{"id":252,"date":"2024-03-03T22:57:09","date_gmt":"2024-03-03T14:57:09","guid":{"rendered":"https:\/\/www.xuzhe.tj.cn\/?p=252"},"modified":"2025-05-03T09:31:03","modified_gmt":"2025-05-03T01:31:03","slug":"252","status":"publish","type":"post","link":"https:\/\/www.xuzhe.tj.cn\/index.php\/2024\/03\/03\/252\/","title":{"rendered":"\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\u539f\u7406 \uff5c \u673a\u5668\u5b66\u4e60\u7684\u57fa\u7840"},"content":{"rendered":"<p>[latexpage]<br \/>\n\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\uff1a\u4e00\u4e2a\u7f8e\u4e3d\u7684\u60f3\u6cd5\uff0c\u5b83\u5c06\u7edf\u8ba1\u5b66\u3001\u4fe1\u606f\u8bba\u548c\u54f2\u5b66\u7684\u6982\u5ff5\u7ed3\u5408\u5728\u4e00\u8d77\uff0c\u4e3a\u673a\u5668\u5b66\u4e60\u5960\u5b9a\u4e86\u57fa\u7840\u3002<\/p>\n<h1>\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\uff08MDL\uff09\u7684\u6982\u5ff5<\/h1>\n<p>\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\uff08Minimum Description Length, 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b\u7f29\u7b97\u6cd5\uff0c\u7528\u4e8e\u67e5\u627e\u5e76\u538b\u7f29\u91cd\u590d\u5b57\u7b26\u3002<\/li>\n<li>\u590d\u6742\u6a21\u578b\uff1a\u4e00\u79cd\u66f4\u9ad8\u7ea7\u7684\u7b97\u6cd5\uff0c\u65e8\u5728\u53d1\u73b0\u5e76\u7f16\u7801\u66f4\u590d\u6742\u7684\u6a21\u5f0f\u3002<\/li>\n<\/ul>\n<p>MDL\u5206\u6790\uff1a<\/p>\n<ul>\n<li>\u6587\u4ef6A\uff1a\u7b80\u5355\u6a21\u578b\u53ef\u4ee5\u901a\u8fc7\u6807\u8bb0\u91cd\u590d\u7684\u2018A\u2019\u5b57\u7b26\uff08\u4f8b\u5982\uff0c\u201cB\u91cd\u590d10\u6b21\u201d\uff09\u6765\u6709\u6548\u538b\u7f29\u5b83\u3002\u590d\u6742\u6a21\u578b\u4e0d\u4f1a\u63d0\u4f9b\u592a\u591a\u4f18\u52bf\uff0c\u5e76\u4e14\u4f1a\u589e\u52a0\u4e0d\u5fc5\u8981\u7684\u590d\u6742\u6027\u3002<\/li>\n<li>\u6587\u4ef6B\uff1a\u7531\u4e8e\u6ca1\u6709\u7b80\u5355\u7684\u91cd\u590d\uff0c\u7b80\u5355\u6a21\u578b\u65e0\u6cd5\u6709\u6548\u538b\u7f29\u5b83\u3002\u7531\u4e8e\u7f3a\u4e4f\u6a21\u5f0f\uff0c\u590d\u6742\u6a21\u578b\u53ef\u80fd\u4e5f\u4f1a\u9047\u5230\u56f0\u96be\u3002<\/li>\n<\/ul>\n<p>MDL\u51b3\u7b56\uff1a<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u6587\u4ef6A\uff0c\u7b80\u5355\u6a21\u578b\u7684\u201c\u63cf\u8ff0\u957f\u5ea6\u201d\u8f83\u77ed\uff0c\u56e0\u4e3a\u5b83\u5728\u964d\u4f4e\u590d\u6742\u6027\u7684\u540c\u65f6\u63d0\u4f9b\u4e86\u8db3\u591f\u7684\u538b\u7f29\u3002<\/li>\n<li>\u5bf9\u4e8e\u6587\u4ef6B\uff0c\u4e24\u79cd\u6a21\u578b\u53ef\u80fd\u90fd\u8868\u73b0\u4e0d\u4f73\uff0c\u4f46\u7531\u4e8e\u7b80\u5355\u6a21\u578b\u7684\u590d\u6742\u6027\u8f83\u4f4e\uff0c\u53ef\u80fd\u4ecd\u7136\u66f4\u53d7\u9752\u7750\uff0c\u9664\u975e\u590d\u6742\u6a21\u578b