{"id":1194,"date":"2023-07-27T08:19:55","date_gmt":"2023-07-27T08:19:55","guid":{"rendered":"https:\/\/statorials.org\/tr\/rde-tepe-regresyonu\/"},"modified":"2023-07-27T08:19:55","modified_gmt":"2023-07-27T08:19:55","slug":"rde-tepe-regresyonu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rde-tepe-regresyonu\/","title":{"rendered":"R&#39;de ridge regresyon (ad\u0131m ad\u0131m)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/sirtin-gerilemesi\/\" target=\"_blank\" rel=\"noopener noreferrer\">Ridge regresyonu,<\/a> verilerde <a href=\"https:\/\/statorials.org\/tr\/coklu-baglanti-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00e7oklu ba\u011flant\u0131<\/a> mevcut oldu\u011funda regresyon modeline uyum sa\u011flamak i\u00e7in kullanabilece\u011fimiz bir y\u00f6ntemdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6zetle, en k\u00fc\u00e7\u00fck kareler regresyonu, kalan kareler toplam\u0131n\u0131 (RSS) en aza indiren katsay\u0131 tahminlerini bulmaya \u00e7al\u0131\u015f\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS = \u03a3(y <sub>ben<\/sub> \u2013 \u0177 <sub>ben<\/sub> )2<\/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;\">Tersine, s\u0131rt regresyonu a\u015fa\u011f\u0131dakileri en aza indirmeyi ama\u00e7lar:<\/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<\/em> \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenlere 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. S\u0131rt regresyonunda, \u03bb i\u00e7in m\u00fcmk\u00fcn olan en d\u00fc\u015f\u00fck MSE testini (ortalama kare hatas\u0131) \u00fcreten bir de\u011fer se\u00e7eriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde R&#8217;de ridge regresyonunun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin ad\u0131m ad\u0131m bir \u00f6rnek sunulmaktad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>1. Ad\u0131m: Verileri y\u00fckleyin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnek i\u00e7in R&#8217;nin <strong>mtcars<\/strong> ad\u0131 verilen yerle\u015fik veri k\u00fcmesini kullanaca\u011f\u0131z. Yan\u0131t de\u011fi\u015fkeni olarak <strong>hp&#8217;yi<\/strong> ve yorday\u0131c\u0131lar olarak a\u015fa\u011f\u0131daki de\u011fi\u015fkenleri kullanaca\u011f\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">mpg<\/span><\/li>\n<li> <span style=\"color: #000000;\">a\u011f\u0131rl\u0131k<\/span><\/li>\n<li> <span style=\"color: #000000;\">bok<\/span><\/li>\n<li> <span style=\"color: #000000;\">qsec<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ridge regresyonunu ger\u00e7ekle\u015ftirmek i\u00e7in <strong>glmnet<\/strong> paketindeki fonksiyonlar\u0131 kullanaca\u011f\u0131z. Bu paket, <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">yan\u0131t de\u011fi\u015fkeninin<\/a> bir vekt\u00f6r olmas\u0131n\u0131 ve tahmin de\u011fi\u015fkenleri k\u00fcmesinin <strong>data.matrix<\/strong> s\u0131n\u0131f\u0131ndan olmas\u0131n\u0131 gerektirir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod verilerimizi nas\u0131l tan\u0131mlayaca\u011f\u0131m\u0131z\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define response variable<\/span>\ny &lt;- mtcars$hp\n\n<span style=\"color: #008080;\">#define matrix of predictor variables\n<\/span>x &lt;- data.matrix(mtcars[, c('mpg', 'wt', 'drat', 'qsec')])\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Ridge Regresyon Modelini Yerle\u015ftirin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha sonra, Ridge regresyon modeline uyum sa\u011flamak i\u00e7in <strong>glmnet()<\/strong> i\u015flevini kullanaca\u011f\u0131z ve <strong>alpha=0<\/strong> de\u011ferini belirleyece\u011fiz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alfay\u0131 1&#8217;e e\u015fitlemenin Kement regresyonunu kullanmaya e\u015fde\u011fer oldu\u011funu ve alfay\u0131 0 ile 1 aras\u0131nda bir de\u011fere ayarlaman\u0131n elastik a\u011f kullanmaya e\u015fde\u011fer oldu\u011funu unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ayr\u0131ca, ridge regresyonunun, her \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenin ortalamas\u0131 0 ve standart sapmas\u0131 1 olacak \u015fekilde verilerin standartla\u015ft\u0131r\u0131lmas\u0131n\u0131 gerektirdi\u011fini unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Neyse ki <strong>glmnet()<\/strong> bu standardizasyonu sizin i\u00e7in otomatik olarak yap\u0131yor. De\u011fi\u015fkenleri zaten standartla\u015ft\u0131rd\u0131ysan\u0131z <strong>standardize=False<\/strong> belirtebilirsiniz.