{"id":477408,"date":"2023-08-09T09:14:25","date_gmt":"2023-08-09T09:14:25","guid":{"rendered":""},"modified":"2023-09-05T11:14:40","modified_gmt":"2023-09-05T11:14:40","slug":"hamiltonian-monte-carlo","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/cn\/wiki\/hamiltonian-monte-carlo\/","title":{"rendered":"\u54c8\u5bc6\u987f\u8499\u7279\u5361\u7f57"},"content":{"rendered":"

\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57 (HMC) \u662f\u4e00\u79cd\u7528\u4e8e\u8d1d\u53f6\u65af\u7edf\u8ba1\u548c\u8ba1\u7b97\u7269\u7406\u5b66\u7684\u590d\u6742\u91c7\u6837\u6280\u672f\u3002\u5b83\u65e8\u5728\u901a\u8fc7\u91c7\u7528\u6c49\u5bc6\u5c14\u987f\u52a8\u529b\u5b66\uff08\u4e00\u79cd\u6e90\u81ea\u7ecf\u5178\u529b\u5b66\u7684\u6570\u5b66\u6846\u67b6\uff09\u6765\u9ad8\u6548\u63a2\u7d22\u9ad8\u7ef4\u6982\u7387\u5206\u5e03\u3002\u901a\u8fc7\u6a21\u62df\u7269\u7406\u7cfb\u7edf\u7684\u884c\u4e3a\uff0cHMC \u751f\u6210\u7684\u6837\u672c\u5728\u63a2\u7d22\u590d\u6742\u7a7a\u95f4\u65b9\u9762\u6bd4 Metropolis-Hastings \u7b97\u6cd5\u7b49\u4f20\u7edf\u65b9\u6cd5\u66f4\u6709\u6548\u3002HMC \u7684\u5e94\u7528\u8303\u56f4\u5df2\u8d85\u51fa\u5176\u539f\u59cb\u9886\u57df\uff0c\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u548c\u4ee3\u7406\u670d\u52a1\u5668\u64cd\u4f5c\u7b49\u5404\u4e2a\u9886\u57df\u90fd\u6709\u7740\u5e7f\u9614\u7684\u5e94\u7528\u524d\u666f\u3002<\/p>\n

\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u7684\u8d77\u6e90\u5386\u53f2\u53ca\u5176\u9996\u6b21\u63d0\u53ca\u3002<\/h2>\n

\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u7b97\u6cd5\u6700\u65e9\u7531 Simon Duane\u3001Adrienne Kennedy\u3001Brian Pendleton \u548c Duncan Roweth \u5728 1987 \u5e74\u53d1\u8868\u7684\u9898\u4e3a\u201c\u6df7\u5408\u8499\u7279\u5361\u7f57\u201d\u7684\u8bba\u6587\u4e2d\u63d0\u51fa\u3002\u8be5\u65b9\u6cd5\u6700\u521d\u7528\u4e8e\u6a21\u62df\u7406\u8bba\u7269\u7406\u5b66\u9886\u57df\u683c\u70b9\u573a\u8bba\u4e2d\u7684\u91cf\u5b50\u7cfb\u7edf\u3002\u8be5\u7b97\u6cd5\u7684\u6df7\u5408\u65b9\u9762\u662f\u6307\u5176\u8fde\u7eed\u53d8\u91cf\u548c\u79bb\u6563\u53d8\u91cf\u7684\u7ec4\u5408\u3002<\/p>\n

\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\uff0c\u8d1d\u53f6\u65af\u7edf\u8ba1\u5b66\u7684\u7814\u7a76\u4eba\u5458\u8ba4\u8bc6\u5230\u8fd9\u79cd\u6280\u672f\u4ece\u590d\u6742\u6982\u7387\u5206\u5e03\u4e2d\u62bd\u6837\u7684\u6f5c\u529b\uff0c\u56e0\u6b64\u201c\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u201d\u4e00\u8bcd\u5f00\u59cb\u6d41\u884c\u8d77\u6765\u3002 20 \u4e16\u7eaa 90 \u5e74\u4ee3\u521d\uff0cRadford Neal \u7684\u8d21\u732e\u5927\u5927\u63d0\u9ad8\u4e86 HMC \u7684\u6548\u7387\uff0c\u4f7f\u5176\u6210\u4e3a\u4e00\u79cd\u5b9e\u7528\u800c\u5f3a\u5927\u7684\u8d1d\u53f6\u65af\u63a8\u7406\u5de5\u5177\u3002<\/p>\n

