{"id":947,"date":"2024-07-12T21:00:24","date_gmt":"2024-07-12T21:00:24","guid":{"rendered":"http:\/\/www.ohsumin.com\/?p=947"},"modified":"2025-06-11T01:23:00","modified_gmt":"2025-06-11T01:23:00","slug":"%ec%b5%9c%eb%8c%80%ec%9a%b0%eb%8f%84%ec%b6%94%ec%a0%95mle-maximum-liklyhood-estimation","status":"publish","type":"post","link":"http:\/\/www.inmining.co.kr\/?p=947","title":{"rendered":"\ucd5c\ub300\uc6b0\ub3c4\ucd94\uc815(MLE : Maximum Liklyhood Estimation)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\ucd5c\ub300\uc6b0\ub3c4\ucd94\uc815(Maximum Likelihood Estimation, MLE)\uc740 \uc8fc\uc5b4\uc9c4 \ub370\uc774\ud130\ub85c\ubd80\ud130 \ud655\ub960 \ubaa8\ub378\uc758 \ub9e4\uac1c\ubcc0\uc218\ub97c \ucd94\uc815\ud558\ub294 \ud1b5\uacc4\uc801 \ubc29\ubc95\uc785\ub2c8\ub2e4. MLE\ub294 \uad00\ucc30\ub41c \ub370\uc774\ud130\ub97c \uac00\uc7a5 \uc798 \uc124\uba85\ud558\ub294 \ub9e4\uac1c\ubcc0\uc218 \uac12\uc744 \ucc3e\uae30 \uc704\ud574 \uc6b0\ub3c4(likelihood)\ub97c \ucd5c\ub300\ud654\ud558\ub294 \uc6d0\ub9ac\ub97c \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%EA%B0%9C%EB%85%90\"><\/span>\uac1c\ub150<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1.<strong>\uc6b0\ub3c4 \ud568\uc218(Likelihood Function)<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uc6b0\ub3c4 \ud568\uc218\ub294 \uc8fc\uc5b4\uc9c4 \ub370\uc774\ud130\uac00 \ud2b9\uc815 \ub9e4\uac1c\ubcc0\uc218 \uac12\uc5d0\uc11c \uc5bc\ub9c8\ub098 \uac00\ub2a5\uc131\uc774 \ub192\uc740\uc9c0\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<\/li>\n\n\n\n<li>\ud655\ub960 \ubc00\ub3c4 \ud568\uc218\uc640 \uc720\uc0ac\ud558\uc9c0\ub9cc, \ub370\uc774\ud130\ub97c \uace0\uc815\ud558\uace0 \ub9e4\uac1c\ubcc0\uc218\ub97c \ubcc0\ub3d9\uc2dc\ucf1c \ub9e4\uac1c\ubcc0\uc218\uc758 \uac00\ub2a5\uc131\uc744 \ud3c9\uac00\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li>\uc8fc\uc5b4\uc9c4 \ub370\uc774\ud130 \\(\\mathbf{x} = (x_1, x_2, \\ldots, x_n)\\)\uc640 \ub9e4\uac1c\ubcc0\uc218 \\(\\theta\\)\uc5d0 \ub300\ud574, \uc6b0\ub3c4 \ud568\uc218\ub294 \\(L(\\theta | \\mathbf{x}) = P(\\mathbf{x} | \\theta)\\)\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">2.<strong>\ub85c\uadf8 \uc6b0\ub3c4 \ud568\uc218(Log-Likelihood Function)<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uacc4\uc0b0\uc758 \ud3b8\ub9ac\ud568\uc744 \uc704\ud574 \uc6b0\ub3c4 \ud568\uc218\uc758 \ub85c\uadf8\ub97c \ucde8\ud558\uc5ec \ub85c\uadf8 \uc6b0\ub3c4 \ud568\uc218\ub85c \ubcc0\ud658\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li>\\( \\ell(\\theta | \\mathbf{x}) = \\log L(\\theta | \\mathbf{x}) \\).<\/li>\n\n\n\n<li>\ub85c\uadf8\ub97c \ucde8\ud558\uba74 \uacf1\uc148\uc774 \ub367\uc148\uc73c\ub85c \ubc14\ub00c\uc5b4 \uacc4\uc0b0\uc774 \uac04\ub2e8\ud574\uc9d1\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">3.