{"id":1150,"date":"2023-07-27T12:12:52","date_gmt":"2023-07-27T12:12:52","guid":{"rendered":"https:\/\/statorials.org\/tr\/onyargi-varyansi-uzlasmasi\/"},"modified":"2023-07-27T12:12:52","modified_gmt":"2023-07-27T12:12:52","slug":"onyargi-varyansi-uzlasmasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/onyargi-varyansi-uzlasmasi\/","title":{"rendered":"Makine \u00f6\u011freniminde \u00f6nyarg\u0131-varyans de\u011fi\u015fimi nedir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Bir modelin veri seti \u00fczerindeki performans\u0131n\u0131 de\u011ferlendirmek i\u00e7in modelin tahminlerinin g\u00f6zlemlenen verilerle ne kadar iyi e\u015fle\u015fti\u011fini \u00f6l\u00e7memiz gerekir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/regresyon-ve-siniflandirma\/\" target=\"_blank\" rel=\"noopener noreferrer\">Regresyon modelleri<\/a> i\u00e7in en yayg\u0131n kullan\u0131lan \u00f6l\u00e7\u00fcm, a\u015fa\u011f\u0131daki \u015fekilde hesaplanan ortalama karesel hatad\u0131r (MSE):<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE = (1\/n)*\u03a3(y <sub>ben<\/sub> \u2013 f(x <sub>ben<\/sub> )) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> toplam g\u00f6zlem say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y <sub>i<\/sub> :<\/strong> <sup>i&#8217;inci<\/sup> g\u00f6zlemin yan\u0131t de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>f(x <sub>i<\/sub> ):<\/strong> <sup>i&#8217;inci<\/sup> g\u00f6zlemin tahmin edilen tepki de\u011feri<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Model tahminleri g\u00f6zlemlere ne kadar yak\u0131nsa MSE o kadar d\u00fc\u015f\u00fck olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak modelimiz g\u00f6r\u00fcnmeyen verilere uyguland\u0131\u011f\u0131nda yaln\u0131zca <strong>MSE testini<\/strong> (MSE) \u00f6nemsiyoruz. Bunun nedeni, modelin mevcut veriler \u00fczerinde de\u011fil, yaln\u0131zca bilinmeyen veriler \u00fczerinde nas\u0131l performans g\u00f6sterece\u011fiyle ilgilenmemizdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, hisse senedi fiyatlar\u0131n\u0131 tahmin eden bir modelin ge\u00e7mi\u015f verilerde d\u00fc\u015f\u00fck bir MSE&#8217;ye sahip olmas\u0131 sorun de\u011fil, ancak modeli gelecekteki verileri do\u011fru bir \u015fekilde tahmin etmek i\u00e7in <em>ger\u00e7ekten<\/em> kullanabilmeyi istiyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE testinin hala iki b\u00f6l\u00fcme ayr\u0131labilece\u011fi ortaya \u00e7\u0131kt\u0131:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>(1) Varyans:<\/strong> <em>f<\/em> fonksiyonumuzun farkl\u0131 bir e\u011fitim seti kullanarak tahmin etmemiz durumunda de\u011fi\u015fece\u011fi miktar\u0131 ifade eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>(2) \u00d6nyarg\u0131:<\/strong> Son derece karma\u015f\u0131k olabilecek ger\u00e7ek bir soruna \u00e7ok daha basit bir modelle yakla\u015f\u0131lmas\u0131n\u0131n ortaya \u00e7\u0131kard\u0131\u011f\u0131 hatay\u0131 ifade eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Matematiksel terimlerle yaz\u0131lm\u0131\u015ft\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE testi = Var( <em class=\"ph i\">f\u0302(<\/em> x <sub>0<\/sub> )) + [Bias( <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 testi = Varyans + Sapma <sup>2<\/sup> + \u0130ndirgenemez hata<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00dc\u00e7\u00fcnc\u00fc terim olan indirgenemez hata, a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler k\u00fcmesi ile <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">yan\u0131t de\u011fi\u015fkeni<\/a> aras\u0131ndaki ili\u015fkide her zaman <em>g\u00fcr\u00fclt\u00fc<\/em> olmas\u0131 nedeniyle herhangi bir model taraf\u0131ndan azalt\u0131lamayan hatad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Y\u00fcksek yanl\u0131l\u0131\u011fa<\/strong> sahip modeller <strong>d\u00fc\u015f\u00fck varyansa<\/strong> sahip olma e\u011filimindedir. \u00d6rne\u011fin, do\u011frusal regresyon modelleri y\u00fcksek yanl\u0131l\u0131\u011fa (a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler ile yan\u0131t de\u011fi\u015fkeni aras\u0131nda basit bir do\u011frusal ili\u015fki varsay\u0131larak) ve d\u00fc\u015f\u00fck varyansa (model tahminleri \u00f6rnekten \u00f6rne\u011fe \u00e7ok fazla de\u011fi\u015fmeyecektir) sahip olma e\u011filimindedir. di\u011feri).