\u5173\u4e8e\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u7684\u8be6\u7ec6\u4fe1\u606f\u3002\u6269\u5c55\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u4e3b\u9898\u3002<\/h2>\n

\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u7b97\u6cd5\u901a\u8fc7\u5728\u6807\u51c6 Metropolis-Hastings \u7b97\u6cd5\u4e2d\u5f15\u5165\u8f85\u52a9\u52a8\u91cf\u53d8\u91cf\u6765\u8fd0\u884c\u3002\u8fd9\u4e9b\u52a8\u91cf\u53d8\u91cf\u662f\u4eba\u5de5\u7684\u8fde\u7eed\u53d8\u91cf\uff0c\u5b83\u4eec\u4e0e\u76ee\u6807\u5206\u5e03\u7684\u4f4d\u7f6e\u53d8\u91cf\u76f8\u4e92\u4f5c\u7528\u5f62\u6210\u4e86\u4e00\u4e2a\u6df7\u5408\u7cfb\u7edf\u3002\u4f4d\u7f6e\u53d8\u91cf\u8868\u793a\u76ee\u6807\u5206\u5e03\u4e2d\u611f\u5174\u8da3\u7684\u53c2\u6570\uff0c\u800c\u52a8\u91cf\u53d8\u91cf\u5219\u6709\u52a9\u4e8e\u6307\u5bfc\u7a7a\u95f4\u7684\u63a2\u7d22\u3002<\/p>\n

\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u6d1b\u7684\u5185\u90e8\u5de5\u4f5c\u539f\u7406\u53ef\u4ee5\u6982\u62ec\u5982\u4e0b\uff1a<\/p>\n

    \n
  1. \n

    \u6c49\u5bc6\u5c14\u987f\u52a8\u529b\u5b66\uff1a<\/strong> HMC \u91c7\u7528\u6c49\u5bc6\u5c14\u987f\u52a8\u529b\u5b66\uff0c\u7531\u6c49\u5bc6\u5c14\u987f\u8fd0\u52a8\u65b9\u7a0b\u63a7\u5236\u3002\u6c49\u5bc6\u5c14\u987f\u51fd\u6570\u7ed3\u5408\u4e86\u52bf\u80fd\uff08\u4e0e\u76ee\u6807\u5206\u5e03\u6709\u5173\uff09\u548c\u52a8\u80fd\uff08\u4e0e\u52a8\u91cf\u53d8\u91cf\u6709\u5173\uff09\u3002<\/p>\n<\/li>\n

  2. \n

    \u8de8\u8d8a\u5f0f\u6574\u5408\uff1a<\/strong> \u4e3a\u4e86\u6a21\u62df\u6c49\u5bc6\u5c14\u987f\u52a8\u529b\u5b66\uff0c\u6211\u4eec\u4f7f\u7528\u4e86\u86d9\u8df3\u79ef\u5206\u65b9\u6848\u3002\u8be5\u65b9\u6848\u5c06\u65f6\u95f4\u6b65\u9aa4\u79bb\u6563\u5316\uff0c\u4ece\u800c\u5b9e\u73b0\u9ad8\u6548\u800c\u51c6\u786e\u7684\u6570\u503c\u89e3\u3002<\/p>\n<\/li>\n

  3. \n

    \u5927\u90fd\u4f1a\u9a8c\u6536\u6b65\u9aa4\uff1a<\/strong> \u5728\u6a21\u62df\u4e00\u5b9a\u6b65\u6570\u7684\u6c49\u5bc6\u5c14\u987f\u52a8\u529b\u5b66\u540e\uff0c\u6267\u884c Metropolis-Hastings \u63a5\u53d7\u6b65\u9aa4\u3002\u6839\u636e\u8be6\u7ec6\u7684\u5e73\u8861\u6761\u4ef6\uff0c\u786e\u5b9a\u662f\u63a5\u53d7\u8fd8\u662f\u62d2\u7edd\u6240\u63d0\u51fa\u7684\u72b6\u6001\u3002<\/p>\n<\/li>\n

  4. \n

    \u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u7b97\u6cd5\uff1a<\/strong> HMC \u7b97\u6cd5\u5305\u62ec\u4ece\u9ad8\u65af\u5206\u5e03\u4e2d\u53cd\u590d\u91c7\u6837\u52a8\u91cf\u53d8\u91cf\u5e76\u6a21\u62df\u6c49\u5bc6\u5c14\u987f\u52a8\u529b\u5b66\u3002\u63a5\u53d7\u6b65\u9aa4\u786e\u4fdd\u4ece\u76ee\u6807\u5206\u5e03\u4e2d\u63d0\u53d6\u7ed3\u679c\u6837\u672c\u3002<\/p>\n<\/li>\n<\/ol>\n

