{"id":1214,"date":"2023-07-27T06:38:25","date_gmt":"2023-07-27T06:38:25","guid":{"rendered":"https:\/\/statorials.org\/tr\/cok-degiskenli-uyarlanabilir-regresyon-egrileri\/"},"modified":"2023-07-27T06:38:25","modified_gmt":"2023-07-27T06:38:25","slug":"cok-degiskenli-uyarlanabilir-regresyon-egrileri","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/cok-degiskenli-uyarlanabilir-regresyon-egrileri\/","title":{"rendered":"\u00c7ok de\u011fi\u015fkenli uyarlanabilir regresyon e\u011frilerine giri\u015f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Bir dizi yorday\u0131c\u0131 de\u011fi\u015fken ile bir <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">yan\u0131t de\u011fi\u015fkeni<\/a> aras\u0131ndaki ili\u015fki do\u011frusal oldu\u011funda, genellikle belirli bir yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkinin \u015fu bi\u00e7imi ald\u0131\u011f\u0131n\u0131 varsayan <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener noreferrer\">do\u011frusal regresyonu<\/a> kullanabiliriz<\/span> <span style=\"color: #000000;\">:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> X + \u03b5<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak pratikte de\u011fi\u015fkenler aras\u0131ndaki ili\u015fki asl\u0131nda do\u011frusal olmayabilir ve do\u011frusal regresyon kullanmaya \u00e7al\u0131\u015fmak, modelin zay\u0131f bir \u015fekilde uyum sa\u011flamas\u0131yla sonu\u00e7lanabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tahminci ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki do\u011frusal olmayan ili\u015fkiyi a\u00e7\u0131klaman\u0131n bir yolu, a\u015fa\u011f\u0131daki formu alan<a href=\"https:\/\/statorials.org\/tr\/polinom-regresyonu-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">polinom regresyonunu<\/a> kullanmakt\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Y = \u03b2 <sub>0<\/sub> <sup>+<\/sup> \u03b2 <sub>1<\/sub> X + \u03b2 <sub>2<\/sub> X <sup>2<\/sup> + \u2026 + \u03b2 <sub>h<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu denklemde <em>h&#8217;ye<\/em> polinomun &#8220;derecesi&#8221; denir. <em>h<\/em> de\u011ferini artt\u0131rd\u0131k\u00e7a model daha esnek hale gelir ve do\u011frusal olmayan verilere uyum sa\u011flayabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Ancak polinom regresyonun baz\u0131 dezavantajlar\u0131 vard\u0131r:<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> E\u011fer <em>h<\/em> derecesi \u00e7ok b\u00fcy\u00fck se\u00e7ilirse, polinom regresyon bir veri setini kolayl\u0131kla <a href=\"https:\/\/statorials.org\/tr\/makine-ogrenimi-asiri-uyumu\/\" target=\"_blank\" rel=\"noopener noreferrer\">a\u015fabilir<\/a> . Uygulamada <em>h<\/em> nadiren 3 veya 4&#8217;ten b\u00fcy\u00fckt\u00fcr \u00e7\u00fcnk\u00fc bu noktan\u0131n \u00f6tesinde basit\u00e7e bir e\u011fitim setinin g\u00fcr\u00fclt\u00fcs\u00fcne kar\u015f\u0131l\u0131k gelir ve g\u00f6r\u00fcnmeyen verilere iyi bir \u015fekilde genelleme yapmaz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><b>2.<\/b> Polinom regresyon, t\u00fcm veri setine her zaman kesin olmayan global bir i\u015flev y\u00fckler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Polinom regresyonun bir alternatifi, <strong>\u00e7ok de\u011fi\u015fkenli uyarlanabilir regresyon e\u011frileridir<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Temel fikir<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00c7ok de\u011fi\u015fkenli uyarlanabilir regresyon e\u011frileri \u015fu \u015fekilde \u00e7al\u0131\u015f\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Bir veri k\u00fcmesini <em>k<\/em> par\u00e7aya b\u00f6l\u00fcn.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6ncelikle bir veri k\u00fcmesini <em>k<\/em> farkl\u0131 \u00f6\u011feye b\u00f6l\u00fcyoruz. Veri setini b\u00f6ld\u00fc\u011f\u00fcm\u00fcz noktalara <em>d\u00fc\u011f\u00fcm<\/em> ad\u0131 verilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her tahminci i\u00e7in her noktay\u0131 potansiyel bir d\u00fc\u011f\u00fcm olarak de\u011ferlendirip aday \u00f6zellikleri kullanarak do\u011frusal bir regresyon modeli olu\u015fturarak d\u00fc\u011f\u00fcmleri belirliyoruz. Modelde en fazla hatay\u0131 azaltabilecek nokta d\u00fc\u011f\u00fcmd\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130lk d\u00fc\u011f\u00fcm\u00fc belirledikten sonra di\u011fer d\u00fc\u011f\u00fcmleri bulmak i\u00e7in i\u015flemi tekrarl\u0131yoruz. Ba\u015flang\u0131\u00e7 i\u00e7in makul oldu\u011funu d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcn\u00fcz say\u0131da d\u00fc\u011f\u00fcm bulabilirsiniz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Bir mente\u015fe fonksiyonu olu\u015fturmak i\u00e7in her par\u00e7aya bir regresyon fonksiyonu yerle\u015ftirin.