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bununla birlikte, <strong>d\u00fc\u015f\u00fck yanl\u0131l\u0131\u011fa<\/strong> sahip modeller <strong>y\u00fcksek varyansa<\/strong> sahip olma e\u011filimindedir. \u00d6rne\u011fin, karma\u015f\u0131k do\u011frusal olmayan modeller d\u00fc\u015f\u00fck yanl\u0131l\u0131\u011fa (a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler ile yan\u0131t de\u011fi\u015fkeni aras\u0131nda belirli bir ili\u015fki oldu\u011funu varsaymay\u0131n) ve y\u00fcksek varyansa (model tahminleri bir \u00f6\u011frenme \u00f6rne\u011finden di\u011ferine \u00f6nemli \u00f6l\u00e7\u00fcde de\u011fi\u015febilir) sahip olma e\u011filimindedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6nyarg\u0131-varyans de\u011fi\u015fimi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>\u00d6nyarg\u0131-varyans dengelemesi,<\/strong> genellikle varyans\u0131 art\u0131ran \u00f6nyarg\u0131y\u0131 azaltmay\u0131 veya genellikle \u00f6nyarg\u0131y\u0131 art\u0131ran varyans\u0131 azaltmay\u0131 se\u00e7ti\u011fimizde ger\u00e7ekle\u015fen dengelemeyi ifade eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki grafik bu \u00f6d\u00fcnle\u015fimi g\u00f6rselle\u015ftirmenin bir yolunu sunmaktad\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11515 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/biais_variance1.png\" alt=\"\u00d6nyarg\u0131-varyans de\u011fi\u015f toku\u015fu\" width=\"551\" height=\"400\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Modelin karma\u015f\u0131kl\u0131\u011f\u0131 artt\u0131k\u00e7a toplam hata azal\u0131r, ancak bu yaln\u0131zca belirli bir noktaya kadar olur. Belirli bir noktadan sonra varyans artmaya ba\u015flar ve toplam hata da artmaya ba\u015flar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Uygulamada, yaln\u0131zca bir modelin toplam hatas\u0131n\u0131 en aza indirmeyi \u00f6nemsiyoruz, varyans\u0131 veya \u00f6nyarg\u0131y\u0131 mutlaka en aza indirmeyi de\u011fil.<\/span> <span style=\"color: #000000;\">Toplam hatay\u0131 en aza indirmenin yolunun varyans ve \u00f6nyarg\u0131 aras\u0131nda do\u011fru dengeyi bulmak oldu\u011fu ortaya \u00e7\u0131kt\u0131.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ba\u015fka bir deyi\u015fle, a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ger\u00e7ek ili\u015fkiyi yakalayacak kadar karma\u015f\u0131k, ancak ger\u00e7ekte var olmayan kal\u0131plar\u0131 tespit edemeyecek kadar karma\u015f\u0131k olmayan bir model istiyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir model \u00e7ok karma\u015f\u0131k oldu\u011funda verilere <a href=\"https:\/\/statorials.org\/tr\/makine-ogrenimi-asiri-uyumu\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>gere\u011finden fazla uyum sa\u011flar<\/strong><\/a> . Bunun nedeni, e\u011fitim verilerinde \u015fans eseri olu\u015fan kal\u0131plar\u0131 bulman\u0131n \u00e7ok zor olmas\u0131d\u0131r. Bu t\u00fcr bir modelin g\u00f6r\u00fcnmez veriler \u00fczerinde d\u00fc\u015f\u00fck performans g\u00f6stermesi muhtemeldir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak bir model \u00e7ok basit oldu\u011funda verileri <strong>k\u00fc\u00e7\u00fcmser<\/strong> . Bunun nedeni, a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ger\u00e7ek ili\u015fkinin ger\u00e7ekte oldu\u011fundan daha basit oldu\u011funun varsay\u0131lmas\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Makine \u00f6\u011freniminde en uygun modelleri se\u00e7menin yolu, modeli gelecekteki g\u00f6r\u00fcnmeyen veriler \u00fczerinde test etme hatas\u0131n\u0131 en aza indirmek i\u00e7in \u00f6nyarg\u0131 ve varyans aras\u0131nda bir denge bulmakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Uygulamada testlerin MSE&#8217;sini en aza indirmenin en yayg\u0131n yolu <a href=\"https:\/\/statorials.org\/tr\/k-kat-capraz-dogrulama\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00e7apraz do\u011frulama<\/a> kullanmakt\u0131r.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir modelin veri seti \u00fczerindeki performans\u0131n\u0131 de\u011ferlendirmek i\u00e7in modelin tahminlerinin g\u00f6zlemlenen verilerle ne kadar iyi e\u015fle\u015fti\u011fini \u00f6l\u00e7memiz gerekir. Regresyon modelleri i\u00e7in en yayg\u0131n kullan\u0131lan \u00f6l\u00e7\u00fcm, a\u015fa\u011f\u0131daki \u015fekilde hesaplanan ortalama karesel hatad\u0131r (MSE): MSE = (1\/n)*\u03a3(y ben \u2013 f(x ben )) 2 Alt\u0131n: n: toplam g\u00f6zlem say\u0131s\u0131 y i : i&#8217;inci g\u00f6zlemin yan\u0131t de\u011feri f(x i [&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-1150","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>Makine \u00f6\u011freniminde \u00f6nyarg\u0131-varyans de\u011fi\u015fimi nedir?<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, \u00f6rnekler de dahil olmak \u00fczere, makine 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