    \u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u7684\u4e3b\u8981\u7279\u5f81\u5206\u6790\u3002<\/h2>\n

    \u4e0e\u4f20\u7edf\u91c7\u6837\u65b9\u6cd5\u76f8\u6bd4\uff0c\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u6d1b\u6709\u51e0\u4e2a\u4e3b\u8981\u4f18\u52bf\uff1a<\/p>\n

      \n
    1. \n

      \u9ad8\u6548\u63a2\u7d22\uff1a<\/strong> \u4e0e\u8bb8\u591a\u5176\u4ed6\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u6d1b (MCMC) \u6280\u672f\u76f8\u6bd4\uff0cHMC \u80fd\u591f\u66f4\u6709\u6548\u5730\u63a2\u7d22\u590d\u6742\u548c\u9ad8\u7ef4\u6982\u7387\u5206\u5e03\u3002<\/p>\n<\/li>\n

    2. \n

      \u81ea\u9002\u5e94\u6b65\u957f\uff1a<\/strong> \u8be5\u7b97\u6cd5\u53ef\u4ee5\u5728\u6a21\u62df\u8fc7\u7a0b\u4e2d\u81ea\u9002\u5e94\u5730\u8c03\u6574\u5176\u6b65\u957f\uff0c\u4ece\u800c\u6709\u6548\u5730\u63a2\u7d22\u5177\u6709\u53d8\u5316\u66f2\u7387\u7684\u533a\u57df\u3002<\/p>\n<\/li>\n

    3. \n

      \u65e0\u9700\u624b\u52a8\u8c03\u6574\uff1a<\/strong> \u4e0e\u4e00\u4e9b\u9700\u8981\u624b\u52a8\u8c03\u6574\u63d0\u8bae\u5206\u5e03\u7684 MCMC \u65b9\u6cd5\u4e0d\u540c\uff0cHMC \u901a\u5e38\u9700\u8981\u8f83\u5c11\u7684\u8c03\u6574\u53c2\u6570\u3002<\/p>\n<\/li>\n

    4. \n

      \u964d\u4f4e\u81ea\u76f8\u5173\uff1a<\/strong> HMC \u503e\u5411\u4e8e\u4ea7\u751f\u81ea\u76f8\u5173\u6027\u8f83\u4f4e\u7684\u6837\u672c\uff0c\u4ece\u800c\u5b9e\u73b0\u66f4\u5feb\u7684\u6536\u655b\u548c\u66f4\u51c6\u786e\u7684\u4f30\u8ba1\u3002<\/p>\n<\/li>\n

    5. \n

      \u907f\u514d\u968f\u673a\u6e38\u8d70\u884c\u4e3a\uff1a<\/strong> \u4e0e\u4f20\u7edf\u7684 MCMC \u65b9\u6cd5\u4e0d\u540c\uff0cHMC \u5229\u7528\u786e\u5b9a\u6027\u52a8\u529b\u5b66\u6765\u6307\u5bfc\u63a2\u7d22\uff0c\u51cf\u5c11\u968f\u673a\u6e38\u8d70\u884c\u4e3a\u548c\u6f5c\u5728\u7684\u7f13\u6162\u6df7\u5408\u3002<\/p>\n<\/li>\n<\/ol>\n

      \u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u6d1b\u7684\u7c7b\u578b<\/h2>\n