\u80fd\u591f\u53d1\u73b0\u4e00\u4e9b\u4e0d\u90a3\u4e48\u660e\u663e\u7684\u6a21\u5f0f\u6765\u8fdb\u884c\u538b\u7f29\u3002<\/li>\n<\/ul>\n<p>\u6a21\u578b\u590d\u6742\u5ea6\u4e0e\u62df\u5408\u4e4b\u95f4\u7684\u6743\u8861\uff1a<\/p>\n<ul>\n<li>\u7b80\u5355\u6a21\u578b\u53ef\u80fd\u65e0\u6cd5\u5f88\u597d\u5730\u62df\u5408\u6570\u636e\uff0c\u9700\u8981\u66f4\u957f\u7684\u63cf\u8ff0\u6765\u89e3\u91ca\u6b8b\u5dee\uff08\u6a21\u578b\u672a\u80fd\u89e3\u91ca\u7684\u6570\u636e\u90e8\u5206\uff09\u3002<\/li>\n<li>\u590d\u6742\u6a21\u578b\u53ef\u80fd\u66f4\u597d\u5730\u62df\u5408\u6570\u636e\uff0c\u4f46\u81ea\u8eab\u9700\u8981\u66f4\u957f\u7684\u63cf\u8ff0\u3002<\/li>\n<\/ul>\n<p>\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\u539f\u5219\uff08MDL\uff09\u5bfb\u6c42\u8fd9\u4e24\u8005\u4e4b\u95f4\u7684\u5e73\u8861\u3002<\/p>\n<p>\u8fd9\u610f\u5473\u7740\uff0c\u5982\u679c\u4e00\u4e2a\u6a21\u578b\u80fd\u591f\u66f4\u7b80\u6d01\u5730\u63cf\u8ff0\u6570\u636e\uff0c\u90a3\u4e48\u5b83\u901a\u5e38\u88ab\u8ba4\u4e3a\u662f\u66f4\u4f18\u7684\u3002\u4ece\u672c\u8d28\u4e0a\u8bb2\uff0cMDL\u662f\u4e00\u79cd\u5b9e\u73b0\u5965\u5361\u59c6\u5243\u5200\u539f\u5219\uff08\u5373\u5728\u6ee1\u8db3\u540c\u7b49\u89e3\u91ca\u529b\u7684\u524d\u63d0\u4e0b\uff0c\u5e94\u9009\u62e9\u5047\u8bbe\u6700\u7b80\u7684\u7406\u8bba\uff09\u7684\u5f62\u5f0f\u5316\u65b9\u6cd5\u3002\u5728MDL\u4e2d\uff0c\u5965\u5361\u59c6\u5243\u5200\u539f\u5219\u4e2d\u7684\u201c\u7b80\u5355\u201d\uff0c\u5c31\u662f\u6700\u77ed\u7684\u4e8c\u8fdb\u5236\u4e32\u957f\u5ea6\u3002<\/p>\n<h1>MDL\u7684\u57fa\u672c\u5047\u8bbe\u5206\u6790<\/h1>\n<p>MDL\u9009\u62e9\u6700\u7b80\u5355\u7684\u63cf\u8ff0\u6a21\u578b\uff0c\u90a3\u662f\u4e0d\u662f\u610f\u5473\u7740MDL\u8ba4\u4e3a\u81ea\u7136\u754c\u5fc5\u7136\u7b80\u5355\u7684\u4fe1\u5ff5\uff1f<\/p>\n<p>\u76f8\u53cd\uff0c\u5b83\u66f4\u5173\u6ce8\u4e8e\u63d0\u4f9b\u4e00\u79cd\u6709\u6548\u7684\u5b66\u4e60\u7b56\u7565\uff0c\u5c24\u5176\u662f\u5728\u9762\u5bf9\u6709\u9650\u7684\u6837\u672c\u6570\u636e\u65f6\u3002MDL\u539f\u7406\u7684\u6838\u5fc3\u5728\u4e8e\u901a\u8fc7\u4f18\u5316\u6a21\u578b\u63cf\u8ff0\u957f\u5ea6\u6765\u9632\u6b62\u8fc7\u62df\u5408\uff0c\u5373\u5728\u5c3d\u53ef\u80fd\u5c11\u7684\u4fe1\u606f\u91cf\u4e0b\u5bf9\u6570\u636e\u8fdb\u884c\u51c6\u786e\u63cf\u8ff0\u3002<\/p>\n<p>\u5728\u6837\u672c\u91cf\u8f83\u5c0f\u7684\u60c5\u51b5\u4e0b\uff0c\u8f83\u590d\u6742\u7684\u6a21\u578b\u5bb9\u6613\u6355\u6349\u5230\u6837\u672c\u4e2d\u7684\u968f\u673a\u566a\u58f0\uff0c\u800c\u4e0d\u662f\u771f\u5b9e\u7684\u3001\u6f5c\u5728\u7684\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u3002\u8fd9\u79cd\u8fc7\u62df\u5408\u73b0\u8c61\u4f1a\u964d\u4f4e\u6a21