{"id":148,"date":"2022-11-15T21:10:18","date_gmt":"2022-11-15T13:10:18","guid":{"rendered":"http:\/\/blog.minegician.cn\/?p=148"},"modified":"2023-01-20T11:28:29","modified_gmt":"2023-01-20T03:28:29","slug":"%e5%8d%b7%e7%a7%af%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e5%ad%a6%e4%b9%a0%e7%ac%94%e8%ae%b0","status":"publish","type":"post","link":"http:\/\/blog.minegician.cn\/?p=148","title":{"rendered":"\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u5b66\u4e60\u7b14\u8bb0"},"content":{"rendered":"

\u56fe\u50cf\u5377\u79ef<\/h3>\n

\u4ece\u516c\u5f0f\u5f15\u5165<\/h4>\n
\n

$\\int _{-\u221e}^\u221e f(\u03c4)g(x-\u03c4)d\u03c4$ <\/p>\n<\/blockquote>\n

\u7b80\u4f8b\uff1a<\/p>\n

\u5047\u8bbe\u6709\u4e00\u4e2a\u7cfb\u7edf\uff0c\u5168\u5929\u4e0d\u95f4\u65ad\u8f93\u5165\u4e0d\u5b9a\u91cf\u7684\u80fd\u91cf\uff0c\u540c\u65f6\u6309\u67d0\u4e2a\u66f2\u7ebf\u6d88\u8017\u80fd\u91cf<\/p>\n

\u67d0\u65f6\u523b\u8f93\u5165\u91cf\u4e0e\u65f6\u95f4\u5173\u7cfb\u4e3a $f(x)$ \uff1b\u540c\u65f6\uff0c\u6bcf\u4e00\u4efd\u80fd\u91cf\u7684\u5269\u4f59\u6bd4\u4f8b\u4e0e\u8f93\u5165\u540e\u65f6\u95f4\u5173\u7cfb\u4e3a $g(x)$ <\/p>\n

\n

\u5bf9\u4e8e\u65f6\u95f4\u70b9 $\u03c4$ \u7684\u80fd\u91cf\u8f93\u5165\uff0c\u5728\u65f6\u95f4\u4e3a $x$ \u65f6\u5269\u4f59\u91cf\u4e3a $f(\u03c4)g(x-\u03c4)$ <\/p>\n<\/blockquote>\n

    \n
  • \u8bbe $x$ \u4e3a\u603b\u7684\u80fd\u91cf\u8f93\u5165\u65f6\u95f4\u8f74\uff0c\u6c42 $t$ \u65f6\u523b\u603b\u7684\u5269\u4f59\u80fd\u91cf\u2014\u2014 $\\int _0^t f(x)g(t-x)dx$ <\/li>\n<\/ul>\n

    \"uTools_1665456235074\"<\/div><\/p>\n
    \n

    \u4e00\u4e2a\u65f6\u95f4\u70b9\u7684\u603b\u80fd\u91cf\uff0c\u662f\u8fc7\u53bb\u6bcf\u4e2a\u65f6\u95f4\u70b9\u8f93\u5165\u80fd\u91cf\u7684\u79ef\u5206<\/p>\n

    \u800c\u88ab\u79ef\u5206\u7684\u662f\u4e24\u4e2a\u51fd\u6570\uff0c\u4ed6\u4eec\u7684\u53c2\u6570\u5206\u522b\u662f\u4e00\u4e2a\u65f6\u95f4\u70b9\u548c\u4e00\u4e2a\u65f6\u95f4\u5dee\uff0c\u4e14\u5bfc\u6570\u6070\u76f8\u53cd<\/p>\n<\/blockquote>\n

    \"image-20221011105222243\"<\/div><\/p>\n
      \n
    • \u82e5\u5c06\u4ee5\u4e0a\u79ef\u5206\u7684\u65f6\u95f4\u4e0a\u4e0b\u9650\u7531 0 ~ $t$ \u6539\u4e3a\u65e0\u7a77\u5927\uff0c\u5c31\u5f97\u5230\u4e86\u6807\u51c6\u7684\u5377\u79ef\u516c\u5f0f<\/li>\n<\/ul>\n

      \u56fe\u50cf\u7684\u5377\u79ef<\/h4>\n

      \u5bf9\u50cf\u7d20\u77e9\u9635\u4f7f\u7528 3*3 \u5377\u79ef\u6838\uff0c\u6700\u5916\u5708\u4e3a 0\uff0c\u6bcf\u6b21\u5377\u79ef\u6838\u79fb\u52a8\u65f6\uff0c\u91cd\u53e0\u4f4d\u7f6e\u76f8\u4e58\u540e\u5e76\u6c42\u548c\uff0c\u4fdd\u5b58\u5728\u4e2d\u5fc3\u4f4d\u7f6e<\/p>\n

      \u76f8\u5f53\u4e8e\u5377\u79ef\u6838\u6bcf\u6b21\u79fb\u52a8\uff0c\u90fd\u4f1a\u6c42\u4e00\u6b21 3*3 \u533a\u95f4\u5185\u51fd\u6570\u76f8\u4e58\u7ed3\u679c\u7684\u79ef\u5206<\/p>\n