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #993300;\">library<\/span> (glmnet)<\/span>\n\n#fit ridge regression model\n<\/span>model &lt;- glmnet(x, y, alpha = <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#view summary of model\n<\/span>summary(model)\n\n          Length Class Mode   \na0 100 -none- numeric\nbeta 400 dgCMatrix S4     \ndf 100 -none- numeric\ndim 2 -none- numeric\nlambda 100 -none- numeric\ndev.ratio 100 -none- numeric\nnulldev 1 -none- numeric\nnpasses 1 -none- numeric\njerr 1 -none- numeric\noffset 1 -none- logical\ncall 4 -none- call   \nnobs 1 -none- numeric\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>3. Ad\u0131m: Lambda i\u00e7in en uygun de\u011feri se\u00e7in<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha sonra, <a href=\"https:\/\/statorials.org\/tr\/k-kat-capraz-dogrulama\/\" target=\"_blank\" rel=\"noopener noreferrer\">k-katl\u0131 \u00e7apraz do\u011frulamay\u0131<\/a> kullanarak en d\u00fc\u015f\u00fck test ortalama kare hatas\u0131n\u0131 (MSE) \u00fcreten lambda de\u011ferini tan\u0131mlayaca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Neyse ki <strong>glmnet<\/strong> , k = 10 kez kullan\u0131larak otomatik olarak k-katl\u0131 \u00e7apraz do\u011frulama ger\u00e7ekle\u015ftiren <strong>cv.glmnet()<\/strong> i\u015flevine sahiptir.<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#perform k-fold cross-validation to find optimal lambda value\n<\/span>cv_model &lt;- cv. <span style=\"color: #3366ff;\">glmnet<\/span> (x, y, alpha = <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#find optimal lambda value that minimizes test MSE\n<\/span>best_lambda &lt;- cv_model$ <span style=\"color: #3366ff;\">lambda<\/span> . <span style=\"color: #3366ff;\">min<\/span>\nbest_lambda\n\n[1] 10.04567\n\n<span style=\"color: #008080;\">#produce plot of test MSE by lambda value<\/span>\nplot(cv_model) \n<\/strong><\/span><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11860 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/faiter1.png\" alt=\"R'de s\u0131rt regresyonu i\u00e7in \u00e7apraz do\u011frulama\" width=\"443\" height=\"426\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">MSE testini minimuma indiren lambda de\u011feri ise <strong>10,04567<\/strong> olarak \u00e7\u0131k\u0131yor.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>4. Ad\u0131m: Son modeli analiz edin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Son olarak optimal lambda de\u011ferinin \u00fcretti\u011fi son modeli analiz edebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu model i\u00e7in katsay\u0131 tahminlerini elde etmek i\u00e7in a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#find coefficients of best model\n<\/span>best_model &lt;- glmnet(x, y, alpha = <span style=\"color: #008000;\">0<\/span> , lambda = best_lambda)\ncoef(best_model)\n\n5 x 1 sparse Matrix of class \"dgCMatrix\"\n                    s0\n(Intercept) 475.242646\nmpg -3.299732\nwt 19.431238\ndrat -1.222429\nqsec -17.949721<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Ayr\u0131ca lambdadaki art\u0131\u015fa ba\u011fl\u0131 olarak katsay\u0131 tahminlerinin nas\u0131l de\u011fi\u015fti\u011fini g\u00f6rselle\u015ftirmek i\u00e7in bir \u0130zleme grafi\u011fi de \u00fcretebiliriz:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#produce Ridge trace plot<\/span>\nplot(model, xvar = \" <span style=\"color: #008000;\">lambda<\/span> \")<\/strong><\/span> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11861 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/creter2.png\" alt=\"R'de s\u0131rt izi\" width=\"419\" height=\"411\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Son olarak <a href=\"https:\/\/statorials.org\/tr\/iyi-r-kare-degeri\/\" target=\"_blank\" rel=\"noopener noreferrer\">modelin R-karesini<\/a> e\u011fitim verileri \u00fczerinden hesaplayabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#use fitted best model to make predictions\n<\/span>y_predicted &lt;- <span style=\"color: #3366ff;\">predict<\/span> (model, s = best_lambda, newx = x)\n\n<span style=\"color: #008080;\">#find OHS and SSE<\/span>\nsst &lt;- <span style=\"color: #3366ff;\">sum<\/span> ((y - <span style=\"color: #3366ff;\">mean<\/span> (y))^2)\nsse &lt;- <span style=\"color: #3366ff;\">sum<\/span> ((y_predicted - y)^2)\n\n<span style=\"color: #008080;\">#find R-Squared\n<\/span>rsq &lt;- 1 - sse\/sst\nrsq\n\n[1] 0.7999513\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">R kare <strong>0,7999513<\/strong> olarak \u00e7\u0131k\u0131yor. Yani en iyi model, e\u011fitim verilerinin yan\u0131t de\u011ferlerindeki varyasyonun <strong>%79,99&#8217;unu<\/strong> a\u00e7\u0131klayabilmi\u015ftir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte kullan\u0131lan R kodunun tamam\u0131n\u0131 <a href=\"https:\/\/github.com\/Statorials\/R-Guides\/blob\/main\/ridge_regression.R\" target=\"_blank\" rel=\"noopener noreferrer\">burada<\/a> bulabilirsiniz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ridge regresyonu, verilerde \u00e7oklu ba\u011flant\u0131 mevcut oldu\u011funda regresyon modeline uyum sa\u011flamak i\u00e7in kullanabilece\u011fimiz bir y\u00f6ntemdir. \u00d6zetle, en k\u00fc\u00e7\u00fck kareler regresyonu, kalan kareler toplam\u0131n\u0131 (RSS) en aza indiren katsay\u0131 tahminlerini bulmaya \u00e7al\u0131\u015f\u0131r: RSS = \u03a3(y ben \u2013 \u0177 ben )2 Alt\u0131n: \u03a3 : Toplam anlam\u0131na gelen bir Yunan sembol\u00fc y i : i&#8217;inci g\u00f6zlem i\u00e7in ger\u00e7ek [&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-1194","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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