      \u5df2\u7ecf\u63d0\u51fa\u4e86\u51e0\u79cd\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u7684\u53d8\u4f53\u548c\u6269\u5c55\uff0c\u7528\u4e8e\u89e3\u51b3\u7279\u5b9a\u6311\u6218\u6216\u9488\u5bf9\u7279\u5b9a\u573a\u666f\u5b9a\u5236\u65b9\u6cd5\u3002\u4e00\u4e9b\u503c\u5f97\u6ce8\u610f\u7684 HMC \u7c7b\u578b\u5305\u62ec\uff1a<\/p>\n\n\n\n\n\n\n\n\n
      HMC \u7c7b\u578b<\/strong><\/th>\n\u63cf\u8ff0<\/strong><\/th>\n<\/tr>\n<\/thead>\n
      \u65e0\u6389\u5934\u91c7\u6837\u5668 (NUTS)<\/strong><\/td>\nNUTS \u662f HMC \u7684\u6269\u5c55\uff0c\u53ef\u5728\u6a21\u62df\u8fc7\u7a0b\u4e2d\u81ea\u52a8\u786e\u5b9a\u8df3\u8dc3\u6b65\u6570\u3002\u5f53\u8f68\u8ff9\u53d1\u751f U \u578b\u8f6c\u5f2f\u65f6\uff0c\u5b83\u4f1a\u52a8\u6001\u505c\u6b62\u6a21\u62df\uff0c\u4ece\u800c\u5b9e\u73b0\u66f4\u9ad8\u6548\u7684\u63a2\u7d22\u3002<\/td>\n<\/tr>\n
      \u9ece\u66fc HMC<\/strong><\/td>\n\u9ece\u66fc HMC \u5c06 HMC \u7b97\u6cd5\u5e94\u7528\u4e8e\u6d41\u5f62\uff0c\u4ece\u800c\u80fd\u591f\u4ece\u5b9a\u4e49\u5728\u66f2\u7ebf\u7a7a\u95f4\u4e0a\u7684\u6982\u7387\u5206\u5e03\u4e2d\u8fdb\u884c\u9ad8\u6548\u91c7\u6837\u3002\u8fd9\u5728\u5bf9\u6d41\u5f62\u8fdb\u884c\u7ea6\u675f\u6216\u53c2\u6570\u5316\u7684\u8d1d\u53f6\u65af\u6a21\u578b\u4e2d\u5c24\u5176\u6709\u7528\u3002<\/td>\n<\/tr>\n
      \u968f\u673a\u68af\u5ea6 HMC<\/strong><\/td>\n\u8be5\u53d8\u4f53\u5c06\u968f\u673a\u68af\u5ea6\u7eb3\u5165\u6a21\u62df\u4e2d\uff0c\u4f7f\u5176\u9002\u7528\u4e8e\u5927\u89c4\u6a21\u8d1d\u53f6\u65af\u63a8\u7406\u95ee\u9898\uff0c\u4f8b\u5982\u673a\u5668\u5b66\u4e60\u5e94\u7528\u4e2d\u9047\u5230\u7684\u95ee\u9898\u3002<\/td>\n<\/tr>\n
      \u5e7f\u4e49HMC<\/strong><\/td>\n\u5e7f\u4e49 HMC \u5c06\u8be5\u65b9\u6cd5\u6269\u5c55\u81f3\u975e\u54c8\u5bc6\u987f\u52a8\u529b\u5b66\uff0c\u4ece\u800c\u5c06\u5176\u9002\u7528\u6027\u6269\u5c55\u5230\u66f4\u5e7f\u6cdb\u7684\u95ee\u9898\u4e2d\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u7684\u4f7f\u7528\u65b9\u6cd5\uff0c\u4ee5\u53ca\u4e0e\u4f7f\u7528\u76f8\u5173\u7684\u95ee\u9898\u53ca\u5176\u89e3\u51b3\u65b9\u6848\u3002<\/h2>\n

      \u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u53ef\u5e94\u7528\u4e8e\u5404\u4e2a\u9886\u57df\uff0c\u5305\u62ec\uff1a<\/p>\n

        \n
      1. \n

        \u8d1d\u53f6\u65af\u63a8\u7406\uff1a<\/strong> HMC \u5e7f\u6cdb\u7528\u4e8e\u8d1d\u53f6\u65af\u53c2\u6570\u4f30\u8ba1\u548c\u6a21\u578b\u9009\u62e9\u4efb\u52a1\u3002\u5b83\u5728\u63a2\u7d22\u590d\u6742\u540e\u9a8c\u5206\u5e03\u65b9\u9762\u7684\u6548\u7387\u4f7f\u5176\u6210\u4e3a\u8d1d\u53f6\u65af\u6570\u636e\u5206\u6790\u7684\u7406\u60f3\u9009\u62e9\u3002<\/p>\n<\/li>\n

      2. \n

        \u673a\u5668\u5b66\u4e60\uff1a<\/strong> \u5728\u8d1d\u53f6\u65af\u6df1\u5ea6\u5b66\u4e60\u548c\u6982\u7387\u673a\u5668\u5b66\u4e60\u7684\u80cc\u666f\u4e0b\uff0cHMC \u63d0\u4f9b\u4e86\u4e00\u79cd\u4ece\u795e\u7ecf\u7f51\u7edc\u6743\u91cd\u7684\u540e\u9a8c\u5206\u5e03\u4e2d\u91c7\u6837\u7684\u65b9\u6cd5\uff0c\u4ece\u800c\u5b9e\u73b0\u4e86\u9884\u6d4b\u548c\u6a21\u578b\u6821\u51c6\u4e2d\u7684\u4e0d\u786e\u5b9a\u6027\u4f30\u8ba1\u3002<\/p>\n<\/li>\n