      \u8fdb\u4e00\u6b65\u7406\u89e3<\/h4>\n

      \u62bd\u8c61\u4e00\u4e0b\uff0c\u5c31\u53d8\u6210\u2014\u2014<\/p>\n

      \u67d0\u4e2a\u53d8\u91cf\u4f1a\u4ea7\u751f\u5f71\u54cd\uff0c\u968f\u7740\u4e00\u5b9a\u56e0\u7d20\u4f1a\u4e0d\u65ad\u53d8\u5316\u3001\u7d2f\u79ef\u3002$33$ \u5377\u79ef\u6838\u7684\u4f5c\u7528\u5c31\u662f\u8ba1\u7b97\u5468\u56f4\u4e00\u5708\u50cf\u7d20\u5bf9\u5f53\u524d\u50cf\u7d20\u5f71\u54cd\u7684\u7ed3\u679c\u3002\u4e00\u822c\u5982\u679c $3<\/em>3$ \u80fd\u6e05\u695a\u53cd\u6620\u6574\u4f53\u7279\u5f81\u5c31\u4e0d\u4f1a\u8003\u8651\u66f4\u5927\u7684\u5377\u79ef\u6838<\/p>\n

      \n

      \u4f8b\u5982\uff0c9 \u4e2a 1\/9 \u7684\u5377\u79ef\u6838\uff0c\u53ef\u4ee5\u5bf9\u6bcf\u4e2a 3*3 \u533a\u57df\u6c42\u5e73\u5747\u503c\uff0c\u6700\u7ec8\u6548\u679c\u5c31\u662f\u8ba9\u56fe\u50cf\u5e73\u6ed1<\/p>\n<\/blockquote>\n

      \u8bbe\u5b9a\u70b9\u50cf\u7d20\u4e3a $(m,n)$\uff0c\u663e\u7136\u6574\u4e2a\u56fe\u50cf\u6bcf\u4e2a\u70b9\u5f53\u524d\u7684\u503c\u662f $f(x,y)$\uff0c\u5468\u56f4\u70b9\u7684\u5f71\u54cd\u53ef\u4ee5\u8bbe\u4e3a $g(m-x,n-y)$\u3002\u6bcf\u4e2a\u50cf\u7d20\u70b9\u5377\u79ef\u540e\u7684\u503c\u5c31\u662f\u79bb\u6563\u7684 $\\sum f*g$<\/p>\n

      \u5f53\u524d\u70b9\u8bbe\u4e3a $(x,y)$\uff0c\u53d6\u5de6\u4e0b\u89d2 $(x-1,y-1)$<\/p>\n

      \u5219 $f*g=f(x,y)g(x-(x-1)),y-(y-1))=f(x,y)g(1,1)$ <\/p>\n

      \u53ef\u4ee5\u53d1\u73b0\uff0c\u5377\u79ef\u540e\u5448\u73b0\u7684 $g$ \u88ab\u7ffb\u5230\u4e86\u53f3\u4e0a\u89d2<\/p>\n

      \u51fa\u4e8e\u8ba1\u7b97\u673a\u8003\u8651\uff0c\u5c06\u7ffb\u8f6c\u540e\u7684 $g$ \u5b9a\u4e49\u4e3a\u5377\u79ef\u6838\uff0c\u81f3\u6b64\u5377\u79ef\u7684\u521d\u6b65\u8ba4\u8bc6\u8fbe\u6210<\/p>\n

      \u5377\u79ef\u795e\u7ecf\u7f51\u7edc<\/h4>\n

      \u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u53ef\u4ee5\u8bf4\u5c31\u662f\u7528\u4e8e\u56fe\u50cf\u8bc6\u522b\u7684<\/p>\n

      \u76f8\u6bd4\u4e8e\u5e73\u6ed1\u5377\u79ef\u6838\uff0c\u901a\u8fc7\u4fee\u6539\u6bcf\u4e2a\u4f4d\u7f6e\u7684\u7cfb\u6570<\/strong>\uff0c\u53ef\u4ee5\u8bd5\u63a2\u5e76\u4e13\u95e8\u6355\u6349<\/strong>\u548c\u7b5b\u9009\u5468\u56f4\u4e00\u5708\u7279\u5b9a\u5f62\u5f0f\u7684\u6392\u5217<\/strong><\/p>\n

      \u5904\u7406\u540e\u7684\u56fe\u50cf\u53ea\u4fdd\u7559\u4e86\u63cf\u8ff0\u7279\u5f81\u7684\u6570\u503c\u77e9\u9635\uff0c\u4ea4\u7531\u795e\u7ecf\u7f51\u7edc\u5904\u7406<\/p>\n

      \u603b\u7ed3<\/h4>\n
        \n
      1. \u5377\u79ef\u53ef\u4ee5\u5bf9\u4e0d\u7a33\u5b9a\u7684\u8f93\u5165\u5f97\u5230\u7a33\u5b9a\u7684\u8f93\u51fa\u503c<\/li>\n
      2. \u7528\u4e8e\u56fe\u50cf\u5904\u7406\uff0c\u53ef\u4ee5\u6355\u6349\u56fe\u50cf\u5c40\u90e8\u7279\u5f81<\/li>\n<\/ol>\n

