelir ve modele aktar\u0131lamayan tahmin de\u011fi\u015fkenleri s\u0131f\u0131ra indirilir ve hatta baz\u0131lar\u0131 modelden \u00e7\u0131kar\u0131l\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Neden Lasso regresyonunu kullanmal\u0131y\u0131m?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Kement regresyonunun en k\u00fc\u00e7\u00fck kareler regresyonuna g\u00f6re avantaj\u0131 <a href=\"https:\/\/statorials.org\/tr\/onyargi-varyansi-uzlasmasi\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00f6nyarg\u0131 varyans\u0131 de\u011fi\u015f toku\u015fudur<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ortalama Karesel Hatan\u0131n (MSE) belirli bir modelin do\u011frulu\u011funu \u00f6l\u00e7mek i\u00e7in kullanabilece\u011fimiz bir \u00f6l\u00e7\u00fcm oldu\u011funu ve \u015fu \u015fekilde hesapland\u0131\u011f\u0131n\u0131 hat\u0131rlay\u0131n:<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE = Var( <em class=\"ph i\">f\u0302(<\/em> x <sub>0<\/sub> )) + [\u00d6nyarg\u0131( <em class=\"ph i\">f\u0302(<\/em> x <sub>0<\/sub> ))] <sup>2<\/sup> + Var(\u03b5)<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE = Varyans + \u00d6nyarg\u0131 <sup>2<\/sup> + \u0130ndirgenemez hata<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kement regresyonunun temel fikri, varyans\u0131n \u00f6nemli \u00f6l\u00e7\u00fcde azalt\u0131labilmesi i\u00e7in k\u00fc\u00e7\u00fck bir \u00f6nyarg\u0131 eklemek ve b\u00f6ylece daha d\u00fc\u015f\u00fck bir genel MSE&#8217;ye yol a\u00e7makt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu a\u00e7\u0131klamak i\u00e7in a\u015fa\u011f\u0131daki grafi\u011fi inceleyin:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11851 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/crete1.png\" alt=\"Ridge Regresyon \u00d6nyarg\u0131-Varyans Dengesi\" width=\"468\" height=\"341\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u03bb artt\u0131k\u00e7a sapmadaki \u00e7ok k\u00fc\u00e7\u00fck bir art\u0131\u015fla varyans\u0131n \u00f6nemli \u00f6l\u00e7\u00fcde azald\u0131\u011f\u0131n\u0131 unutmay\u0131n. Ancak belirli bir noktadan sonra varyans daha yava\u015f azal\u0131r ve katsay\u0131lardaki azalma onlar\u0131n \u00f6nemli \u00f6l\u00e7\u00fcde eksik tahmin edilmesine yol a\u00e7ar, bu da yanl\u0131l\u0131\u011f\u0131n keskin bir \u015fekilde artmas\u0131na neden olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Grafikten, \u03bb i\u00e7in \u00f6nyarg\u0131 ve varyans aras\u0131nda optimal bir denge sa\u011flayan bir de\u011fer se\u00e7ti\u011fimizde testin MSE&#8217;sinin en d\u00fc\u015f\u00fck oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bb = 0 oldu\u011funda, kement regresyonundaki ceza teriminin hi\u00e7bir etkisi yoktur ve bu nedenle en k\u00fc\u00e7\u00fck kareler ile ayn\u0131 katsay\u0131 tahminlerini \u00fcretir. Ancak \u03bb&#8217;y\u0131 belirli bir noktaya art\u0131rarak testin genel MSE&#8217;sini azaltabiliriz.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11874 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/lasso1.png\" alt=\"Kement Regresyon \u00d6nyarg\u0131-Varyans Dengesi\" width=\"490\" height=\"357\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu, kement regresyonuyla model uydurman\u0131n, en k\u00fc\u00e7\u00fck kareler regresyonuyla model uydurmaya g\u00f6re daha k\u00fc\u00e7\u00fck test hatalar\u0131 \u00fcretece\u011fi anlam\u0131na gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Kement regresyonu ve Ridge regresyonu<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Kement regresyonu ve <a href=\"https:\/\/statorials.org\/tr\/sirtin-gerilemesi\/\" target=\"_blank\" rel=\"noopener