{"id":479495,"date":"2023-08-09T10:40:54","date_gmt":"2023-08-09T10:40:54","guid":{"rendered":""},"modified":"2023-09-05T11:18:56","modified_gmt":"2023-09-05T11:18:56","slug":"vapnik-chervonenkis-vc-dimension","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/cn\/wiki\/vapnik-chervonenkis-vc-dimension\/","title":{"rendered":"\u74e6\u666e\u5c3c\u514b-\u5207\u5c14\u6c83\u5e74\u57fa\u65af (VC) \u7ef4\u6570"},"content":{"rendered":"

Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u662f\u8ba1\u7b97\u5b66\u4e60\u7406\u8bba\u548c\u7edf\u8ba1\u5b66\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u6982\u5ff5\uff0c\u7528\u4e8e\u5206\u6790\u5047\u8bbe\u7c7b\u6216\u5b66\u4e60\u7b97\u6cd5\u7684\u5bb9\u91cf\u3002\u5b83\u5728\u7406\u89e3\u673a\u5668\u5b66\u4e60\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u65b9\u9762\u8d77\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u4eba\u5de5\u667a\u80fd\u3001\u6a21\u5f0f\u8bc6\u522b\u548c\u6570\u636e\u6316\u6398\u7b49\u9886\u57df\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u63a2\u8ba8 Vapnik-Chervonenkis \u7ef4\u5ea6\u7684\u5386\u53f2\u3001\u7ec6\u8282\u3001\u5e94\u7528\u548c\u672a\u6765\u524d\u666f\u3002<\/p>\n

Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u7684\u8d77\u6e90\u5386\u53f2\u53ca\u5176\u9996\u6b21\u63d0\u53ca<\/h2>\n

VC \u7ef4\u5ea6\u7684\u6982\u5ff5\u6700\u65e9\u7531 Vladimir Vapnik \u548c Alexey Chervonenkis \u5728 20 \u4e16\u7eaa 70 \u5e74\u4ee3\u521d\u63d0\u51fa\u3002\u8fd9\u4e24\u4f4d\u7814\u7a76\u4eba\u5458\u90fd\u6765\u81ea\u82cf\u8054\u63a7\u5236\u79d1\u5b66\u7814\u7a76\u6240\uff0c\u4ed6\u4eec\u7684\u5de5\u4f5c\u4e3a\u7edf\u8ba1\u5b66\u4e60\u7406\u8bba\u5960\u5b9a\u4e86\u57fa\u7840\u3002\u8be5\u6982\u5ff5\u6700\u521d\u662f\u5728\u4e8c\u5143\u5206\u7c7b\u95ee\u9898\u7684\u80cc\u666f\u4e0b\u5f00\u53d1\u7684\uff0c\u5176\u4e2d\u6570\u636e\u70b9\u88ab\u5206\u4e3a\u4e24\u7c7b\u4e4b\u4e00\u3002<\/p>\n

VC \u7ef4\u6570\u9996\u6b21\u88ab\u63d0\u53ca\u51fa\u73b0\u5728 1971 \u5e74 Vapnik \u548c Chervonenkis \u7684\u4e00\u7bc7\u5f00\u521b\u6027\u8bba\u6587\u4e2d\uff0c\u9898\u4e3a\u201c\u5173\u4e8e\u4e8b\u4ef6\u76f8\u5bf9\u9891\u7387\u4e0e\u5176\u6982\u7387\u7684\u4e00\u81f4\u6536\u655b\u201d\u3002\u5728\u8fd9\u7bc7\u8bba\u6587\u4e2d\uff0c\u4ed6\u4eec\u5f15\u5165\u4e86 VC \u7ef4\u6570\u4f5c\u4e3a\u5047\u8bbe\u7c7b\u590d\u6742\u6027\u7684\u5ea6\u91cf\uff0c\u5047\u8bbe\u7c7b\u662f\u5b66\u4e60\u7b97\u6cd5\u53ef\u4ee5\u4ece\u4e2d\u9009\u62e9\u7684\u4e00\u7ec4\u53ef\u80fd\u6a21\u578b\u3002<\/p>\n

\u5173\u4e8e Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u7684\u8be6\u7ec6\u4fe1\u606f\uff1a\u6269\u5c55\u4e3b\u9898<\/h2>\n

Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u662f\u4e00\u4e2a\u6982\u5ff5\uff0c\u7528\u4e8e\u91cf\u5316\u5047\u8bbe\u7c7b\u7c89\u788e\u6570\u636e\u70b9\u7684\u80fd\u529b\u3002\u5982\u679c\u5047\u8bbe\u7c7b\u80fd\u591f\u4ee5\u4efb\u4f55\u53ef\u80fd\u7684\u65b9\u5f0f\u5bf9\u4e00\u7ec4\u6570\u636e\u70b9\u8fdb\u884c\u5206\u7c7b\uff0c\u5373\u5bf9\u4e8e\u6570\u636e\u70b9\u7684\u4efb\u4f55\u4e8c\u5143\u6807\u8bb0\uff0c\u5047\u8bbe\u7c7b\u4e2d\u90fd\u5b58\u5728\u4e00\u4e2a\u6a21\u578b\u53ef\u4ee5\u6b63\u786e\u5730\u5bf9\u6bcf\u4e2a\u70b9\u8fdb\u884c\u76f8\u5e94\u7684\u5206\u7c7b\uff0c\u5219\u79f0\u8be5\u5047\u8bbe\u7c7b\u80fd\u591f\u7c89\u788e\u8fd9\u4e9b\u6570\u636e\u70b9\u3002<\/p>\n

\u5047\u8bbe\u7c7b\u7684 VC \u7ef4\u6570\u662f\u8be5\u7c7b\u53ef\u4ee5\u62c6\u5206\u7684\u6700\u5927\u6570\u636e\u70b9\u6570\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u8868\u793a\u53ef\u4ee5\u4ee5\u4efb\u4f55\u53ef\u80fd\u7684\u65b9\u5f0f\u6392\u5217\u7684\u6700\u5927\u70b9\u6570\uff0c\u4f7f\u5f97\u5047\u8bbe\u7c7b\u53ef\u4ee5\u5b8c\u7f8e\u5730\u5c06\u5b83\u4eec\u5206\u5f00\u3002<\/p>\n

VC \u7ef4\u5ea6\u5bf9\u4e8e\u5b66\u4e60\u7b97\u6cd5\u7684\u6cdb\u5316\u80fd\u529b\u5177\u6709\u91cd\u8981\u5f71\u54cd\u3002\u5982\u679c\u5047\u8bbe\u7c7b\u7684 VC \u7ef4\u5ea6\u8f83\u5c0f\uff0c\u5219\u8be5\u7c7b\u66f4\u6709\u53ef\u80fd\u4ece\u8bad\u7ec3\u6570\u636e\u5f88\u597d\u5730\u63a8\u5e7f\u5230\u672a\u77e5\u6570\u636e\uff0c\u4ece\u800c\u964d\u4f4e\u8fc7\u5ea6\u62df\u5408\u7684\u98ce\u9669\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c VC \u7ef4\u5ea6\u8f83\u5927\uff0c\u5219\u8fc7\u5ea6\u62df\u5408\u7684\u98ce\u9669\u8f83\u9ad8\uff0c\u56e0\u4e3a\u6a21\u578b\u53ef\u80fd\u4f1a\u8bb0\u4f4f\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u566a\u58f0\u3002<\/p>\n

Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u7684\u5185\u90e8\u7ed3\u6784\uff1a\u5176\u5de5\u4f5c\u539f\u7406<\/h2>\n

\u4e3a\u4e86\u7406\u89e3 VC \u7ef4\u5ea6\u7684\u5de5\u4f5c\u539f\u7406\uff0c\u8ba9\u6211\u4eec\u8003\u8651\u4e00\u4e2a\u5305\u542b\u4e00\u7ec4\u6570\u636e\u70b9\u7684\u4e8c\u5143\u5206\u7c7b\u95ee\u9898\u3002\u76ee\u6807\u662f\u627e\u5230\u4e00\u4e2a\u80fd\u591f\u5c06\u6570\u636e\u70b9\u6b63\u786e\u5206\u4e3a\u4e24\u7c7b\u7684\u5047\u8bbe\uff08\u6a21\u578b\uff09\u3002\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u662f\u6839\u636e\u67d0\u4e9b\u7279\u5f81\u5c06\u7535\u5b50\u90ae\u4ef6\u5206\u7c7b\u4e3a\u5783\u573e\u90ae\u4ef6\u6216\u975e\u5783\u573e\u90ae\u4ef6\u3002<\/p>\n