      3. \n

        \u4f18\u5316\uff1a<\/strong> HMC \u53ef\u4ee5\u9002\u7528\u4e8e\u4f18\u5316\u4efb\u52a1\uff0c\u5b83\u53ef\u4ee5\u4ece\u6a21\u578b\u53c2\u6570\u7684\u540e\u9a8c\u5206\u5e03\u4e2d\u91c7\u6837\u5e76\u6709\u6548\u5730\u63a2\u7d22\u4f18\u5316\u524d\u666f\u3002<\/p>\n<\/li>\n<\/ol>\n

        \u4e0e HMC \u4f7f\u7528\u76f8\u5173\u7684\u6311\u6218\u5305\u62ec\uff1a<\/p>\n

          \n
        1. \n

          \u8c03\u6574\u53c2\u6570\uff1a<\/strong> \u5c3d\u7ba1 HMC \u6bd4\u5176\u4ed6\u4e00\u4e9b MCMC \u65b9\u6cd5\u9700\u8981\u66f4\u5c11\u7684\u8c03\u6574\u53c2\u6570\uff0c\u4f46\u8bbe\u7f6e\u6b63\u786e\u7684\u6b65\u957f\u548c\u8df3\u8dc3\u6b65\u6570\u5bf9\u4e8e\u6709\u6548\u63a2\u7d22\u4ecd\u7136\u81f3\u5173\u91cd\u8981\u3002<\/p>\n<\/li>\n

        2. \n

          \u8ba1\u7b97\u5bc6\u96c6\u578b\uff1a<\/strong> \u6a21\u62df\u6c49\u5bc6\u5c14\u987f\u52a8\u529b\u5b66\u6d89\u53ca\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b\uff0c\u8fd9\u5728\u8ba1\u7b97\u4e0a\u975e\u5e38\u6602\u8d35\uff0c\u7279\u522b\u662f\u5728\u9ad8\u7ef4\u7a7a\u95f4\u6216\u5927\u578b\u6570\u636e\u96c6\u4e2d\u3002<\/p>\n<\/li>\n

        3. \n

          \u7ef4\u6570\u707e\u96be\uff1a<\/strong> \u4e0e\u4efb\u4f55\u91c7\u6837\u6280\u672f\u4e00\u6837\uff0c\u5f53\u76ee\u6807\u5206\u5e03\u7684\u7ef4\u6570\u8fc7\u9ad8\u65f6\uff0c\u7ef4\u6570\u707e\u96be\u4f1a\u5e26\u6765\u6311\u6218\u3002<\/p>\n<\/li>\n<\/ol>\n

          \u89e3\u51b3\u8fd9\u4e9b\u6311\u6218\u7684\u65b9\u6cd5\u5305\u62ec\u5229\u7528\u81ea\u9002\u5e94\u65b9\u6cd5\u3001\u4f7f\u7528\u9884\u70ed\u8fed\u4ee3\u4ee5\u53ca\u91c7\u7528 NUTS \u7b49\u4e13\u95e8\u7b97\u6cd5\u6765\u81ea\u52a8\u8c03\u6574\u53c2\u6570\u3002<\/p>\n