        \u795e\u7ecf\u7f51\u7edc<\/h3>\n

        \u611f\u77e5\u673a\u4e0e\u795e\u7ecf\u7f51\u7edc<\/h4>\n

        \u795e\u7ecf\u7f51\u7edc\u7684\u59cb\u7956\uff0c\u5bf9\u6570\u636e\u8fdb\u884c\u5206\u7c7b\u3002\u7ed9\u6570\u636e\u8bad\u7ec3\uff0c\u5e76\u5b9e\u65f6\u8c03\u6574\u5206\u754c\u7ebf\uff0c\u5bf9\u4e8e\u66f4\u591a\u7279\u5f81\u7684\u5206\u7c7b\u5219\u4e3a\u5206\u754c\u9762\u7b49<\/p>\n

        \u8bf4\u767d\u4e86\u8981\u5f97\u5230\u4e00\u4e2a\u53d8\u91cf\u5bf9\u5e94\u7ef4\u5ea6\u7684\u8d85\u5e73\u9762\u3002\u56e0\u6b64\u611f\u77e5\u673a\u7684\u8868\u8fbe\u5f0f\u4e3a<\/p>\n

        $$t=f(\\sum^n_{i=1}w_ix_i+b)=f(W^TX)$$ W X \u662f n \u7ef4\u5411\u91cf\uff0c\u7b2c\u4e00\u7ef4\u7684\u503c\u662f b \u548c 1<\/p>\n

        \u4e24\u4e2a\u90e8\u5206\u53c8\u53eb\u7ebf\u6027\u51fd\u6570\u548c\u6fc0\u6d3b\u51fd\u6570<\/p>\n

        50\u5e74\u524d\u4eba\u4eec\u53d1\u73b0\u4e86\u611f\u77e5\u673a\u7684\u81f4\u547d\u7f3a\u9677\u2014\u2014\u65e0\u6cd5\u7528\u5404\u79cd\u5404\u6837\u7684\u66f2\u7ebf\u7279\u522b\u662f\u5706\u5708\u505a\u5206\u7c7b<\/p>\n

        \u4f46\u5bf9\u4e8e\u73b0\u5728\u7684\u5b66\u751f\uff0c\u90fd\u4e0d\u7b97\u662f\u95ee\u9898\u4e86\u2014\u2014<\/p>\n

        \u591a\u4e2a\u611f\u77e5\u673a\u7ec4\u5408\u4e3a\u5f02\u6216\u7ed3\u6784\uff0c\u5206\u4e24\u5c42\uff0c\u6bcf\u4e00\u5c42\u90fd\u662f\u5355\u4e2a\u903b\u8f91\u8fd0\u7b97\uff0c\u6bcf\u6b21\u53ea\u9700\u6839\u636e\u524d\u4e00\u6b65\u7684\u8f93\u5165\u786e\u5b9a\u6807\u51c6\u7ebf<\/p>\n

        \u5148\u5728\u5e95\u5c42\u8f93\u5165 x\uff0c\u7ecf\u8fc7\u4e24\u5c42\u7f51\u7edc\u5f97\u5230\u7ed3\u679c<\/p>\n

        \u4e8e\u662f\uff0c\u795e\u7ecf\u7f51\u7edc\u96cf\u5f62\u521d\u73b0\uff0c\u611f\u77e5\u673a\u5c31\u662f\u201c\u795e\u7ecf\u5143\u201d\uff0c\u8f93\u5165\u591a\u4e2a\u6570\u636e\uff0c\u8f93\u51fa\u4e00\u4e2a\u6807\u51c6\u7ebf<\/p>\n

        \u795e\u7ecf\u7f51\u7edc<\/h4>\n

        \u57fa\u672c\u7ed3\u6784<\/h5>\n

        \u8f93\u5165\u5c42\u2014\u2014\u9690\u85cf\u5c42\u2014\u2014\u8f93\u51fa\u5c42\uff0c\u6bcf\u5c42\u90fd\u80fd\u6709\u591a\u4e2a\u7ed3\u70b9<\/p>\n

        \u5206\u7c7b\u65b9\u5f0f\u4f8b<\/h5>\n

        \u5168\u8fde\u63a5\u795e\u7ecf\u7f51\u7edc\uff08\u6bcf\u4e2a\u7ed3\u70b9\u90fd\u63a5\u6536\u4e0a\u4e00\u5c42\u6240\u6709\u8f93\u5165\uff09<\/p>\n

        \u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff08\u4ece\u524d\u5411\u540e\u5355\u5411\u63a8\u8fdb\uff09<\/p>\n

        \u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff08\u7ed3\u70b9\u81ea\u5faa\u73af\uff09<\/p>\n

        \u5de5\u4f5c<\/h5>\n

        \u8f93\u5165\u6240\u6709\u7279\u5f81\uff0c\u7528\u611f\u77e5\u673a\u627e\u5230\u63cf\u8ff0\u7684\u7ebf\u6027\u51fd\u6570\u548c\u5224\u65ad\u7684\u6fc0\u6d3b\u51fd\u6570\uff0c\u9010\u5c42\u5224\u65ad\uff0c\u6700\u7ec8\u9009\u51fa\u6743\u91cd\u6700\u5927\u7684\u7ed3\u679c<\/p>\n