\u578b\u5728\u65b0\u6570\u636e\u4e0a\u7684\u9884\u6d4b\u7cbe\u5ea6\u548c\u6cdb\u5316\u80fd\u529b\u3002\u56e0\u6b64\uff0cMDL\u539f\u7406\u901a\u8fc7\u504f\u597d\u7b80\u5355\u7684\u5047\u8bbe\u6765\u63d0\u9ad8\u6a21\u578b\u7684\u6cdb\u5316\u6027\u80fd\uff0c\u8fd9\u662f\u4e00\u79cd\u57fa\u4e8e\u6a21\u578b\u9009\u62e9\u548c\u7edf\u8ba1\u5b66\u4e60\u7406\u8bba\u7684\u5b9e\u7528\u7b56\u7565\uff0c\u800c\u975e\u57fa\u4e8e\u5bf9\u81ea\u7136\u754c\u672c\u8d28\u7684\u5047\u8bbe\u3002<\/p>\n<p>MDL\u539f\u7406\u5f3a\u8c03\u7684\u662f\u5728\u6a21\u578b\u9009\u62e9\u65f6\u627e\u5230\u63cf\u8ff0\u957f\u5ea6\u548c\u6a21\u578b\u590d\u6742\u5ea6\u4e4b\u95f4\u7684\u6700\u4f73\u5e73\u8861\u70b9\uff0c\u4ee5\u5b9e\u73b0\u5728\u7ed9\u5b9a\u6570\u636e\u4e0a\u7684\u6700\u4f73\u6cdb\u5316\u6027\u80fd\uff0c\u800c\u4e0d\u662f\u8bd5\u56fe\u5bf9\u81ea\u7136\u754c\u7684\u771f\u5b9e\u590d\u6742\u6027\u505a\u51fa\u5148\u9a8c\u7684\u8bc4\u4ef7\u3002<\/p>\n<h1>MDL\u7684\u8ba1\u7b97\u65b9\u6cd5\u00a0<\/h1>\n<p>MDL\u539f\u7406\u8ba4\u4e3a\uff0c\u6700\u4f18\u6a21\u578b\u662f\u80fd\u6700\u5c0f\u5316\u4ee5\u4e0b\u603b\u63cf\u8ff0\u957f\u5ea6\uff08Total Description Length, TDL\uff09\u7684\u6a21\u578b\uff1a<\/p>\n<p>$$\\text{TDL} = L(M) + L(D|M) $$<\/p>\n<p>\u5176\u4e2d:<\/p>\n<ul>\n<li>L(M)\u662f\u6a21\u578b[M]\u7684\u63cf\u8ff0\u957f\u5ea6\uff0c\u5373\u63cf\u8ff0\u6a21\u578b\u672c\u8eab\u6240\u9700\u7684\u6bd4\u7279\u6570<\/li>\n<li>$L(D|M)$\u662f\u7ed9\u5b9a\u6a21\u578b$M$\u4e0b\uff0c\u6570\u636e$D$\u7684\u63cf\u8ff0\u957f\u5ea6\uff0c\u5373\u7528\u6a21\u578b$M$\u6765\u63cf\u8ff0\u6570\u636e$D$\u6240\u9700\u7684\u6bd4\u7279\u6570<\/li>\n<\/ul>\n<p>MDL\u539f\u7406\u7684\u5177\u4f53\u5b9e\u73b0\u4f9d\u8d56\u4e8e\u6240\u9009\u62e9\u7684\u7f16\u7801\u65b9\u6848\u3002\u6709\u4e24\u79cd\u7f16\u7801\u65b9\u6848\uff1a\u5355\u9636\u6bb5\u901a\u7528\u7f16\u7801\uff08one stage universal codes \u6216 refined MDL\uff09\uff0c\u53e6\u4e00\u79cd\u4e3a\u4e24\u9636\u6bb5\u7f16\u7801\uff08two-stage codes \u6216 crude MDL\uff09\u3002\u5176\u4e2d\u4e24\u9636\u6bb5\u7f16\u7801\u8f83\u4e3a\u5e38\u7528\u3002\u4e24\u9636\u6bb5\u7f16\u7801\u7684\u65b9\u5f0f\u4e3a\uff1a\u00a0<\/p>\n<ol>\n<li>\n<p>\u6a21\u578b\u7f16\u7801\uff1a\u9996\u5148\uff0c\u9700\u8981\u9009\u62e9\u4e00\u79cd\u7f16\u7801\u65b9\u6848\u6765\u63cf\u8ff0\u6a21\u578b\u3002\u8fd9\u5305\u62ec\u6a21\u578b\u7684\u7c7b\u578b\u3001\u53c2\u6570\u7b49\u3002\u6a21\u578b\u8d8a\u590d\u6742\uff0cL(M)\u901a\u5e38\u8d8a\u5927\u3002<\/p>\n<\/li>\n<li>\n<p>\u6570\u636e\u7ed9\u5b9a\u6a21\u578b\u7684\u7f16\u7801\uff1a\u5176\u6b21\uff0c\u7ed9\u5b9a\u6a21\u578b\u540e\uff0c\u4f7f\u7528\u8be5\u6a21\u578b\u6765\u7f16\u7801\u6570\u636e\u3002\u5982\u679c\u6a21\u578b\u4e0e\u6570\u636e\u7684\u5339\u914d\u5ea6\u9ad8\uff0cL(D|M)\u5c06\u8f83\u5c0f\uff0c\u56e0\u4e3a\u6a21\u578b\u53ef\u4ee5\u6709\u6548\u5730\u201c\u89e3\u91ca\u201d\u6570\u636e\u3002<\/p>\n<\/li>\n<\/ol>\n<p>$L(D|M)$ \u7684\u8fdb\u4e00\u6b65\u89e3\u91ca :<\/p>\n<p>$L(D|M)$\u6307\u7684\u662f\u5728\u5df2\u7ecf\u9009\u62e9\u4e86\u4e00\u4e2a\u7279\u5b9a\u6a21\u578b$M$\u7684\u60c5\u51b5\u4e0b\uff0c\u7528\u8fd9\u4e2a\u6a21\u578b\u6765\u63cf\u8ff0\u89c2\u6d4b\u5230\u7684\u6570\u636e$D$\u6240\u9700\u8981\u7684\u7f16\u7801\u957f\u5ea6\u3002\u8fd9\u91cc\u7684\u7f16\u7801\u957f\u5ea6\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u7528\u6765\u91cf\u5316\u6a21\u578b$M$\u5bf9\u6570\u636e$D$\u62df\u5408\u7a0b\u5ea6\u7684\u4e00\u79cd\u65b9\u5f0f\u3002<\/p>\n<p>\u5982\u679c\u4e00\u4e2a\u6a21\u578b$M$\u4e0e\u6570\u636e$D$\u7684\u5339\u914d\u5ea6\u5f88\u9ad8\uff0c\u610f\u5473\u7740\u6a21\u578b\u80fd\u591f\u5f88\u597d\u5730\u6355\u6349\u5230\u6570\u636e\u4e2d\u7684\u89c4\u5f8b\u548c\u7ed3\u6784\uff0c\u90a3\u4e48\u6211\u4eec\u9700\u8981\u7684\u989d\u5916\u4fe1\u606f\u91cf\u6765\u63cf\u8ff0\u6570\u636e\u4e2d\u672a\u88ab\u6a21\u578b\u6355\u6349\u5230\u7684\u90e8\u5206\u5c31\u4f1a\u5f88\u5c0f\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6a21\u578b$M$\u53ef\u4ee5\u7528\u8f83\u5c11\u7684\u4fe1\u606f\u91cf\u6765\u201c\u89e3\u91ca\u201d\u6570\u636e$D$\uff0c\u56e0\u6b64$L(D|M)$\u5c31\u4f1a\u8f83\u5c0f\u3002<\/p>\n<p>\u76f8\u53cd\uff0c\u5982\u679c\u6a21\u578b$M$\u4e0e\u6570\u636e$D$\u7684\u5339\u914d\u5ea6\u4e0d\u9ad8\uff0c\u6a21\u578b\u65e0\u6cd5\u51c6\u786e\u5730\u6355\u6349\u6570\u636e\u7684\u7279\u6027\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u9700\u8981\u66f4\u591a\u7684\u4fe1\u606f\u6765\u63cf\u8ff0\u6570\u636e\u4e2d\u7684\u90a3\u4e9b\u672a\u88ab\u6a21\u578b\u6240\u89e3\u91ca\u7684\u90e8\u5206\u3002\u8fd9\u610f\u5473\u7740$L(D|M)$\u4f1a\u8f83\u5927\uff0c\u56e0\u4e3a\u6a21\u578b$M$\u9700\u8981\u66f4\u591a\u7684\u4fe1\u606f\u91cf\u6765\u8865\u5145\u90a3\u4e9b\u5b83\u672a\u80fd\u63cf\u8ff0\u7684\u6570\u636e\u7ec6\u8282\u3002<\/p>\n<p>\u56e0\u6b64\uff0c$L(D|M)$\u5b9e\u9645\u4e0a\u53cd\u6620\u4e86\u6a21\u578b$M$\u5bf9\u6570\u636e$D$\u7684\u62df\u5408\u7a0b\u5ea6\u3002<\/p>\n<h1>\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\uff08MDL\uff09\u7684\u5386\u53f2\u80cc\u666f<\/h1>\n<p>\u5b83\u662f\u5728\u4fe1\u606f\u8bba\u548c\u7f16\u7801\u7406\u8bba\u6df1\u523b\u5f71\u54cd\u4e0b\u53d1\u5c55\u8d77\u6765\u7684\uff0c\u7279\u522b\u662f\u514b\u52b3\u5fb7\u00b7\u9999\u519c\u5728\u4fe1\u606f\u8bba\u9886\u57df\u7684\u5f00\u521b\u6027\u5de5\u4f5c\u4e3aMDL\u63d0\u4f9b\u4e86\u7406\u8bba\u57fa\u7