          \u4ee5\u8868\u683c\u548c\u5217\u8868\u7684\u5f62\u5f0f\u5217\u51fa\u4e3b\u8981\u7279\u5f81\u4ee5\u53ca\u4e0e\u7c7b\u4f3c\u672f\u8bed\u7684\u5176\u4ed6\u6bd4\u8f83\u3002<\/h2>\n\n\n\n\n\n\n\n\n\n
          \u7279\u5f81<\/strong><\/th>\n\u4e0e Metropolis-Hastings \u7684\u6bd4\u8f83<\/strong><\/th>\n<\/tr>\n<\/thead>\n
          \u52d8\u63a2\u6548\u7387<\/strong><\/td>\n\u4e0eMetropolis-Hastings\u7684\u968f\u673a\u6e38\u8d70\u884c\u4e3a\u76f8\u6bd4\uff0cHMC \u8868\u73b0\u51fa\u66f4\u9ad8\u7684\u63a2\u7d22\u6548\u7387\uff0c\u53ef\u4ee5\u5b9e\u73b0\u66f4\u5feb\u7684\u6536\u655b\u548c\u66f4\u51c6\u786e\u7684\u91c7\u6837\u3002<\/td>\n<\/tr>\n
          \u8c03\u6574\u590d\u6742\u6027<\/strong><\/td>\nHMC \u901a\u5e38\u9700\u8981\u6bd4 Metropolis-Hastings \u66f4\u5c11\u7684\u8c03\u6574\u53c2\u6570\uff0c\u56e0\u6b64\u5728\u5b9e\u8df5\u4e2d\u66f4\u5bb9\u6613\u4f7f\u7528\u3002<\/td>\n<\/tr>\n
          \u5904\u7406\u590d\u6742\u7a7a\u95f4<\/strong><\/td>\nHMC \u53ef\u4ee5\u6709\u6548\u5730\u63a2\u7d22\u590d\u6742\u7684\u9ad8\u7ef4\u7a7a\u95f4\uff0c\u800c Metropolis-Hastings \u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u53ef\u80fd\u4f1a\u9047\u5230\u56f0\u96be\u3002<\/td>\n<\/tr>\n
          \u81ea\u76f8\u5173<\/strong><\/td>\nHMC \u4ea7\u751f\u7684\u6837\u672c\u81ea\u76f8\u5173\u6027\u8f83\u4f4e\uff0c\u4ece\u800c\u51cf\u5c11\u91c7\u6837\u94fe\u4e2d\u7684\u5197\u4f59\u3002<\/td>\n<\/tr>\n
          \u53ef\u6269\u5c55\u6027<\/strong><\/td>\n\u5bf9\u4e8e\u9ad8\u7ef4\u95ee\u9898\uff0cHMC \u5f80\u5f80\u4f18\u4e8e Metropolis-Hastings\uff0c\u56e0\u4e3a\u5b83\u6539\u8fdb\u4e86\u63a2\u7d22\u5e76\u51cf\u5c11\u4e86\u968f\u673a\u6e38\u8d70\u884c\u4e3a\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          \u4e0e\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u76f8\u5173\u7684\u672a\u6765\u89c2\u70b9\u548c\u6280\u672f\u3002<\/h2>\n

          \u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u5df2\u88ab\u8bc1\u660e\u662f\u8d1d\u53f6\u65af\u7edf\u8ba1\u3001\u8ba1\u7b97\u7269\u7406\u548c\u673a\u5668\u5b66\u4e60\u4e2d\u4e00\u79cd\u6709\u4ef7\u503c\u7684\u91c7\u6837\u6280\u672f\u3002\u7136\u800c\uff0c\u8be5\u9886\u57df\u7684\u6301\u7eed\u7814\u7a76\u548c\u8fdb\u6b65\u7ee7\u7eed\u5b8c\u5584\u548c\u6269\u5c55\u8be5\u65b9\u6cd5\u7684\u529f\u80fd\u3002<\/p>\n

          HMC \u7684\u4e00\u4e9b\u6709\u524d\u666f\u7684\u53d1\u5c55\u9886\u57df\u5305\u62ec\uff1a<\/p>\n

            \n
          1. \n

            \u5e76\u884c\u5316\u548c GPU\uff1a<\/strong> \u5e76\u884c\u5316\u6280\u672f\u548c\u56fe\u5f62\u5904\u7406\u5355\u5143 (GPU) \u7684\u5229\u7528\u53ef\u4ee5\u52a0\u901f\u6c49\u5bc6\u5c14\u987f\u52a8\u529b\u5b66\u7684\u8ba1\u7b97\uff0c\u4f7f\u5f97 HMC \u66f4\u9002\u7528\u4e8e\u89e3\u51b3\u5927\u89c4\u6a21\u95ee\u9898\u3002<\/p>\n<\/li>\n

          2. \n

            \u81ea\u9002\u5e94HMC\u65b9\u6cd5\uff1a<\/strong> \u81ea\u9002\u5e94 HMC \u7b97\u6cd5\u7684\u6539\u8fdb\u53ef\u4ee5\u51cf\u5c11\u624b\u52a8\u8c03\u6574\u7684\u9700\u8981\u5e76\u66f4\u6709\u6548\u5730\u9002\u5e94\u590d\u6742\u7684\u76ee\u6807\u5206\u5e03\u3002<\/p>\n<\/li>\n

          3. \n

            \u8d1d\u53f6\u65af\u6df1\u5ea6\u5b66\u4e60\uff1a<\/strong> \u5c06 HMC \u96c6\u6210\u5230\u8d1d\u53f6\u65af\u6df1\u5ea6\u5b66\u4e60\u6846\u67b6\u4e2d\u53ef\u4ee5\u5e26\u6765\u66f4\u7a33\u5065\u7684\u4e0d\u786e\u5b9a\u6027\u4f30\u8ba1\u548c\u66f4\u7cbe\u786e\u7684\u9884\u6d4b\u3002<\/p>\n<\/li>\n