noreferrer\">Ridge regresyonu<\/a> <em>d\u00fczenlile\u015ftirme y\u00f6ntemleri<\/em> olarak bilinir \u00e7\u00fcnk\u00fc her ikisi de art\u0131k kareler toplam\u0131n\u0131 (RSS) ve belirli bir ceza s\u00fcresini en aza indirmeye \u00e7al\u0131\u015f\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ba\u015fka bir deyi\u015fle, model katsay\u0131lar\u0131n\u0131n tahminlerini k\u0131s\u0131tlar veya <em>d\u00fczenlerler<\/em> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak kulland\u0131klar\u0131 ceza terimleri biraz farkl\u0131d\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Kement regresyonu <strong>RSS&#8217;yi en aza indirmeye \u00e7al\u0131\u015f\u0131r + \u03bb\u03a3|\u03b2 <sub>j<\/sub> |<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Ridge regresyonu <strong>RSS + \u03bb\u03a3\u03b2 <sub>j<\/sub> <sup>2&#8217;yi<\/sup><\/strong> en aza indirmeye \u00e7al\u0131\u015f\u0131r<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ridge regresyonunu kulland\u0131\u011f\u0131m\u0131zda her bir yorday\u0131c\u0131n\u0131n katsay\u0131lar\u0131 s\u0131f\u0131ra indirgenir ancak hi\u00e7biri <em>tamamen s\u0131f\u0131ra<\/em> inemez.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tersine, kement regresyonunu kulland\u0131\u011f\u0131m\u0131zda, \u03bb yeterince b\u00fcy\u00fck oldu\u011funda baz\u0131 katsay\u0131lar\u0131n <em>tamamen s\u0131f\u0131r<\/em> olmas\u0131 m\u00fcmk\u00fcnd\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Teknik a\u00e7\u0131dan, kement regresyonu &#8220;seyrek&#8221; modeller, yani yaln\u0131zca tahmin edici de\u011fi\u015fkenlerin bir alt k\u00fcmesini i\u00e7eren modeller \u00fcretme kapasitesine sahiptir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u015fu soruyu akla getiriyor: <strong>S\u0131rt regresyonu mu yoksa kement regresyonu mu daha iyi?<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Cevap: duruma g\u00f6re de\u011fi\u015fir!<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yaln\u0131zca az say\u0131da \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenin anlaml\u0131 oldu\u011fu durumlarda, kement regresyonu daha iyi \u00e7al\u0131\u015fma e\u011filimindedir \u00e7\u00fcnk\u00fc \u00f6nemsiz de\u011fi\u015fkenleri tamamen s\u0131f\u0131ra indirebilir ve bunlar\u0131 modelden \u00e7\u0131karabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bununla birlikte, bir\u00e7ok yorday\u0131c\u0131 de\u011fi\u015fken modelde anlaml\u0131 oldu\u011funda ve katsay\u0131lar\u0131 yakla\u015f\u0131k olarak e\u015fit oldu\u011funda, ridge regresyonu daha iyi \u00e7al\u0131\u015fma e\u011filimindedir \u00e7\u00fcnk\u00fc t\u00fcm yorday\u0131c\u0131lar\u0131 modelde tutar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Hangi modelin tahmin yapmada en etkili oldu\u011funu belirlemek i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/k-kat-capraz-dogrulama\/\" target=\"_blank\" rel=\"noopener noreferrer\">k-katl\u0131 \u00e7apraz do\u011frulama<\/a> yap\u0131yoruz. Hangi model en d\u00fc\u015f\u00fck ortalama kare hatas\u0131n\u0131 (MSE) \u00fcretirse kullan\u0131lacak en iyi modeldir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Uygulamada kement regresyonu ger\u00e7ekle\u015ftirme ad\u0131mlar\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Kement regresyonu ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar kullan\u0131labilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: Yorday\u0131c\u0131 de\u011fi\u015fkenler i\u00e7in korelasyon matrisini ve VIF de\u011ferlerini hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6ncelikle bir <a href=\"https:\/\/statorials.org\/tr\/korelasyon-matrisi-nasil-okunur\/\" target=\"_blank\" rel=\"noopener