        \u6539\u8fdb<\/h5>\n

        \uff08\u53c2\u8003\u5434\u6069\u8fbe\uff09\u6fc0\u6d3b\u51fd\u6570\u7531 01 \u6539\u4e3a\u8fde\u7eed\u9636\u8dc3\u66f2\u7ebf\uff0c\u4ece\u975e\u9ed1\u5373\u767d\u6539\u4e3a\u53ef\u80fd\u6027\u8bc4\u4f30\u3002\u6548\u679c\u662f\u6bcf\u6b21\u5206\u7c7b\u4e0d\u518d\u9650\u4e8e 2 \u7c7b<\/p>\n

        \u7ec4\u7ec7\u795e\u7ecf\u7f51\u7edc\u8fc7\u7a0b\u4e2d\uff0c\u867d\u7136\u6ca1\u6709\u7ed9\u5b9a\u5224\u65ad\u6807\u51c6\uff0c\u4f46\u795e\u7ecf\u7f51\u7edc\u4f1a\u9010\u6e10\u5f62\u6210\u5bf9\u7279\u5f81\u7684\u4e00\u79cd\u6807\u51c6\u63cf\u8ff0<\/strong>\uff0c\u7528\u4e8e\u540e\u7eed\u5224\u65ad\u6570\u636e\u4e0e\u6807\u51c6\u7684\u504f\u5dee\u3002\u968f\u7740\u8bad\u7ec3\u8fdb\u7a0b\uff0c\u795e\u7ecf\u7f51\u7edc\u7684\u63cf\u8ff0\u80fd\u529b\u8d8a\u53d1\u719f\u7ec3<\/p>\n

        \n

        \u9636\u8dc3\u66f2\u7ebf\u5728\u7a7a\u95f4\u4e5f\u80fd\u4f53\u73b0\uff0c\u6539\u53d8\u8f93\u5165\u7279\u5f81\uff0c\u6bcf\u4e2a\u8f93\u51fa\u66f2\u9762\u90fd\u4f1a\u53d8\u5316<\/p>\n<\/blockquote>\n

        \u603b\u7ed3<\/h5>\n
          \n
        1. \n

          \u6fc0\u6d3b\u51fd\u6570\u8d4b\u4e88\u4e86\u9009\u62e9\u8fc7\u7a0b\uff0c\u4f7f\u7ed3\u679c\u4e0d\u80fd\u4ee5\u4e00\u822c\u5f62\u5f0f\u5448\u73b0\uff0c\u4f7f\u5f97\u795e\u7ecf\u7f51\u7edc\u5f00\u59cb\u590d\u73b0\u4eba\u7684\u975e\u7ebf\u6027\u8ba4\u77e5\u8fc7\u7a0b<\/p>\n<\/li>\n

        2. \n

          \u76ee\u524d AI \u7684\u9009\u62e9\u6709\u7528\u5230\u7edf\u8ba1\u5b66\uff0c\u4e0d\u8fc7\u672a\u6765\u76ee\u6807\u4ecd\u7136\u662f\u4ee5\u4eba\u8111\u4e3a\u8303\u5f0f<\/p>\n

          \n

          \u8eab\u4e3a AI \u4e50\u89c2\u4e3b\u4e49\u8005\uff0c\u6211\u8ba4\u4e3a\u76ee\u524d AI \u7f3a\u7684\u8fd8\u662f\u7b97\u529b\uff0c\u4eba\u8111\u7684\u590d\u6742\u7a0b\u5ea6\u4f17\u6240\u5468\u77e5\uff08\u6211\u4e0d\u5426\u8ba4\u5fc3\u7406\u4e0a\u7684\u6050\u6016\u8c37<\/p>\n

          \u4ec5\u9488\u5bf9\u8ba4\u77e5\u8fc7\u7a0b\u800c\u8a00\uff0c\u56e0\u4e3a\u6211\u8ba4\u4e3a\u673a\u5668\u7ed3\u6784\u548c\u7ec6\u80de\u751f\u7269\u672c\u8eab\u5c31\u6ca1\u6709\u53ef\u6bd4\u6027\uff08\u5f88\u957f\u4e00\u6bb5\u65f6\u95f4\u5185<\/p>\n<\/blockquote>\n<\/li>\n<\/ol>\n

          \u635f\u5931\u51fd\u6570<\/h3>\n

          \u635f\u5931\u51fd\u6570<\/h4>\n

          \u6700\u5c0f\u4e8c\u4e58\u6cd5<\/h5>\n
            \n
          • \u6570\u636e\u5e0c\u671b\u5f97\u5230\u7684\u6807\u7b7e $x_i$\uff0c\u795e\u7ecf\u7f51\u7edc\u8f93\u51fa\u7684\u7ed3\u679c $yi$\uff0c\u76f4\u63a5\u7528 $\\sum<\/em>{i=1}^n(y_i-x_i)^2$ \u8868\u793a\u635f\u5931<\/li>\n<\/ul>\n
            \n

            \u5e73\u65b9\u662f\u65b9\u4fbf\u540e\u7eed\u68af\u5ea6\u4e0b\u964d\u6c42\u5bfc\uff0c\u6709\u65f6\u524d\u9762\u53ef\u4ee5\u52a0 $\\frac{1}{2}$ \u8f85\u52a9\u6c42\u5bfc<\/p>\n