          4. \n

            \u786c\u4ef6\u52a0\u901f\uff1a<\/strong> \u5229\u7528\u4e13\u7528\u786c\u4ef6\uff0c\u4f8b\u5982\u5f20\u91cf\u5904\u7406\u5355\u5143 (TPU) \u6216\u4e13\u7528 HMC \u52a0\u901f\u5668\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u57fa\u4e8e HMC \u7684\u5e94\u7528\u7a0b\u5e8f\u7684\u6027\u80fd\u3002<\/p>\n<\/li>\n<\/ol>\n

            \u5982\u4f55\u4f7f\u7528\u4ee3\u7406\u670d\u52a1\u5668\u6216\u5c06\u5176\u4e0e\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u6d1b\u5173\u8054\u3002<\/h2>\n

            \u4ee3\u7406\u670d\u52a1\u5668\u5145\u5f53\u7528\u6237\u548c\u4e92\u8054\u7f51\u4e4b\u95f4\u7684\u4e2d\u4ecb\u3002\u5b83\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e24\u79cd\u4e3b\u8981\u65b9\u5f0f\u4e0e\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u6d1b\u76f8\u5173\u8054\uff1a<\/p>\n

              \n
            1. \n

              \u589e\u5f3a\u9690\u79c1\u548c\u5b89\u5168\uff1a<\/strong> \u5c31\u50cf\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u6d1b\u53ef\u4ee5\u901a\u8fc7\u6709\u6548\u7684\u91c7\u6837\u548c\u4e0d\u786e\u5b9a\u6027\u4f30\u8ba1\u6765\u63d0\u9ad8\u6570\u636e\u7684\u9690\u79c1\u548c\u5b89\u5168\u6027\u4e00\u6837\uff0c\u4ee3\u7406\u670d\u52a1\u5668\u53ef\u4ee5\u901a\u8fc7\u63a9\u76d6\u7528\u6237\u7684 IP \u5730\u5740\u548c\u52a0\u5bc6\u6570\u636e\u4f20\u8f93\u6765\u63d0\u4f9b\u989d\u5916\u7684\u9690\u79c1\u4fdd\u62a4\u3002<\/p>\n<\/li>\n

            2. \n

              \u8d1f\u8f7d\u5e73\u8861\u548c\u4f18\u5316\uff1a<\/strong> \u4ee3\u7406\u670d\u52a1\u5668\u53ef\u7528\u4e8e\u5728\u591a\u4e2a\u540e\u7aef\u670d\u52a1\u5668\u4e4b\u95f4\u5206\u914d\u8bf7\u6c42\uff0c\u4ece\u800c\u4f18\u5316\u8d44\u6e90\u5229\u7528\u7387\u5e76\u63d0\u9ad8\u7cfb\u7edf\u7684\u6574\u4f53\u6548\u7387\u3002\u6b64\u8d1f\u8f7d\u5e73\u8861\u65b9\u9762\u4e0e HMC \u5982\u4f55\u6709\u6548\u63a2\u7d22\u9ad8\u7ef4\u7a7a\u95f4\u5e76\u907f\u514d\u5728\u4f18\u5316\u4efb\u52a1\u671f\u95f4\u9677\u5165\u5c40\u90e8\u6700\u5c0f\u503c\u6709\u76f8\u4f3c\u4e4b\u5904\u3002<\/p>\n<\/li>\n<\/ol>\n

              \u76f8\u5173\u94fe\u63a5<\/h2>\n

              \u6709\u5173\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u7684\u66f4\u591a\u4fe1\u606f\uff0c\u60a8\u53ef\u4ee5\u63a2\u7d22\u4ee5\u4e0b\u8d44\u6e90\uff1a<\/p>\n

