{"id":1193,"date":"2023-07-27T08:26:08","date_gmt":"2023-07-27T08:26:08","guid":{"rendered":"https:\/\/statorials.org\/tr\/sirtin-gerilemesi\/"},"modified":"2023-07-27T08:26:08","modified_gmt":"2023-07-27T08:26:08","slug":"sirtin-gerilemesi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/sirtin-gerilemesi\/","title":{"rendered":"Ridge 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.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Belirli \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenleri modelden tamamen \u00e7\u0131karmadan bu sorunu \u00e7\u00f6zmenin bir yolu, <strong>ridge 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> <sup>2<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">burada <em>j<\/em> 1&#8217;den <em>p&#8217;ye<\/em> gider ve<\/span> <span style=\"color: #000000;\">\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 s\u0131rt regresyonu, en k\u00fc\u00e7\u00fck kareler ile ayn\u0131 katsay\u0131 tahminlerini \u00fcretir. Ancak \u03bb sonsuza yakla\u015ft\u0131k\u00e7a b\u00fcz\u00fclme cezas\u0131 daha etkili hale gelir ve tepe regresyon katsay\u0131s\u0131 tahminleri s\u0131f\u0131ra yakla\u015f\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Genel olarak, modeldeki en az etkili yorday\u0131c\u0131 de\u011fi\u015fkenler en h\u0131zl\u0131 \u015fekilde s\u0131f\u0131ra do\u011fru azalacakt\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Neden Ridge Regresyonunu kullanmal\u0131s\u0131n\u0131z?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ridge 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 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;\">Ridge regresyonunun temel fikri, varyans\u0131n \u00f6nemli \u00f6l\u00e7\u00fcde azalt\u0131labilmesi ve b\u00f6ylece daha d\u00fc\u015f\u00fck bir genel MSE&#8217;ye yol a\u00e7abilmesi i\u00e7in k\u00fc\u00e7\u00fck bir \u00f6nyarg\u0131 eklemektir.<\/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, s\u0131rt 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-11852 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/crete2.png\" alt=\"Ridge Regresyon Testi MSE Azaltma\" width=\"529\" height=\"378\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu, s\u0131rt 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>Uygulamada Ridge Regresyonunu Ger\u00e7ekle\u015ftirme Ad\u0131mlar\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">S\u0131rt regresyonunu 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&#8217;u kullan\u0131r), o zaman ridge regresyonu muhtemelen uygundur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak verilerde \u00e7oklu ba\u011flant\u0131 yoksa ilk etapta ridge regresyonu yap\u0131lmas\u0131 gerekmeyebilir. 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: Her yorday\u0131c\u0131 de\u011fi\u015fkeni standartla\u015ft\u0131r\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ridge regresyonunu ger\u00e7ekle\u015ftirmeden \u00f6nce verileri, her \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenin ortalamas\u0131 0 ve standart sapmas\u0131 1 olacak \u015fekilde \u00f6l\u00e7eklendirmemiz gerekir. Bu, bir ridge regresyonu \u00e7al\u0131\u015ft\u0131r\u0131rken hi\u00e7bir tek yorday\u0131c\u0131 de\u011fi\u015fkenin a\u015f\u0131r\u0131 bir etkiye sahip olmamas\u0131n\u0131 sa\u011flar.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: S\u0131rt regresyon modelini yerle\u015ftirin ve \u03bb i\u00e7in bir de\u011fer se\u00e7in.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bb i\u00e7in hangi de\u011ferin kullan\u0131laca\u011f\u0131n\u0131 belirlemek i\u00e7in kullanabilece\u011fimiz kesin bir form\u00fcl yoktur. Pratikte \u03bb&#8217;y\u0131 se\u00e7menin iki yayg\u0131n yolu vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>(1) Bir Ridge izleme grafi\u011fi olu\u015fturun.<\/strong> Bu, \u03bb sonsuza do\u011fru artt\u0131k\u00e7a katsay\u0131 tahminlerinin de\u011ferlerini g\u00f6rselle\u015ftiren bir grafiktir. Tipik olarak \u00e7o\u011fu katsay\u0131 tahmininin istikrar kazanmaya ba\u015flad\u0131\u011f\u0131 de\u011fer olarak \u03bb&#8217;y\u0131 se\u00e7eriz.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11853 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/crete3.png\" alt=\"S\u0131rt izi\" width=\"539\" height=\"389\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>(2) Her \u03bb de\u011feri i\u00e7in MSE testini hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bb&#8217;y\u0131 se\u00e7menin ba\u015fka bir yolu, her modelin test MSE&#8217;sini farkl\u0131 \u03bb de\u011ferleri ile hesaplamak ve \u03bb&#8217;y\u0131 en d\u00fc\u015f\u00fck test MSE&#8217;sini \u00fcreten de\u011fer olarak se\u00e7mektir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ridge Regresyonunun Avantajlar\u0131 ve Dezavantajlar\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ridge regresyonunun en b\u00fcy\u00fck <strong>avantaj\u0131<\/strong> , \u00e7oklu ba\u011flant\u0131 mevcut oldu\u011funda en k\u00fc\u00e7\u00fck karelerden daha d\u00fc\u015f\u00fck bir test ortalama kare hatas\u0131 (MSE) \u00fcretme yetene\u011fidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak Ridge regresyonunun en b\u00fcy\u00fck <strong>dezavantaj\u0131<\/strong> , t\u00fcm yorday\u0131c\u0131 de\u011fi\u015fkenleri nihai modele dahil etmesi nedeniyle de\u011fi\u015fken se\u00e7imi yapamamas\u0131d\u0131r. Baz\u0131 tahmin ediciler s\u0131f\u0131ra \u00e7ok yak\u0131n bir de\u011fere indirilece\u011fi i\u00e7in bu durum model sonu\u00e7lar\u0131n\u0131n yorumlanmas\u0131n\u0131 zorla\u015ft\u0131rabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Uygulamada Ridge regresyonu, en k\u00fc\u00e7\u00fck kareler modeline k\u0131yasla daha iyi tahminler yapabilen bir model \u00fcretme potansiyeline sahiptir, ancak modelin sonu\u00e7lar\u0131n\u0131 yorumlamak genellikle daha zordur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Model yorumlaman\u0131n m\u0131 yoksa tahmin do\u011frulu\u011funun mu sizin i\u00e7in daha \u00f6nemli oldu\u011funa ba\u011fl\u0131 olarak, farkl\u0131 senaryolarda s\u0131radan en k\u00fc\u00e7\u00fck kareler veya s\u0131rt regresyonunu kullanmay\u0131 se\u00e7ebilirsiniz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ar-Ge ve Python&#8217;da Ridge Regresyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler, ridge regresyon modellerini uydurmak i\u00e7in en yayg\u0131n kullan\u0131lan iki dil olan R ve Python&#8217;da ridge regresyonunun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini a\u00e7\u0131klamaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/rde-tepe-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">R&#8217;de Ridge Regresyon (ad\u0131m ad\u0131m)<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/pythonda-kret-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">Python&#8217;da Ridge 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-1193","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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