            \u5b9e\u9645\u4f7f\u7528\u6709\u9650\u5236<\/p>\n<\/blockquote>\n

            \u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u6cd5<\/h5>\n

            \u6982\u7387\u5b66\u7684\u5185\u5bb9<\/p>\n

            \u5f53\u6ee1\u8db3\u6761\u4ef6 $\u03b8$ \u65f6\uff0c\u5bf9\u4e8e\u6240\u6709\u53ef\u80fd\u7ed3\u679c\u4e2d\u7684\u4e00\u9879\uff0c\u6982\u7387\u4e3a $\\prod_{i=1}^kP(C_i|\u03b8)$ \uff0c\u5176\u4e2d\u4e00\u9879\u53d1\u751f\u548c\u5176\u4ed6\u9879\u4e0d\u53d1\u751f\u662f\u540c\u65f6\u51fa\u73b0\u7684\uff0c\u6545\u4e3a\u6982\u7387\u4e58\u79ef\uff0c\u5bf9\u4e8e\u5df2\u77e5\u7684\u53ef\u80fd\u6027\uff0c\u9009\u51fa<\/strong>\u7ed3\u679c\uff08\u4f3c\u7136\u503c<\/strong>\uff09\u6700\u5927\u7684<\/strong>\u4e00\u4e2a\u4e3a\u6700\u53ef\u80fd\u7684\u6a21\u578b<\/strong><\/p>\n

            \u4eba\u53bb\u5224\u65ad\u6216\u4f30\u8ba1\u4e00\u4ef6\u4e8b\u65f6\uff0c\u662f\u9075\u5faa\u5df2\u5b58\u5728\u7684\u8ba4\u77e5\uff0c\u795e\u7ecf\u7f51\u7edc\u5982\u679c\u80fd\u591f\u8ba4\u77e5\uff0c\u81ea\u7136\u80fd\u901a\u8fc7\u4e0d\u65ad\u5c1d\u8bd5\uff0c\u903c\u8fd1\u4eba\u8111\u5185\u6a21\u578b<\/p>\n

            \u786e\u5b9a\u4e00\u4e2a\u6a21\u578b\u7136\u540e\u7ed9\u51fa\u4f3c\u7136\u503c\uff0c\u5219 $\u03b8$ \u4e0e\u795e\u7ecf\u7f51\u7edc\u7ed3\u70b9\u7684\u7ebf\u6027\u7cfb\u6570 $W,b$ \u76f8\u5173\uff0c\u8fdb\u800c\u4e0e\u5224\u65ad\u7ed3\u679c $y_i$ \u76f8\u5173\uff0c\u5176\u4e2d\u4e3a\u67d0\u4e2a\u6807\u7b7e $x_i$ \u7684\u6982\u7387\u53ef\u4ee5\u76f4\u63a5\u7528\u5f0f\u5b50\u8868\u793a\u51fa\u6765\u3002\u6bd4\u5982\u5728\u5224\u65ad 01 \u65f6\uff0c\u5224\u65ad\u4e3a $y_i$ \u6982\u7387\u76f4\u63a5\u53d8\u6210 $y_i^{x_i}(1-y_i)^{1-x_i}$ \u518d\u6c42 $\\prod$ <\/p>\n

              \n
            • \n

              \u7136\u540e\u6211\u4eec\u7528 log \u5c06 $\\prod$ \u8f6c\u4e3a $\\sum$ \u5c31\u5f97\u5230\u4e86\u7b2c\u4e8c\u79cd\u635f\u5931\u51fd\u6570\uff1a$\\sum_{i=1}^n(x_i\u00b7logy_i+(1-x_i)\u00b7log(1-y_i))$<\/p>\n

              \u663e\u7136\u8981\u6c42\u4e0a\u5f0f\u7684\u6781\u5927\u503c\uff0c\u4f46\u4e3a\u7edf\u4e00\u6807\u51c6\uff0c\u5728\u524d\u9762\u52a0\u4e0a\u8d1f\u53f7\u6c42\u6781\u5c0f\u503c<\/strong><\/p>\n<\/li>\n<\/ul>\n

              \u4ea4\u53c9\u71b5<\/h5>\n
                \n
              1. \n

                \u4fe1\u606f\u91cf<\/p>\n

                \u4fe1\u606f\u91cf\u5927\u5c0f\u53ef\u4ee5\u7406\u89e3\u4e3a\u8be6\u7ec6\u7a0b\u5ea6\uff0c\u5373\u6982\u7387\u4e8b\u4ef6\u53d8\u4e3a\u786e\u5b9a\u4e8b\u4ef6\u9700\u8981\u7684\u201c\u80fd\u91cf\u201d\uff0c\u82e5\u5728\u4e00\u4efd\u786e\u5b9a\u7684\u57fa\u7840\u4e0a\u518d\u52a0\u786e\u5b9a\uff0c\u80fd\u5f97\u5230\u65b0\u7684\u4fe1\u606f\u91cf\uff0c\u5b9a\u4e49\u4e3a\u52a0\u6cd5\u3002\u9996\u5148\u53ef\u4ee5\u786e\u5b9a\uff0c\u4fe1\u606f\u91cf\u8d8a\u5927\uff0c\u6982\u7387\u8d8a\u5c0f\uff0c\u53cd\u76f8\u5173\uff0c\u6982\u7387 < 1\uff0c\u4fe1\u606f\u91cf > 0<\/p>\n