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">D\u00fc\u011f\u00fcmleri se\u00e7tikten ve veri k\u00fcmesindeki her \u00f6\u011feye bir regresyon modeli uydurduktan sonra, <em>h(xa)<\/em> ile g\u00f6sterilen <em>mente\u015fe i\u015flevi<\/em> ad\u0131 verilen bir i\u015flev elde ederiz; burada <em>a,<\/em> de\u011fer(ler)in e\u015fi\u011fidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, tek d\u00fc\u011f\u00fcml\u00fc bir model i\u00e7in mente\u015fe i\u015flevi \u015fu \u015fekilde olabilir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> (4,3 \u2013 x) e\u011fer x &lt; 4,3 ise<\/span><\/li>\n<li> <span style=\"color: #000000;\">y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> (x \u2013 4,3) e\u011fer x &gt; 4,3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu durumda e\u015fik de\u011feri olarak <strong>4.3<\/strong> se\u00e7ilmesinin olas\u0131 t\u00fcm e\u015fik de\u011ferleri aras\u0131nda maksimum hata azalt\u0131m\u0131na olanak sa\u011flad\u0131\u011f\u0131 belirlendi. Daha sonra 4,3&#8217;\u00fcn alt\u0131ndaki de\u011ferlere ve 4,3&#8217;\u00fcn \u00fczerindeki de\u011ferlere farkl\u0131 bir regresyon modeli uyguluyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki d\u00fc\u011f\u00fcml\u00fc bir mente\u015fe fonksiyonu a\u015fa\u011f\u0131daki gibi olabilir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> (4,3 \u2013 x) e\u011fer x &lt; 4,3 ise<\/span><\/li>\n<li> <span style=\"color: #000000;\">y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> (x \u2013 4,3) e\u011fer x &gt; 4,3 ve x &lt; 6,7 ise<\/span><\/li>\n<li> <span style=\"color: #000000;\">y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> (6,7 \u2013 x) e\u011fer x &gt; 6,7 ise<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu durumda e\u015fik de\u011feri olarak <strong>4.3<\/strong> ve <strong>6.7<\/strong> se\u00e7ilmesinin olas\u0131 t\u00fcm e\u015fik de\u011ferleri aras\u0131nda maksimum hata azalt\u0131m\u0131na olanak sa\u011flad\u0131\u011f\u0131 belirlendi. Daha sonra bir regresyon modelini 4,3&#8217;\u00fcn alt\u0131ndaki de\u011ferlere, ba\u015fka bir regresyon modelini 4,3 ile 6,7 aras\u0131ndaki de\u011ferlere ve ba\u015fka bir regresyon modelini 4,3&#8217;\u00fcn \u00fczerindeki de\u011ferlere s\u0131\u011fd\u0131r\u0131yoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. K-katl\u0131 \u00e7apraz do\u011frulamaya g\u00f6re <em>k&#8217;yi<\/em> se\u00e7in.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak, her model i\u00e7in farkl\u0131 say\u0131da d\u00fc\u011f\u00fcm kullanarak birka\u00e7 farkl\u0131 modeli yerle\u015ftirdikten sonra, en d\u00fc\u015f\u00fck test ortalama kare hatas\u0131n\u0131 (MSE) \u00fcreten modeli 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> ger\u00e7ekle\u015ftirebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">En d\u00fc\u015f\u00fck MSE testine sahip model, yeni verilere en iyi genelleme yapan model olarak se\u00e7ilir.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Avantajlar ve dezavantajlar<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u00c7ok de\u011fi\u015fkenli uyarlamal\u0131 regresyon e\u011frileri a\u015fa\u011f\u0131daki avantaj ve dezavantajlara sahiptir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Avantajlar\u0131<\/strong> :<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Hem <a href=\"https:\/\/statorials.org\/tr\/regresyon-ve-siniflandirma\/\" target=\"_blank\" rel=\"noopener noreferrer\">regresyon hem de s\u0131n\u0131fland\u0131rma problemlerinde<\/a> kullan\u0131labilir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bu, b\u00fcy\u00fck veri k\u00fcmelerinde iyi \u00e7al\u0131\u015f\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\">H\u0131zl\u0131 hesaplama olana\u011f\u0131 sunar.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bu, \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenleri standartla\u015ft\u0131rman\u0131z\u0131 gerektirmez.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Dezavantajlar:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Rastgele ormanlar ve gradyan art\u0131rma makineleri gibi do\u011frusal olmayan y\u00f6ntemler kadar iyi performans g\u00f6stermeme e\u011filimindedir.<\/span><\/li>\n<\/ul>\n<h3> <strong><span style=\"color: #000000;\">MARS modelleri R &amp; Python&#8217;a nas\u0131l s\u0131\u011fd\u0131r\u0131l\u0131r<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde, R ve Python&#8217;da \u00e7ok de\u011fi\u015fkenli uyarlamal\u0131 regresyon e\u011frilerinin (MARS) nas\u0131l s\u0131\u011fd\u0131r\u0131laca\u011f\u0131na ili\u015fkin ad\u0131m ad\u0131m \u00f6rnekler verilmektedir:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/rde-cok-degiskenli-uyarlanabilir-regresyon-egrileri\/\" target=\"_blank\" rel=\"noopener noreferrer\">R&#8217;de \u00c7ok De\u011fi\u015fkenli Uyarlanabilir Regresyon Spline&#8217;lar\u0131<\/a><br \/> Python&#8217;da \u00c7ok De\u011fi\u015fkenli Uyarlanabilir Regresyon Spline&#8217;lar\u0131<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir dizi yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fki do\u011frusal oldu\u011funda, genellikle belirli bir yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkinin \u015fu bi\u00e7imi ald\u0131\u011f\u0131n\u0131 varsayan do\u011frusal regresyonu kullanabiliriz : Y = \u03b2 0 + \u03b2 1 X + \u03b5 Ancak pratikte de\u011fi\u015fkenler aras\u0131ndaki ili\u015fki asl\u0131nda do\u011frusal olmayabilir ve do\u011frusal regresyon kullanmaya \u00e7al\u0131\u015fmak, modelin [&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-1214","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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