VC \u7ef4\u6570\u7531\u5047\u8bbe\u7c7b\u53ef\u4ee5\u5206\u89e3\u7684\u6700\u5927\u6570\u636e\u70b9\u6570\u51b3\u5b9a\u3002\u5982\u679c\u5047\u8bbe\u7c7b\u7684 VC \u7ef4\u6570\u8f83\u4f4e\uff0c\u5219\u610f\u5473\u7740\u5b83\u53ef\u4ee5\u6709\u6548\u5730\u5904\u7406\u5404\u79cd\u8f93\u5165\u6a21\u5f0f\u800c\u4e0d\u4f1a\u8fc7\u5ea6\u62df\u5408\u3002\u76f8\u53cd\uff0cVC \u7ef4\u6570\u8f83\u9ad8\u5219\u8868\u793a\u5047\u8bbe\u7c7b\u53ef\u80fd\u8fc7\u4e8e\u590d\u6742\uff0c\u5bb9\u6613\u8fc7\u5ea6\u62df\u5408\u3002<\/p>\n

Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u7684\u4e3b\u8981\u7279\u5f81\u5206\u6790<\/h2>\n

VC \u7ef4\u5ea6\u63d0\u4f9b\u4e86\u51e0\u4e2a\u91cd\u8981\u7684\u7279\u5f81\u548c\u89c1\u89e3\uff1a<\/p>\n

    \n
  1. \n

    \u5bb9\u91cf\u6d4b\u91cf<\/strong>\uff1a\u5b83\u4f5c\u4e3a\u5047\u8bbe\u7c7b\u7684\u5bb9\u91cf\u5ea6\u91cf\uff0c\u8868\u660e\u8be5\u7c7b\u5728\u62df\u5408\u6570\u636e\u65f6\u7684\u8868\u8fbe\u80fd\u529b\u3002<\/p>\n<\/li>\n

  2. \n

    \u6cdb\u5316\u754c\u9650<\/strong>\uff1aVC \u7ef4\u6570\u4e0e\u5b66\u4e60\u7b97\u6cd5\u7684\u6cdb\u5316\u8bef\u5dee\u6709\u5173\u3002\u8f83\u5c0f\u7684 VC \u7ef4\u6570\u901a\u5e38\u53ef\u5e26\u6765\u66f4\u597d\u7684\u6cdb\u5316\u6027\u80fd\u3002<\/p>\n<\/li>\n

  3. \n

    \u9009\u578b<\/strong>\uff1a\u4e86\u89e3 VC \u7ef4\u5ea6\u6709\u52a9\u4e8e\u4e3a\u5404\u79cd\u4efb\u52a1\u9009\u62e9\u5408\u9002\u7684\u6a21\u578b\u67b6\u6784\u3002<\/p>\n<\/li>\n

  4. \n

    \u5965\u5361\u59c6\u5243\u5200<\/strong>\uff1aVC \u7ef4\u5ea6\u652f\u6301\u5965\u5361\u59c6\u5243\u5200\u539f\u7406\uff0c\u8be5\u539f\u7406\u5efa\u8bae\u9009\u62e9\u80fd\u591f\u5f88\u597d\u5730\u62df\u5408\u6570\u636e\u7684\u6700\u7b80\u5355\u7684\u6a21\u578b\u3002<\/p>\n<\/li>\n<\/ol>\n

    Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u7684\u7c7b\u578b<\/h2>\n

    VC\u7ef4\u5ea6\u53ef\u4ee5\u5206\u4e3a\u4ee5\u4e0b\u51e0\u79cd\u7c7b\u578b\uff1a<\/p>\n

      \n
    1. \n

      \u6613\u788e\u5957\u88c5<\/strong>\uff1a\u5982\u679c\u5047\u8bbe\u7c7b\u80fd\u591f\u5b9e\u73b0\u6570\u636e\u70b9\u7684\u6240\u6709\u53ef\u80fd\u7684\u4e8c\u5143\u6807\u8bb0\uff0c\u5219\u79f0\u4e00\u7ec4\u6570\u636e\u70b9\u662f\u53ef\u7834\u788e\u7684\u3002<\/p>\n<\/li>\n

    2. \n

      \u751f\u957f\u51fd\u6570<\/strong>\uff1a\u589e\u957f\u51fd\u6570\u63cf\u8ff0\u4e86\u5047\u8bbe\u7c7b\u5bf9\u4e8e\u7ed9\u5b9a\u6570\u91cf\u7684\u6570\u636e\u70b9\u53ef\u4ee5\u5b9e\u73b0\u7684\u6700\u5927\u4e0d\u540c\u4e8c\u5206\u6cd5\uff08\u4e8c\u5143\u6807\u7b7e\uff09\u6570\u91cf\u3002<\/p>\n<\/li>\n