                \u8bbe\u53d8\u91cf $x$ \uff1a\u53d1\u751f\u6982\u7387\uff0c\u4fe1\u606f\u91cf\u76f8\u52a0\u7b49\u4e8e\u6982\u7387\u76f8\u4e58\uff0c$f(x_1\u00b7x_2)=f(x_1)+f(x_2)$\uff0c\u76f8\u4e58\u53d8\u76f8\u52a0\u662f\u4e0d\u662f\u4f3c\u66fe\u76f8\u8bc6\uff1f\u6240\u4ee5\u8bbe $f(x)$ \u4e3a\u5bf9\u6570\u4f7f\u5176\u5408\u7406\uff0c\u5982\u679c\u6211\u4eec\u4ee5\u6bcf\u79cd 0\/1 \u4e8b\u4ef6\u53d8\u4e3a\u786e\u5b9a\u4e8b\u4ef6\u4e3a\u6807\u51c6\uff0c\u5f97\u5230\u6700\u57fa\u672c\u7684\u516c\u5f0f\u4e3a<\/p>\n

                $f(x)=-log_2x$\uff0c\u800c\u4fe1\u606f\u5355\u4f4d\u6070\u4e3a bit<\/p>\n<\/li>\n

              2. \n

                \u71b5<\/p>\n

                \u71b5\u4ee3\u8868\u7cfb\u7edf\u4e0d\u786e\u5b9a\u5ea6\uff0c\u4e0d\u786e\u5b9a\u5ea6\u53c8\u53d7\u7cfb\u7edf\u4e2d\u5404\u4e2a\u4e8b\u4ef6\u5f71\u54cd\uff0c\u5c06\u71b5\u5b9a\u4e49\u4e3a\u7cfb\u7edf\u4fe1\u606f\u91cf\u7684\u671f\u671b\u5373\u53ef<\/p>\n<\/li>\n

              3. \n

                \u4ea4\u53c9\u71b5<\/p>\n

                \u56de\u5f52\u4e3b\u9898\uff0c\u8981\u6c42\u51fa\u4e24\u4e2a\u7cfb\u7edf $p,q$ \u7684\u8bef\u5dee\uff0c\u4ee5 $p$ \u4e3a\u57fa\u51c6\uff0c\u5173\u4e8e $p$ \u4e2d\u7684\u4e8b\u4ef6\u6982\u7387\uff0c\u6839\u636e\u4fe1\u606f\u91cf\u5dee\u503c\uff0c\u5c31\u53ef\u4ee5\u6c42\u4e24\u4e2a\u7cfb\u7edf\u7684\u76f8\u5bf9\u71b5 $\\sum_{i=1}^mp_i\u00b7(f_Q(q_i)-f_P(pi))$\uff0c\u53c8\u79f0 KL \u6563\u5ea6 $D<\/em>{KL}(P||Q)$\uff0c\u53bb\u6389 $p$ \u7684\u671f\u671b\u71b5\uff0c\u5269\u4f59\u7684\u5c31\u662f\u4ea4\u53c9\u71b5 $H(P,Q)=\\sum_{i=1}^mp_i\u00b7(-log_2q_i)$<\/p>\n

                \u56e0\u4e3a\u5409\u5e03\u65af\u4e0d\u7b49\u5f0f\uff08\u901a\u8fc7\u653e\u7f29\u8bc1\u660e\uff09\uff0c\u4e0a\u9762\u7684\u76f8\u5bf9\u71b5\u503c\u603b\u662f $\\ge0$\uff0c\u56e0\u6b64\u53ea\u8003\u8651\u5355\u8c03\u7684\u4ea4\u53c9\u71b5\u5c31\u53ef\u4ee5\u8861\u91cf\u635f\u5931\u4e86<\/p>\n

                \u5728\u8ba1\u7b97\u65f6\uff0c\u5982\u679c p \u548c q \u7684\u4e8b\u4ef6\u6570\u91cf\u4e0d\u540c\uff0c\u76f4\u63a5\u4ee5\u6570\u91cf\u66f4\u9ad8\u7684\u4e3a\u51c6\uff08\u5206\u5e03\u7cbe\u7ec6\uff09\u5bf9\u76f8\u540c\u4f4d\u7f6e\u7684\u4e8b\u4ef6\u6c42\u671f\u671b<\/p>\n<\/li>\n<\/ol>\n

                  \n
                • \n

                  \u635f\u5931\u51fd\u6570<\/p>\n

                  \u6211\u4eec\u4ee5\u56fe\u50cf\u8bc6\u522b\u4e3a\u4f8b\uff0c\u57fa\u51c6 $p$ \u53ef\u4ee5\u76f4\u63a5\u66ff\u6362\u4e3a\u5df2\u88ab\u786e\u5b9a\u6807\u7b7e\u7684\u201c\u53ef\u80fd\u4e8b\u4ef6\u201d $x$\uff0c\u5373 $p$ \u662f\u786e\u5b9a\u7684 0 \u6216 1\uff0c\u603b\u4e8b\u4ef6\u6570\u53d6 $q$ \u6c42\u671f\u671b\u9700\u8981\u5224\u65ad\u7684\u603b\u56fe\u50cf\u6570\uff08\u66f4\u591a\u7684 p \u548c q \u4e8b\u4ef6\u6570\u6309\u4e0a\u9762\u7684\u65b9\u6cd5\u5747\u5300\u5904\u7406\u5c31\u884c\uff09<\/p>\n