840\uff0c\u5c24\u5176\u662f\u5173\u4e8e\u6570\u636e\u538b\u7f29\u548c\u4fe1\u606f\u91cf\u5ea6\u91cf\u7684\u6982\u5ff5\u3002<\/p>\n<p>MDL\u539f\u7406\u7684\u63d0\u51fa\uff0c\u8d77\u6e90\u4e8eKolmogorov\u590d\u6742\u6027\u7406\u8bba\uff0c\u8fd9\u662f\u4e00\u5957\u63cf\u8ff0\u6570\u636e\u590d\u6742\u5ea6\u7684\u7406\u8bba\u6846\u67b6\uff0c\u7531Solomonoff\u3001Kolmogorov\u548cChaitin\u57281960\u5e74\u4ee3\u53d1\u5c55\u3002\u7279\u522b\u662fSolomonoff\u57281964\u5e74\u7684\u5de5\u4f5c\uff0c\u4e3a\u540e\u6765\u7684MDL\u7814\u7a76\u5960\u5b9a\u4e86\u57fa\u7840\uff0c\u867d\u7136Rissanen\u6700\u521d\u5e76\u4e0d\u4e86\u89e3Solomonoff\u7684\u5de5\u4f5c\uff0c\u4f46\u4ed6\u7684MDL\u539f\u7406\u53d7\u5230\u4e86Kolmogorov\u57281965\u5e74\u5de5\u4f5c\u7684\u542f\u53d1\u3002<\/p>\n<p>\u6b64\u5916\uff0cRissanen\u7684MDL\u539f\u7406\u8fd8\u53d7\u5230\u4e86Akaike\u7684\u8d64\u6c60\u4fe1\u606f\u51c6\u5219\uff08AIC\uff09\u7684\u5f71\u54cd\uff0cAIC\u662f\u57fa\u4e8e\u4fe1\u606f\u8bba\u601d\u60f3\u7684\u6a21\u578b\u9009\u62e9\u65b9\u6cd5\u3002\u5c3d\u7ba1MDL\u4e0eAIC\u5728\u5b9e\u9645\u65b9\u6cd5\u548c\u57fa\u672c\u7406\u5ff5\u4e0a\u6709\u5f88\u5927\u4e0d\u540c\uff0c\u4f46AIC\u5bf9\u4e8eRissanen\u5f00\u53d1MDL\u7684\u542f\u793a\u4f5c\u7528\u4e0d\u5bb9\u5ffd\u89c6\u3002<\/p>\n<p>MDL\u539f\u7406\u4e0e\u6700\u5c0f\u6d88\u606f\u957f\u5ea6\uff08MML\uff09\u539f\u5219\u5bc6\u5207\u76f8\u5173\uff0cMML\u7531Wallace\u53ca\u5176\u540c\u4e8b\u57281968\u5e74\u5f00\u59cb\u63d0\u51fa\u3002\u867d\u7136Rissanen\u7684MDL\u601d\u60f3\u5927\u591a\u662f\u72ec\u7acb\u53d1\u5c55\u7684\uff0c\u4f46\u5b83\u4e0eWallace\u7684MML\u5728\u5b9e\u8df5\u4e2d\u975e\u5e38\u76f8\u4f3c\uff0c\u5c3d\u7ba1\u57fa\u672c\u7406\u5ff5\u5927\u4e0d\u76f8\u540c\u3002<\/p>\n<p>\u81eaRissanen\u57281978\u5e74\u9996\u6b21\u63d0\u51faMDL\u539f\u7406\u4ee5\u6765\uff0c\u8fd9\u4e2a\u6982\u5ff5\u7ecf\u5386\u4e86\u591a\u6b21\u53d1\u5c55\u548c\u5b8c\u5584\u3002\u65e9\u671f\u7684MDL\u5e94\u7528\u4e3b\u8981\u96c6\u4e2d\u5728\u6570\u636e\u538b\u7f29\u548c\u7b80\u5355\u6a21\u578b\u9009\u62e9\u95ee\u9898\u4e0a\u30021984\u5e74\uff0cRissanen\u5f15\u5165\u524d\u9a8c\u7801\uff0c1987\u5e74\u53c8\u5f15\u5165\u8d1d\u53f6\u65af\u6df7\u5408\u7801\uff0c\u8fd9\u4e9b\u5de5\u4f5c\u5bf9MDL\u7406\u8bba\u7684\u53d1\u5c55\u4ea7\u751f\u4e86\u91cd\u8981\u5f71\u54cd\u30021996\u5e74\uff0cRissanen\u4e0eShtarkov\u7684\u5de5\u4f5c\u8fdb\u4e00\u6b65\u5b8c\u5584\u4e86MDL\u7406\u8bba\uff0c\u5c24\u5176\u662f\u5728\u53c2\u6570\u590d\u6742\u6027\u6982\u5ff5\u7684\u5168\u9762\u53d1\u5c55\u65b9\u9762\u3002<\/p>\n<p>MDL\u539f\u7406\u4e0d\u4ec5\u6311\u6218\u4e86\u4f20\u7edf\u7684\u7edf\u8ba1\u5b66\u65b9\u6cd5\uff0c\u4e5f\u4e3a\u5904