    3. \n

      \u65ad\u70b9<\/strong>\uff1a\u65ad\u70b9\u662f\u53ef\u4ee5\u5b9e\u73b0\u6240\u6709\u4e8c\u5206\u6cd5\u7684\u6700\u5927\u70b9\u6570\uff0c\u4f46\u662f\u53ea\u8981\u518d\u6dfb\u52a0\u4e00\u4e2a\u70b9\uff0c\u5c31\u4f1a\u4f7f\u81f3\u5c11\u4e00\u4e2a\u4e8c\u5206\u6cd5\u65e0\u6cd5\u5b9e\u73b0\u3002<\/p>\n<\/li>\n<\/ol>\n

      \u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u5404\u79cd\u7c7b\u578b\uff0c\u8bf7\u8003\u8651\u4ee5\u4e0b\u793a\u4f8b\uff1a<\/p>\n

      \u4f8b\u5b50<\/strong>\uff1a\u8ba9\u6211\u4eec\u8003\u8651\u4e00\u4e2a\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u7684\u7ebf\u6027\u5206\u7c7b\u5668\uff0c\u5b83\u901a\u8fc7\u7ed8\u5236\u76f4\u7ebf\u6765\u5206\u9694\u6570\u636e\u70b9\u3002\u5982\u679c\u6570\u636e\u70b9\u7684\u6392\u5217\u65b9\u5f0f\u4f7f\u5f97\u65e0\u8bba\u6211\u4eec\u5982\u4f55\u6807\u8bb0\u5b83\u4eec\uff0c\u603b\u6709\u4e00\u6761\u7ebf\u53ef\u4ee5\u5c06\u5b83\u4eec\u5206\u5f00\uff0c\u5219\u5047\u8bbe\u7c7b\u7684\u65ad\u70b9\u4e3a 0\u3002\u5982\u679c\u70b9\u7684\u6392\u5217\u65b9\u5f0f\u4f7f\u5f97\u5bf9\u4e8e\u67d0\u4e9b\u6807\u8bb0\uff0c\u6ca1\u6709\u7ebf\u5c06\u5b83\u4eec\u5206\u5f00\uff0c\u5219\u5047\u8bbe\u7c7b\u88ab\u79f0\u4e3a\u7834\u574f\u70b9\u96c6\u3002<\/p>\n

      Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u7684\u4f7f\u7528\u65b9\u6cd5\u3001\u4f7f\u7528\u8fc7\u7a0b\u4e2d\u9047\u5230\u7684\u95ee\u9898\u53ca\u89e3\u51b3\u65b9\u6cd5<\/h2>\n

      VC \u7ef4\u5ea6\u5728\u673a\u5668\u5b66\u4e60\u548c\u6a21\u5f0f\u8bc6\u522b\u7684\u5404\u4e2a\u9886\u57df\u90fd\u6709\u5e94\u7528\u3002\u5b83\u7684\u4e00\u4e9b\u7528\u9014\u5305\u62ec\uff1a<\/p>\n

        \n
      1. \n

        \u9009\u578b<\/strong>\uff1aVC \u7ef4\u5ea6\u6709\u52a9\u4e8e\u4e3a\u7ed9\u5b9a\u7684\u5b66\u4e60\u4efb\u52a1\u9009\u62e9\u9002\u5f53\u7684\u6a21\u578b\u590d\u6742\u5ea6\u3002\u901a\u8fc7\u9009\u62e9\u5177\u6709\u9002\u5f53 VC \u7ef4\u5ea6\u7684\u5047\u8bbe\u7c7b\uff0c\u53ef\u4ee5\u907f\u514d\u8fc7\u5ea6\u62df\u5408\u5e76\u63d0\u9ad8\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n<\/li>\n

      2. \n

        \u754c\u5b9a\u6cdb\u5316\u8bef\u5dee<\/strong>\uff1aVC \u7ef4\u4f7f\u6211\u4eec\u80fd\u591f\u6839\u636e\u8bad\u7ec3\u6837\u672c\u7684\u6570\u91cf\u63a8\u5bfc\u51fa\u5b66\u4e60\u7b97\u6cd5\u6cdb\u5316\u8bef\u5dee\u7684\u754c\u9650\u3002<\/p>\n<\/li>\n