                  \u7531\u4e8e\u8003\u8651\u4fe1\u606f\u65f6 p \u548c q \u90fd\u662f\u786e\u5b9a\u7ed3\u679c\uff0c\u4f46\u5b9e\u9645\u66ff\u6362\u8fc7\u6fc0\u6d3b\u51fd\u6570\u7684\u795e\u7ecf\u7f51\u7edc\u53ea\u4f1a\u8f93\u51fa\u4e00\u4e2a\u53ef\u4fe1\u5ea6\uff0c\u9700\u8981\u4eba\u4e3a\u6dfb\u52a0\u4e00\u6b21\u5224\u65ad\uff0c\u4e5f\u5c31\u662f $x$ \u53d6\u6807\u7b7e 0\/1 \u65f6\u76f8\u5e94\u7684\u8f93\u51fa $y$ \u5728\u6307\u5b9a\u6807\u7b7e\u4e0a\u7684\u53ef\u4fe1\u5ea6\uff08\u6bd4\u5982 0 \u65f6\u5c31\u53d6\u4e0d\u53ef\u4fe1\u5ea6\uff09\u6c42\u671f\u671b\uff0c\u6700\u7ec8\u5f97\u5230<\/p>\n

                  $\\sum_{i=1}^mx_i\u00b7(-log_2qi)=-\\sum<\/em>{i=1}^m(x_i\u00b7log_2y_i+(1-x_i)\u00b7log_2(1-y_i))$<\/p>\n

                  \n

                  \u8fd9\u91cc\u8ba1\u7b97 $1-x_i$ \u662f\u56e0\u4e3a\u53ea\u6709\u4e24\u79cd\u60c5\u51b5\uff0c\u975e\u6b64\u5373\u5f7c\uff0c\u9047\u5230\u66f4\u591a\u60c5\u51b5\uff0c\u5176\u5b9e\u5199\u51fa\u6765\u5f0f\u5b50\u4e5f\u662f\u7c7b\u4f3c\u7684<\/p>\n<\/blockquote>\n

                  \u53ef\u4ee5\u770b\u51fa\u5f62\u5f0f\u548c\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u6cd5\u51e0\u4e4e\u76f8\u540c\uff0c\u4f46\u8fd9\u91cc\u7684\u4fe1\u606f\u662f\u6709\u610f\u4e49\u7684\u4e1c\u897f\uff0c\u8d1f\u53f7\u4e5f\u4e0d\u662f\u540e\u6765\u52a0\u4e0a\u7684<\/p>\n<\/li>\n<\/ul>\n

                  \u68af\u5ea6\u4e0b\u964d<\/h3>\n

                  \u53cd\u5411\u4f20\u64ad<\/h4>\n
                  \n

                  \u4ee5\u611f\u77e5\u673a\u4e3a\u5355\u4f4d\uff0c\u4fe1\u606f\u4f20\u64ad\u7684\u57fa\u7840\u8fd8\u662f\u6bcf\u4e2a\u7ebf\u6027\u51fd\u6570\u4e5f\u5c31\u662f W b<\/p>\n

                  \u6b63\u5411\u4f20\u64ad\u7531 W b \u8f93\u51fa\u4fe1\u606f\uff0c\u53cd\u5411\u4f20\u64ad\u5373\u5c06\u6700\u7ec8\u7684\u504f\u5dee\u5411\u524d\u9006\u63a8\u4ece\u800c\u4fee\u6b63 W b<\/p>\n<\/blockquote>\n

                    \n
                  • \n

                    \u601d\u8def 1<\/p>\n

                    \u6bd4\u5982\u7531\u7b2c 3 \u5c42\u7684\u67d0\u4e00\u4e2a\u8f93\u51fa $a^{[3]}$ \u8ba1\u7b97\u635f\u5931\u51fd\u6570\u503c $J$\uff0c\u51b3\u5b9a\u7684\u56e0\u7d20\u5c31\u662f\u63a5\u53d7\u5230\u7684\u6240\u6709\u7b2c\u4e8c\u5c42\u7684 $W^{[2]}$ $b^{[2]}$ \u548c\u7b2c\u4e8c\u5c42\u8f93\u51fa $a^{[2]}$<\/p>\n

                    \u5176\u4e2d $W$ \u548c $b$ \u53ea\u770b\u4e0a\u4e00\u5c42\uff0c\u76f4\u63a5\u53d1\u6563\u5230\u4e0a\u4e00\u5c42\u5404\u7ed3\u70b9\u7684\u5f71\u54cd\u6743\u91cd\u6765\u4fee\u6b63\uff0c\u524d\u9762\u5404\u5c42\u7684 $W$ $b$ \u7c7b\u63a8<\/p>\n

                    \u800c a \u7684\u53cd\u5411\u4f20\u64ad\u4f1a\u6bd4\u8f83\u6df1\u5165\uff0c\u4e0a\u4e00\u5c42 $a^{[i]}$ \u6bcf\u4e2a\u611f\u77e5\u673a\u7684\u4fee\u6b63\u90fd\u7531\u4e0b\u4e00\u5c42\u8fde\u63a5\u7684\u6240\u6709 $a^{[i+1]}$ \u5f71\u54cd\uff0c\u5c31\u53cd\u5411\u6c42\u6743\u91cd<\/p>\n

