{"id":4644,"date":"2024-11-30T04:43:32","date_gmt":"2024-11-29T19:43:32","guid":{"rendered":"https:\/\/saraheee.com\/?p=4644"},"modified":"2025-03-21T23:20:02","modified_gmt":"2025-03-21T14:20:02","slug":"review14-characteristics-of-scoring-rules","status":"publish","type":"post","link":"https:\/\/saraheee.com\/ko\/2024\/11\/review14-characteristics-of-scoring-rules\/","title":{"rendered":"[review#14] Characteristics of Scoring rules"},"content":{"rendered":"<h4 class=\"wp-block-heading\">1. Symmetry (\ub300\uce6d\uc131)<\/h4>\n\n\n\n<p>\uc8fc\uc5b4\uc9c4 \uc0ac\uac74 t = 0\uacfc t = 1\uc5d0 \ub300\ud574, \uc2a4\ucf54\uc5b4\ub9c1 \ub8f0\uc774 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \uacbd\uc6b0<\/p>\n\n\n\n<p>\\(f_1(x) = f_0(1 &#8211; x)\\)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\(f_0(x)\\): \ud0c0\uc785 t = 0\uc5d0\uc11c \ubcf4\uace0\ub41c \ud6c4\ud589 \ud655\ub960 x\uc758 \uc810\uc218.<\/li>\n\n\n\n<li>\\(f_1(x)\\): \ud0c0\uc785 t = 1\uc5d0\uc11c\uc758 \uc810\uc218.<\/li>\n<\/ul>\n\n\n\n<p>\ud55c\ucabd \ud0c0\uc785\uc5d0\uc11c\uc758 \uc810\uc218\ub294 \ub2e4\ub978 \ud0c0\uc785\uc5d0\uc11c\uc758 \uc810\uc218\ub97c \ubc18\uc804\ud558\uc5ec \ub3d9\uc77c\ud55c \ud615\ud0dc\ub85c \uacc4\uc0b0\ub41c\ub2e4.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2. Strict Properness (\uc5c4\uaca9\ud55c \uc801\ud569\uc131)<\/h4>\n\n\n\n<p>\uc2a4\ucf54\uc5b4\ub9c1 \ub8f0\uc774 \uc5c4\uaca9\ud788 \uc801\ud569\ud558\ub824\uba74 \uc608\uce21 \ud655\ub960 P\uac00 \uad00\uce21 \ud655\ub960 Q\uc640 \uc77c\uce58\ud560 \ub54c\ub9cc \ucd5c\ub300 \uc810\uc218\ub97c \uac00\uc838\uc57c \ud55c\ub2e4.<\/p>\n\n\n\n<p>\\(S(P, Q) \\leq S(Q, Q), \\quad \\text{and equality if and only if } P = Q.\\)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">3. Convexity (\ubcfc\ub85d\uc131)<\/h4>\n\n\n\n<p>\uc2a4\ucf54\uc5b4\ub9c1 \ub8f0\uc758 \uae30\ub300\uac12 \\(G(P) = S(P, P)\\)\ub294 P\uc5d0 \ub300\ud574 \ubcfc\ub85d(convex)\uc774\uc5b4\uc57c \ud55c\ub2e4.<br>\uc801\ud569\uc131\uc744 \ubcf4\uc7a5\ud558\ub294 \ud575\uc2ec \uc131\uc9c8\uc774\uba70, \ud655\ub960 \ubd84\ud3ec \uac04\uc758 \ucc28\uc774\ub97c \uce21\uc815\ud560 \ub54c \uc911\uc694\ud558\ub2e4.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">4. Properness without Strictness (\ube44\uc5c4\uaca9 \uc801\ud569\uc131)<\/h4>\n\n\n\n<p>\\(S(P, Q) = 1 &#8211; |P &#8211; Q|\\): \uc774\ub294 \uc801\ud569\ud558\uc9c0\ub9cc, \uc5c4\uaca9\ud788 \uc801\ud569\ud558\uc9c0\ub294 \uc54a\ub294\ub2e4.