                \n
              1. \u6df7\u5408\u8499\u7279\u5361\u7f57<\/a> \u2013 \u7ef4\u57fa\u767e\u79d1\u4e0a\u6709\u5173\u539f\u59cb\u6df7\u5408\u8499\u7279\u5361\u7f57\u7b97\u6cd5\u7684\u9875\u9762\u3002<\/li>\n
              2. \u54c8\u5bc6\u987f\u8499\u7279\u5361\u7f57<\/a> \u2013 \u7ef4\u57fa\u767e\u79d1\u9875\u9762\u4e13\u95e8\u4ecb\u7ecd\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u6d1b\u3002<\/li>\n
              3. \u65af\u5766\u7528\u6237\u6307\u5357<\/a> \u2013 \u65af\u5766 (Stan) \u4e2d\u6c49\u5bc6\u5c14\u987f\u8499\u7279\u5361\u7f57\u5b9e\u73b0\u7684\u7efc\u5408\u6307\u5357\u3002<\/li>\n
              4. NUTS\uff1a\u65e0 U \u5f62\u8f6c\u5f2f\u91c7\u6837\u5668<\/a> \u2013 \u4ecb\u7ecd HMC \u7684 No-U-Turn Sampler \u6269\u5c55\u7684\u539f\u59cb\u8bba\u6587\u3002<\/li>\n
              5. \u9ed1\u5ba2\u7684\u6982\u7387\u7f16\u7a0b\u548c\u8d1d\u53f6\u65af\u65b9\u6cd5<\/a> \u2013 \u4e00\u672c\u5305\u542b\u8d1d\u53f6\u65af\u65b9\u6cd5\uff08\u5305\u62ec HMC\uff09\u5b9e\u9645\u4f8b\u5b50\u7684\u5728\u7ebf\u4e66\u7c4d\u3002<\/li>\n<\/ol>","protected":false},"featured_media":468513,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-477408","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about Hamiltonian Monte Carlo: A Powerful Sampling Technique for Efficient Proxy Server Operations<\/mark>","faq_items":[{"question":"What is Hamiltonian Monte Carlo (HMC)?","answer":"

                Hamiltonian Monte Carlo (HMC) is an advanced sampling technique used in Bayesian statistics and computational physics. It efficiently explores complex probability distributions by simulating Hamiltonian dynamics, offering faster convergence and more accurate results compared to traditional methods.<\/p>"},{"question":"How does Hamiltonian Monte Carlo work?","answer":"

                HMC introduces auxiliary momentum variables to the standard Metropolis-Hastings algorithm. These continuous variables interact with the position variables representing the parameters of interest, creating a hybrid system. The algorithm uses Hamiltonian dynamics to simulate the behavior of this hybrid system, and a Metropolis acceptance step ensures the resulting samples are drawn from the target distribution.<\/p>"},{"question":"What are the advantages of Hamiltonian Monte Carlo over other methods?","answer":"

                HMC boasts several key advantages, including efficient exploration of high-dimensional spaces, adaptive step size for varying curvature, reduced autocorrelation in samples, and fewer tuning parameters compared to some other MCMC methods.<\/p>"},{"question":"What are the different types of Hamiltonian Monte Carlo?","answer":"

                There are several variations of HMC, each designed to address specific challenges or tailor the method for different scenarios. Some notable types include the No-U-Turn Sampler (NUTS) for adaptive trajectory length, Riemannian HMC for manifolds, Stochastic Gradient HMC for large-scale problems, and Generalized HMC for non-Hamiltonian dynamics.<\/p>"},{"question":"In which fields is Hamiltonian Monte Carlo used?","answer":"

                HMC finds applications in various domains, such as Bayesian inference for parameter estimation and model selection, machine learning for uncertainty estimation and calibration, and optimization tasks to explore optimization landscapes effectively.<\/p>"},{"question":"What are the challenges associated with using Hamiltonian Monte Carlo?","answer":"

                While HMC requires fewer tuning parameters, setting the appropriate step size and number of leapfrog steps is crucial for efficient exploration. Additionally, simulating Hamiltonian dynamics can be computationally intensive, especially in high-dimensional spaces or with large datasets.<\/p>"},{"question":"How can Hamiltonian Monte Carlo be used with proxy servers?","answer":"

                Proxy servers, acting as intermediaries between users and the internet, can benefit from HMC's efficient exploration just as data analysis and optimization tasks do. Proxy servers enhance privacy and security by masking IP addresses and encrypting data, while HMC explores probability distributions effectively and avoids getting stuck in local minima during optimization tasks.<\/p>"},{"question":"Where can I find more information about Hamiltonian Monte Carlo?","answer":"

                For more information about Hamiltonian Monte Carlo, you can explore the Wikipedia page on \"Hamiltonian Monte Carlo,\" the Stan User's Guide for practical implementation, and the No-U-Turn Sampler (NUTS) paper for the NUTS extension. Additionally, the book \"Probabilistic Programming & Bayesian Methods for Hackers\" provides practical examples of Bayesian methods, including HMC.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/477408","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/477408\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media\/468513"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media?parent=477408"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}