noreferrer\">korelasyon matrisi<\/a> \u00fcretip her bir yorday\u0131c\u0131 de\u011fi\u015fken i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/coklu-baglanti-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">VIF (varyans enflasyon fakt\u00f6r\u00fc) de\u011ferlerini<\/a> hesaplamam\u0131z gerekiyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tahmin edici de\u011fi\u015fkenler ile y\u00fcksek VIF de\u011ferleri aras\u0131nda g\u00fc\u00e7l\u00fc bir korelasyon tespit edersek (baz\u0131 metinler &#8220;y\u00fcksek&#8221; VIF de\u011ferini 5 olarak tan\u0131mlarken di\u011ferleri 10 kullan\u0131r), o zaman kement regresyonu muhtemelen uygundur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak verilerde \u00e7oklu ba\u011flant\u0131 yoksa ilk etapta kement regresyonu yap\u0131lmas\u0131na gerek kalmayabilir. Bunun yerine s\u0131radan en k\u00fc\u00e7\u00fck kareler regresyonunu ger\u00e7ekle\u015ftirebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Kement regresyon modelini yerle\u015ftirin ve \u03bb i\u00e7in bir de\u011fer se\u00e7in.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Kement regresyonunun uygun oldu\u011funu belirledikten sonra, \u03bb i\u00e7in en uygun de\u011feri kullanarak modeli (R veya Python gibi pop\u00fcler programlama dillerini kullanarak) s\u0131\u011fd\u0131rabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bb i\u00e7in en uygun de\u011feri belirlemek amac\u0131yla \u03bb i\u00e7in farkl\u0131 de\u011ferler kullanan birden fazla model yerle\u015ftirebilir ve \u03bb&#8217;y\u0131 en d\u00fc\u015f\u00fck MSE testini \u00fcreten de\u011fer olarak se\u00e7ebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: Kement regresyonunu s\u0131rt regresyonu ve s\u0131radan en k\u00fc\u00e7\u00fck kareler regresyonuyla kar\u015f\u0131la\u015ft\u0131r\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak, k-katl\u0131 \u00e7apraz do\u011frulamay\u0131 kullanarak hangi modelin en d\u00fc\u015f\u00fck MSE testini \u00fcretti\u011fini belirlemek i\u00e7in kement regresyon modelimizi bir ridge regresyon modeli ve en k\u00fc\u00e7\u00fck kareler regresyon modeliyle kar\u015f\u0131la\u015ft\u0131rabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yorday\u0131c\u0131 de\u011fi\u015fkenler ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiye ba\u011fl\u0131 olarak, bu \u00fc\u00e7 modelden birinin farkl\u0131 senaryolarda di\u011ferlerinden daha iyi performans g\u00f6stermesi tamamen m\u00fcmk\u00fcnd\u00fcr.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>R ve Python&#8217;da Kement Regresyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde R ve Python&#8217;da kement regresyonunun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/rde-kement-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">R&#8217;de Kement Regresyon (ad\u0131m ad\u0131m)<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/pythonda-kement-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">Python&#8217;da Kement Regresyon (Ad\u0131m Ad\u0131m)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>S\u0131radan \u00e7oklu do\u011frusal regresyonda , formun bir modeline uyacak \u015fekilde bir dizi p tahmin de\u011fi\u015fkeni ve bir yan\u0131t de\u011fi\u015fkeni kullan\u0131r\u0131z: Y = \u03b2 0 + \u03b2 1 X 1 + \u03b2 2 X 2 + \u2026 + \u03b2 p Alt\u0131n: Y : Yan\u0131t de\u011fi\u015fkeni X j : j&#8217;inci tahmin de\u011fi\u015fkeni \u03b2j : Di\u011fer t\u00fcm belirleyicileri [&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-1196","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - 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