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">5. Weighting (\uac00\uc911\uce58 \uc801\uc6a9)<\/h4>\n\n\n\n<p>\ud2b9\uc815 \uc0ac\uac74\uc5d0 \uac00\uc911\uce58\ub97c \ubd80\uc5ec\ud558\uc5ec \uc2a4\ucf54\uc5b4\ub9c1 \ub8f0\uc758 \ubbfc\uac10\ub3c4\ub97c \uc870\uc815<\/p>\n\n\n\n<p>\\(S(P, Q; w) = w(Q) \\cdot S(P, Q)\\)<\/p>\n\n\n\n<p>w(Q): \ud2b9\uc815 \uc0ac\uac74 Q\uc758 \uc911\uc694\uc131\uc744 \ub098\ud0c0\ub0b4\ub294 \uac00\uc911\uce58 \ud568\uc218<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">6. Additivity (\uac00\ubc95\uc131)<\/h4>\n\n\n\n<p>\uc2a4\ucf54\uc5b4\ub9c1 \ub8f0\uc774 \ub3c5\ub9bd\uc801\uc778 \uc0ac\uac74\uc5d0 \ub300\ud574 \uc810\uc218\ub97c \ud569\uc0b0\ud560 \uc218 \uc788\ub294 \uad6c\uc870<\/p>\n\n\n\n<p>\\(S(P_1 \\times P_2, Q_1 \\times Q_2) = S(P_1, Q_1) + S(P_2, Q_2)\\)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">7. Sensitivity to Extremes (\uadf9\ub2e8\uac12 \ubbfc\uac10\uc131)<\/h4>\n\n\n\n<p>\ub85c\uadf8 \uc2a4\ucf54\uc5b4\ub294 \uadf9\ub2e8\uc801 \ud655\ub960\uac12(e.g., \\(P \\to 0\\))\uc5d0 \ub9e4\uc6b0 \ubbfc\uac10\ud558\uba70, \uc810\uc218\uac00 \ubc1c\uc0b0\ud560 \uc218 \uc788\ub2e4.<br>\ubc18\ub300\ub85c, \uc774\ucc28 \uc2a4\ucf54\uc5b4\ub294 \uadf9\ub2e8\uc801 \uac12\uc5d0 \ub35c \ubbfc\uac10\ud558\uc9c0\ub9cc \ud328\ub110\ud2f0\uac00 \uc57d\ud560 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">8. Multi-Class Extension (\ub2e4\uc911 \ud074\ub798\uc2a4 \ud655\uc7a5)<\/h4>\n\n\n\n<p>\ub2e4\uc911 \ud074\ub798\uc2a4 \ubb38\uc81c\uc5d0\uc11c\ub294 \uc2a4\ucf54\uc5b4\ub9c1 \ub8f0\uc744 \uac01 \ud074\ub798\uc2a4\uc758 \ud655\ub960 \ubca1\ud130\ub85c \ud655\uc7a5\ud574\uc57c \ud55c\ub2e4.<\/p>\n\n\n\n<p>\\(S(P, Q) = \\sum_{i=1}^m q_i \\cdot s(p_i)\\)<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h5 class=\"wp-block-heading\">References<\/h5>\n\n\n\n<p>Gneiting, T., &amp; Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation.\u00a0<em>Journal of the American statistical Association<\/em>,\u00a0<em>102<\/em>(477), 359-378.<br>wiki: <a href=\"https:\/\/en.wikipedia.org\/wiki\/Scoring_rule\" rel=\"noopener\">https:\/\/en.wikipedia.org\/wiki\/Scoring_rule<\/a><\/p>\n\n\n\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>I describe the characteristics of scoring rules.<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[108],"tags":[195,194,193],"class_list":["post-4644","post","type-post","status-publish","format-standard","hentry","category-paper-review","tag-nov-30-2024","tag-review","tag-scoring-rules"],"_links":{"self":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/4644"}],"collection":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/comments?post=4644"}],"version-history":[{"count":4,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/4644\/revisions"}],"predecessor-version":[{"id":5206,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/4644\/revisions\/5206"}],"wp:attachment":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/media?parent=4644"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/categories?post=4644"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/tags?post=4644"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}