\u7406\u8fc7\u5ea6\u62df\u5408\u95ee\u9898\u63d0\u4f9b\u4e86\u4e00\u79cd\u5168\u65b0\u7684\u89c6\u89d2\u3002\u901a\u8fc7\u6700\u5c0f\u5316\u63cf\u8ff0\u6570\u636e\u548c\u6a21\u578b\u7684\u603b\u957f\u5ea6\u6765\u81ea\u7136\u5730\u60e9\u7f5a\u8fc7\u4e8e\u590d\u6742\u7684\u6a21\u578b\uff0cMDL\u5f62\u5f0f\u5316\u5730\u91cf\u5316\u4e86\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\uff0c\u7814\u7a76\u8005\u4eec\u5c06MDL\u539f\u7406\u6269\u5c55\u5230\u4e86\u66f4\u5e7f\u6cdb\u7684\u5e94\u7528\u9886\u57df\uff0c\u5305\u62ec\u673a\u5668\u5b66\u4e60\u3001\u7edf\u8ba1\u63a8\u65ad\u3001\u4fe1\u53f7\u5904\u7406\u7b49\uff0c\u6210\u4e3a\u6a21\u578b\u9009\u62e9\u548c\u7edf\u8ba1\u5b66\u4e60\u4e2d\u7684\u4e00\u79cd\u91cd\u8981\u65b9\u6cd5\u8bba\u3002<\/p>\n<p>\u4ee5\u4e0b\u662f\u4e00\u4e9b\u77e5\u540d\u7684MDL\u53d8\u4f53\uff0c\u8fd9\u4e9b\u4e5f\u662f\u9664\u4e0a\u8ff0\u4ecb\u7ecd\u7684\u4e24\u6b65\u90e8\u4e4b\u5916\u7684MDL\u7684\u5177\u4f53\u8ba1\u7b97\u65b9\u5f0f\u3002<\/p>\n<ol>\n<li>\n<p><strong>\u89c4\u8303\u5316\u6700\u5927\u4f3c\u7136\u7f16\u7801\uff08NML\uff09<\/strong>: \u4e00\u79cd\u901a\u8fc7\u8c03\u6574\u6a21\u578b\u590d\u6742\u5ea6\u6765\u60e9\u7f5a\u8fc7\u4e8e\u590d\u6742\u6a21\u578b\u7684\u65b9\u6cd5\uff0c\u5e76\u4e14\u5728\u6570\u636e\u7f16\u7801\u4e0a\u6700\u5927\u5316\u4f3c\u7136\u51fd\u6570\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u8d1d\u53f6\u65af\u4fe1\u606f\u51c6\u5219\uff08BIC\uff09<\/strong>: \u867d\u7136BIC\u6700\u521d\u5e76\u975e\u4e3aMDL\u8bbe\u8ba1\uff0c\u4f46\u5b83\u5728\u5f62\u5f0f\u4e0a\u4e0eMDL\u76f8\u4f3c\uff0c\u5305\u62ec\u4e86\u4e00\u4e2a\u60e9\u7f5a\u9879\u7528\u6765\u8003\u8651\u6a21\u578b\u590d\u6742\u5ea6\uff0c\u901a\u5e38\u4e0e\u6a21\u578b\u4e2d\u53c2\u6570\u7684\u6570\u91cf\u6210\u6b63\u6bd4\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6700\u5c0f\u6d88\u606f\u957f\u5ea6\uff08MML\uff09<\/strong>: \u8fd9\u662f\u4e0eMDL\u975e\u5e38\u76f8\u5173\u7684\u539f\u5219\uff0c\u5b83\u5728\u5b9e\u65bd\u65f6\u540c\u65f6\u8003\u8651\u4e86\u53c2\u6570\u4f30\u8ba1\u7684\u4e0d\u786e\u5b9a\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u9884\u6d4b\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\uff08PMDL\uff09<\/strong>: \u8fd9\u79cd\u65b9\u6cd5\u4e13\u6ce8\u4e8e\u6570\u636e\u7684\u672a\u6765\u503c\u7684\u9884\u6d4b\uff0c\u800c\u4e0d\u662f\u4ec5\u4ec5\u5bf9\u5df2\u77e5\u6570\u636e\u8fdb\u884c\u5efa\u6a21\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u968f\u7740MDL\u539f\u7406\u5728\u4e0d\u540c\u9886\u57df\u7684\u5e94\u7528\u65e5\u76ca\u5e7f\u6cdb\uff0c\u5df2\u7ecf\u5f00\u53d1\u4e86\u591a\u79cd\u8f6f\u4ef6\u5de5\u5177\u548c\u5e93\u6765\u8f85\u52a9\u5b9e\u73b0MDL\u539f\u7406\u3002\u8fd9\u4e9b\u5de5\u5177\u901a\u5e38\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u7684\u529f\u80fd\u548c\u63a5\u53e3\uff0c\u4f7f\u5f97\u7528\u6237\u53ef\u4ee5\u66f4\u5bb9\u6613\u5730\u5e94\u7528MDL\u539f\u7406\u6765\u8fdb\u884c\u6570\u636e\u5206\u6790\u548c\u6a21\u578b\u9009\u62e9\u3002\u67d0\u4e9b\u7edf\u8ba1\u8f6f\u4ef6\u5305\u548c\u673a\u5668\u5b66\u4e60\u5e93\u5305\u542b\u4e86MDL\u76f8\u5173\u7684\u529f\u80fd\u6216\u7b97\u6cd5\u5b9e\u73b0\uff1a<\/p>\n<ol>\n<li><a href=\"[https:\/\/github.com\/hlin117\/mdlp-discretization](https:\/\/github.com\/hlin117\/mdlp-discretization)\">Minimum Description Length Binning<\/a><\/li>\n<li><a href=\"[https:\/\/github.com\/taucompling\/mdlrnn](https:\/\/github.com\/taucompling\/mdlrnn)\">Minimum Description Length Recurrent Neural Networks<\/a><\/li>\n<\/ol>\n<h1>\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\uff08MDL\uff09\u7684\u5e94\u7528\u573a\u666f<\/h1>\n<p>\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\uff08MDL\uff09\u539f\u7406\u56e0\u5176\u72ec\u7279\u7684\u7406\u8bba\u6846\u67b6\u548c\u5e94\u7528\u7075\u6d3b\u6027\uff0c\u5728\u591a\u4e2a\u9886\u57df\u5185\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u573a\u666f\u3002\u4ee5\u4e0b\u662fMDL\u539f\u7406\u7684\u4e00\u4e9b\u4e3b\u8981\u5e94\u7528\u573a\u666f\uff1a<\/p>\n<p><strong>1. \u6570\u636e\u538b\u7f29<\/strong><\/p>\n<p>\u6570\u636e\u538b\u7f29\u662fMDL\u539f\u7406\u6700\u76f4\u63a5\u7684\u5e94\u7528\u4e4b\u4e00\u3002\u5728\u8fd9\u4e2a\u573a\u666f\u4e2d\uff0cMDL\u88ab\u7528\u6765\u5bfb\u627e\u6700\u80fd\u6709\u6548\u538b\u7f29\u6570\u636e\u7684\u7f16\u7801\u65b9\u6848\uff0c\u5373\u5bfb\u6c42\u5728\u7ed9\u5b9a\u6570\u636e\u96c6\u4e0a\u5b9e\u73b0\u6700\u5c0f\u7f16\u7801\u957f\u5ea6\u7684\u6a21\u578b\u3002\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u4ec5\u80fd\u591f\u51cf\u5c11\u5b58\u50a8\u7a7a\u95f4\u7684\u9700\u6c42\uff0c\u800c\u4e14\u8fd8\u80fd\u5728\u4e0d\u635f\u5931\u4fe1\u606f\u7684\u524d\u63d0\u4e0b\u6709\u6548\u4f20\u8f93\u6570\u636e\u3002<\/p>\n<p><strong>2. \u6a21\u578b\u9009\u62e9<\/strong><\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u548c\u673a\u5668\u5b66\u4e60\u9886\u57df\uff0cMDL\u539f\u7406\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6a21\u578b\u9009\u62e9\u95ee\u9898\u3002\u901a\u8fc7\u6bd4\u8f83\u4e0d\u540c\u6a21\u578b\u63cf\u8ff0\u6570\u636e\u6240\u9700\u7684\u603b\u957f\u5ea6\uff0cMDL\u5e2e\u52a9\u9009\u62e9\u65e2\u80fd\u591f\u826f\u597d\u62df\u5408\u6570\u636e\u53c8\u4e0d\u8fc7\u5ea6\u590d\u6742\u7684\u6a21\u578b\u3002\u8fd9\u79cd\u65b9\u6cd5\u7279\u522b\u9002\u7528\u4e8e\u5904\u7406\u8fc7\u62df\u5408\u95ee\u9898\uff0c\u786e\u4fdd\u9009\u51fa\u7684\u6a21\u578b\u5177\u6709\u826f\u597d\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n<p><strong>3. \u53c2\u6570\u4f30\u8ba1<\/strong><\/p>\n<p>MDL\u539f\u7406\u4e5f\u53ef\u7528\u4e8e\u53c2\u6570\u4f30\u8ba1\uff0c\u7279\u522b\u662f\u5728\u5b58\u5728\u5927\u91cf\u53c2\u6570\u65f6\u5bfb\u627e\u6700\u4f73\u53c2\u6570\u8bbe\u7f6e\u7684\u60c5\u51b5\u3002\u901a\u8fc7\u6700\u5c0f\u5316\u63cf\u8ff0\u53c2\u6570\u548c\u6570\u636e\u7684\u603b\u957f\u5ea6\uff0cMDL\u63d0\u4f9b\u4e86\u4e00\u79cd\u91cf\u5316\u7684\u65b9\u5f0f\u6765\u8bc4\u4f30\u4e0d\u540c\u53c2\u6570\u8bbe\u7f6e\u7684\u6548\u679c\uff0c\u4ece\u800c\u627e\u5230\u6700\u5408\u9002\u7684\u53c2\u6570\u503c\u3002<\/p>\n<p><strong>4. \u4fe1\u53f7\u5904\u7406<\/strong><\/p>\n<p>\u5728\u4fe1\u53f7\u5904\u7406\u9886\u57df\uff0cMDL\u539f\u7406\u88ab\u7528\u4e8e\u8bc6\u522b\u4fe1\u53f7\u4e2d\u7684\u6a21\u5f0f\u548c\u7ed3\u6784\uff0c\u4f8b\u5982\u5728\u566a\u58f0\u6570\u636e\u4e2d\u68c0\u6d4b\u4fe1\u53f7\u7684\u5b58\u5728\u6216\u4f30\u8ba1\u4fe1\u53f7\u7684\u53c2\u6570\u3002\u901a\u8fc7\u6700\u5c0f\u5316\u63cf\u8ff0\u4fe1\u53f7\u548c\u566a\u58f0\u7684\u6a21\u578b\u6240\u9700\u7684\u957f\u5ea6\uff0cMDL\u53ef\u4ee5\u5e2e\u52a9\u4ece\u590d\u6742\u7684\u6570\u636e\u4e2d\u63d0\u53d6\u6709\u4ef7\u503c\u7684\u4fe1\u606f\u3002<\/p>\n<p><strong>5. 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de Rooij, Peter D. Gr\u00fcnwald, Luckiness and Regret in Minimum Description Length Inference, 2011, 7, Pages 865-900.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>[latexpage] \u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\uff1a\u4e00\u4e2a\u7f8e\u4e3d\u7684\u60f3\u6cd5\uff0c\u5b83\u5c06\u7edf&#8230;<\/p>\n","protected":false},"author":1,"featured_media":518,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[23],"class_list":["post-252","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-machine-learning","tag-machine-learning"],"_links":{"self":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/252","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/comments?post=252"}],"version-history":[{"count":7,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/252\/revisions"}],"predecessor-version":[{"id":381,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/252\/revisions\/381"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/media\/518"}],"wp:attachment":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/media?parent=252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/categories?post=252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/tags?post=252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}