                    \u6700\u540e\u6240\u6709\u7684\u53c2\u6570\u90fd\u80fd\u83b7\u5f97\u81ea\u5df1\u7684\u6743\u91cd\uff0c\u5c31\u53ef\u4ee5\u5f00\u59cb\u4fee\u6b63\u5de5\u4f5c\u4e86<\/p>\n<\/li>\n

                  • \n

                    \u601d\u8def 2\uff08\u7528\u68af\u5ea6\uff09<\/p>\n

                    \u7528\u5411\u91cf\u4f5c\u8861\u91cf\uff0c\u6c42\u635f\u5931\u503c $J$ \u7684\u68af\u5ea6 $\\nabla J(W,a,b)=(\u03b1,\u03b2,\u03b3)$\uff0c\u5c31\u627e\u5230\u4e86\u4e0b\u964d\u6700\u5feb\u7684\u8def\u5f84\uff0c\u56de\u5fc6\u9ad8\u6570\u8ba1\u7b97\u68af\u5ea6\uff0c\u8bbe $(\u03b1,\u03b2,\u03b3)$ \u4e3a 3 \u53d8\u91cf\u504f\u5bfc\u5411\u91cf\u5373\u68af\u5ea6\uff0c$W,a,b$ \u5404\u51cf\u53bb $\u03b7$ \u500d $\u03b1,\u03b2,\u03b3$ \u4e3a\u76ee\u6807\u503c<\/p>\n

                    \u53ef\u6c42\u51fa $W$ $b$ \u7684\u76ee\u6807\u503c\uff0c\u518d\u8bbe $J{\u524d\u4e00\u5c42}=\\beta=a-a<\/em>{\u76ee\u6807}$\uff0c\u5c31\u53ef\u4ee5\u7531 $a$ \u7ee7\u7eed\u5411\u524d\u4f20\u64ad\uff0c\u5230\u8fbe\u8d77\u59cb\u5c42\u540e $a^{[1]}$ \u4e0d\u518d\u5f71\u54cd\u635f\u5931\uff0c\u6700\u7ec8\u53ea\u5269 $W$ $b$<\/p>\n

                      \n
                    • \u7ed3\u679c\u5f88\u76f4\u89c2\uff0c\u7528\u94fe\u5f0f\u6c42\u504f\u5bfc\u6765\u6c42\u6700\u7ec8 $W$ $b$ \u5982\u4f55\u88ab\u4fee\u6b63<\/li>\n<\/ul>\n
                      \n

                      \u524d\u4e00\u5c42 $a$ \u7684 $J$ \u8ba1\u7b97\u9700\u8981\u5f53\u524d\u5c42 $a$ \u7684\u4fee\u6b63\u503c\uff0c\u6240\u4ee5\u5982\u679c\u6709\u4ece\u524d\u5411\u540e\u4e00\u4f20\u591a\u7684\u60c5\u51b5\uff0c\u6c42 $J_{\u524d\u4e00\u5c42}$ \u9700\u8981\u6c42\u5f53\u524d\u5c42\u6240\u6709\u504f\u5bfc $\u03b2$ \u7684\u5e73\u5747\u503c<\/p>\n

                        \n
                      • \u53e6\u5916\uff0c\u5173\u4e8e $W^{[i]}$ \u548c $b^{[i]}$ \u5982\u4f55\u5f97\u5230 $a^{[i+1]}$\uff0c\u8bbe\u7b2c $l$ \u5c42\u7b2c $i$ \u4e2a\u611f\u77e5\u673a\uff0c\u5148\u6c42\u51fa\u6bcf\u4e2a\u7ebf\u6027\u7ed3\u679c $z^{[l]}_i=W{[l]}_i\u00b7a^{[l]_i}+q^{[l]}_i$ \u518d\u7528\u6fc0\u6d3b\u51fd\u6570\u3002\u4e00\u7ec4\u611f\u77e5\u673a\u5199\u6210\u77e9\u9635\u4e58\u6cd5\u5f62\u5f0f\u5c31\u6bd4\u8f83\u7b80\u4fbf<\/li>\n<\/ul>\n<\/blockquote>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

                        \u56fe\u50cf\u5377\u79ef \u4ece\u516c\u5f0f\u5f15\u5165 $\\int _{-\u221e}^\u221e f(\u03c4)g(x-\u03c4)d\u03c4$ \u7b80\u4f8b\uff1a \u5047\u8bbe\u6709\u4e00\u4e2a\u7cfb\u7edf\uff0c\u5168\u5929\u4e0d\u95f4 […]<\/p>\n","protected":false},"author":1,"featured_media":149,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-148","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-3"],"_links":{"self":[{"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=\/wp\/v2\/posts\/148","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=148"}],"version-history":[{"count":1,"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=\/wp\/v2\/posts\/148\/revisions"}],"predecessor-version":[{"id":151,"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=\/wp\/v2\/posts\/148\/revisions\/151"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=\/wp\/v2\/media\/149"}],"wp:attachment":[{"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=148"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=148"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.minegician.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}