<strong>\ucd5c\ub300\ud654<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ub85c\uadf8 \uc6b0\ub3c4 \ud568\uc218\ub97c \ucd5c\ub300\ud654\ud558\ub294 \ub9e4\uac1c\ubcc0\uc218 \uac12\uc744 \ucc3e\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li>\uc218\ud559\uc801\uc73c\ub85c, \ub9e4\uac1c\ubcc0\uc218 \\(\\theta\\)\uc5d0 \ub300\ud574 \\( \\hat{\\theta} = \\arg \\max_{\\theta} \\ell(\\theta | \\mathbf{x}) \\)\ub97c \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%EC%98%88%EC%A0%9C\"><\/span>\uc608\uc81c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\uc815\uaddc \ubd84\ud3ec(\ud3c9\uade0 \\(\\mu\\), \ubd84\uc0b0 \\(\\sigma^2)\\)\uc758 MLE\ub97c \uc608\ub85c \ub4e4\uc5b4 \uc124\uba85\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\uc6b0\ub3c4 \ud568\uc218<\/strong>:<br>\uc8fc\uc5b4\uc9c4 \ub370\uc774\ud130 \\(\\mathbf{x} = (x_1, x_2, \\ldots, x_n)\\)\uac00 \uc815\uaddc \ubd84\ud3ec\ub97c \ub530\ub978\ub2e4\uace0 \uac00\uc815\ud560 \ub54c, \uc6b0\ub3c4 \ud568\uc218\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<br>\\[<br>L(\\mu, \\sigma^2 | \\mathbf{x}) = \\prod_{i=1}^{n} \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\exp \\left( -\\frac{(x_i &#8211; \\mu)^2}{2 \\sigma^2} \\right)<br>\\]<\/li>\n\n\n\n<li><strong>\ub85c\uadf8 \uc6b0\ub3c4 \ud568\uc218<\/strong>:<br>\ub85c\uadf8\ub97c \ucde8\ud558\uba74:<br>\\[<br>\\ell(\\mu, \\sigma^2 | \\mathbf{x}) = \\sum_{i=1}^{n} \\left( -\\frac{1}{2} \\log(2 \\pi \\sigma^2) &#8211; \\frac{(x_i &#8211; \\mu)^2}{2 \\sigma^2} \\right)<br>\\]<\/li>\n\n\n\n<li><strong>\ucd5c\ub300\ud654<\/strong>:<br>\ub85c\uadf8 \uc6b0\ub3c4 \ud568\uc218\ub97c \ucd5c\ub300\ud654\ud558\uae30 \uc704\ud574, \\(\\mu\\)\uc640 \\(\\sigma^2\\)\uc5d0 \ub300\ud574 \ud3b8\ubbf8\ubd84\ud558\uace0 0\uc73c\ub85c \uc124\uc815\ud569\ub2c8\ub2e4:<br>\\[<br>\\frac{\\partial \\ell}{\\partial \\mu} = 0 \\quad \\Rightarrow \\quad \\hat{\\mu} = \\frac{1}{n} \\sum_{i=1} x_i<br>\\]<br>\\[<br>\\frac{\\partial \\ell}{\\partial \\sigma^2} = 0 \\quad \\Rightarrow \\quad \\hat{\\sigma}^2 = \\frac{1}{n} \\sum_{i=1} (x_i &#8211; \\hat{\\mu})^2<br>\\]<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\ub530\ub77c\uc11c, \uc815\uaddc \ubd84\ud3ec\uc758 MLE\ub294 \uc0d8\ud50c \ud3c9\uade0\uacfc \uc0d8\ud50c \ubd84\uc0b0\uc73c\ub85c \ucd94\uc815\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%EC%9E%A5%EC%A0%90%EA%B3%BC_%EB%8B%A8%EC%A0%90\"><\/span>\uc7a5\uc810\uacfc \ub2e8\uc810<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\uc7a5\uc810<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc77c\ubc18\uc131<\/strong>: MLE\ub294 \ub2e4\uc591\ud55c \ubd84\ud3ec\uc640 \ubaa8\ub378\uc5d0 \uc801\uc6a9\ub420 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ud6a8\uc728\uc131<\/strong>: \ucda9\ubd84\ud55c \uc0d8\ud50c \ud06c\uae30\uac00 \uc788\uc744 \ub54c, MLE \ucd94\uc815\ub7c9\uc740 \ucd5c\uc18c \ubd84\uc0b0\uc744 \uac00\uc9c0\ub294 \ubd88\ud3b8 \ucd94\uc815\ub7c9\uc785\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\ub2e8\uc810<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uacc4\uc0b0 \ubcf5\uc7a1\uc131<\/strong>: \ubcf5\uc7a1\ud55c \ubaa8\ub378\uc758 \uacbd\uc6b0, MLE\ub97c \uacc4\uc0b0\ud558\uae30 \uc704\ud574 \uc218\uce58\uc801 \ucd5c\uc801\ud654 \ubc29\ubc95\uc774 \ud544\uc694\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uadf9\uac12 \ubb38\uc81c<\/strong>: \uc6b0\ub3c4 \ud568\uc218\uac00 \uc5ec\ub7ec \uadf9\uac12\uc744 \uac00\uc9c8 \uc218 \uc788\uc5b4 \uc804\uc5ed \ucd5c\uc801\uac12\uc744 \ucc3e\uae30 \uc5b4\ub824\uc6b8 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc0d8\ud50c \ud06c\uae30 \ubbfc\uac10\uc131<\/strong>: \uc791\uc740 \uc0d8\ud50c \ud06c\uae30\uc5d0\uc11c\ub294 \ucd94\uc815\uac12\uc758 \ubd84\uc0b0\uc774 \ud074 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%EC%98%88%EC%A0%9C2\"><\/span>\uc608\uc81c2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"484\" height=\"347\" src=\"http:\/\/www.ohsumin.com\/sm24_wp\/wp-content\/uploads\/2024\/07\/MLE1-1.jpg\" alt=\"\" class=\"wp-image-952\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/07\/MLE1-1.jpg 484w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/07\/MLE1-1-300x215.jpg 300w\" sizes=\"auto, (max-width: 484px) 100vw, 484px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uc704 \uadf8\ub9bc\uc740 \uc815\uaddc \ubd84\ud3ec\uc758 \ucd5c\ub300\uc6b0\ub3c4\ucd94\uc815(MLE)\uc744 \uc2dc\uac01\ud654\ud55c \uac83\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ub85c\uadf8 \uc6b0\ub3c4 \ud568\uc218<\/strong>: \\(\\mu\\)\uc640 \\(\\sigma\\) \uac12\uc5d0 \ub530\ub978 \ub85c\uadf8 \uc6b0\ub3c4 \ud568\uc218\uc758 \uac12\uc744 \uc0c9\uae54\ub85c \ud45c\ud604\ud55c \ub4f1\uace0\uc120 \uadf8\ub9bc\uc785\ub2c8\ub2e4. \uc9c4\ud55c \uc0c9\uc77c\uc218\ub85d \uc6b0\ub3c4\uac00 \ub192\uc740 \uc601\uc5ed\uc744 \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ucd5c\ub300 \uc6b0\ub3c4 \ucd94\uc815\uac12<\/strong>: \ube68\uac04 \uc810\uc73c\ub85c \ud45c\uc2dc\ub41c \ubd80\ubd84\uc774 \ub85c\uadf8 \uc6b0\ub3c4 \ud568\uc218\uc758 \ucd5c\ub300\uac12\uc744 \uac00\uc9c0\ub294 \\(\\mu\\)\uc640 \\(\\sigma\\)\uc758 \uc870\ud569\uc785\ub2c8\ub2e4. \uc774 \uc810\uc774 \uc8fc\uc5b4\uc9c4 \ub370\uc774\ud130\uc5d0 \ub300\ud574 \uac00\uc7a5 \uac00\ub2a5\uc131\uc774 \ub192\uc740 \ub9e4\uac1c\ubcc0\uc218 \uac12\uc785\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774 \uadf8\ub9bc\uc740 MLE\uac00 \ub370\uc774\ud130\uc758 \ubd84\ud3ec\ub97c \uac00\uc7a5 \uc798 \uc124\uba85\ud558\ub294 \ub9e4\uac1c\ubcc0\uc218\ub97c \ucc3e\uae30 \uc704\ud574 \ub85c\uadf8 \uc6b0\ub3c4 \ud568\uc218\ub97c \ucd5c\ub300\ud654\ud558\ub294 \ubc29\ubc95\uc744 \uc2dc\uac01\uc801\uc73c\ub85c \ubcf4\uc5ec\uc90d\ub2c8\ub2e4.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\ucd5c\ub300\uc6b0\ub3c4\ucd94\uc815(Maximum Likelihood Estimation, MLE)\uc740 \uc8fc\uc5b4\uc9c4 \ub370\uc774\ud130\ub85c\ubd80\ud130 \ud655\ub960 \ubaa8\ub378\uc758 \ub9e4\uac1c\ubcc0\uc218\ub97c \ucd94\uc815\ud558\ub294 \ud1b5\uacc4\uc801 \ubc29\ubc95\uc785\ub2c8\ub2e4. MLE\ub294 \uad00\ucc30\ub41c \ub370\uc774\ud130\ub97c \uac00\uc7a5 \uc798 \uc124\uba85\ud558\ub294&#8230;<\/p>\n","protected":false},"author":1,"featured_media":951,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-947","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-stat","wpcat-6-id"],"_links":{"self":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/947","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=947"}],"version-history":[{"count":5,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/947\/revisions"}],"predecessor-version":[{"id":958,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/947\/revisions\/958"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/media\/951"}],"wp:attachment":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=947"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=947"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=947"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}