      3. \n

        \u7ed3\u6784\u98ce\u9669\u6700\u5c0f\u5316<\/strong>\uff1aVC \u7ef4\u662f\u7ed3\u6784\u98ce\u9669\u6700\u5c0f\u5316\u4e2d\u7684\u4e00\u4e2a\u5173\u952e\u6982\u5ff5\uff0c\u5b83\u662f\u7528\u6765\u5e73\u8861\u7ecf\u9a8c\u8bef\u5dee\u548c\u6a21\u578b\u590d\u6742\u6027\u4e4b\u95f4\u7684\u6743\u8861\u7684\u539f\u5219\u3002<\/p>\n<\/li>\n

      4. \n

        \u652f\u6301\u5411\u91cf\u673a (SVM)<\/strong>\uff1aSVM\u662f\u4e00\u79cd\u6d41\u884c\u7684\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\uff0c\u5b83\u5229\u7528VC\u7ef4\u5728\u9ad8\u7ef4\u7279\u5f81\u7a7a\u95f4\u4e2d\u5bfb\u627e\u6700\u4f18\u5206\u79bb\u8d85\u5e73\u9762\u3002<\/p>\n<\/li>\n<\/ol>\n

        \u7136\u800c\uff0c\u867d\u7136 VC \u7ef4\u5ea6\u662f\u4e00\u4e2a\u6709\u4ef7\u503c\u7684\u5de5\u5177\uff0c\u4f46\u5b83\u4e5f\u5e26\u6765\u4e86\u4e00\u4e9b\u6311\u6218\uff1a<\/p>\n

          \n
        1. \n

          \u8ba1\u7b97\u590d\u6742\u5ea6<\/strong>\uff1a\u8ba1\u7b97\u590d\u6742\u5047\u8bbe\u7c7b\u7684 VC \u7ef4\u5ea6\u7684\u8ba1\u7b97\u6210\u672c\u5f88\u9ad8\u3002<\/p>\n<\/li>\n

        2. \n

          \u975e\u4e8c\u5143\u5206\u7c7b<\/strong>\uff1aVC \u7ef4\u6700\u521d\u662f\u4e3a\u4e8c\u5143\u5206\u7c7b\u95ee\u9898\u5f00\u53d1\u7684\uff0c\u5c06\u5176\u6269\u5c55\u5230\u591a\u7c7b\u95ee\u9898\u53ef\u80fd\u5177\u6709\u6311\u6218\u6027\u3002<\/p>\n<\/li>\n

        3. \n

          \u6570\u636e\u4f9d\u8d56\u6027<\/strong>\uff1aVC\u7ef4\u4f9d\u8d56\u4e8e\u6570\u636e\u7684\u5206\u5e03\uff0c\u6570\u636e\u5206\u5e03\u7684\u53d8\u5316\u53ef\u80fd\u4f1a\u5f71\u54cd\u5b66\u4e60\u7b97\u6cd5\u7684\u6027\u80fd\u3002<\/p>\n<\/li>\n<\/ol>\n

          \u4e3a\u4e86\u5e94\u5bf9\u8fd9\u4e9b\u6311\u6218\uff0c\u7814\u7a76\u4eba\u5458\u5f00\u53d1\u4e86\u5404\u79cd\u8fd1\u4f3c\u7b97\u6cd5\u548c\u6280\u672f\u6765\u4f30\u8ba1 VC \u7ef4\u5ea6\u5e76\u5c06\u5176\u5e94\u7528\u4e8e\u66f4\u590d\u6742\u7684\u573a\u666f\u3002<\/p>\n

          \u4e3b\u8981\u7279\u70b9\u53ca\u4e0e\u540c\u7c7b\u672f\u8bed\u7684\u5176\u4ed6\u6bd4\u8f83<\/h2>\n

          VC \u7ef4\u5ea6\u4e0e\u673a\u5668\u5b66\u4e60\u548c\u7edf\u8ba1\u5b66\u4e2d\u4f7f\u7528\u7684\u5176\u4ed6\u6982\u5ff5\u5177\u6709\u4e00\u4e9b\u5171\u540c\u7279\u5f81\uff1a<\/p>\n

            \n
          1. \n

            \u62c9\u5fb7\u9a6c\u8d6b\u590d\u6742\u6027<\/strong>\uff1aRademacher \u590d\u6742\u5ea6\u8861\u91cf\u5047\u8bbe\u7c7b\u5728\u62df\u5408\u968f\u673a\u566a\u58f0\u65b9\u9762\u7684\u80fd\u529b\u3002\u5b83\u4e0e VC \u7ef4\u5bc6\u5207\u76f8\u5173\uff0c\u7528\u4e8e\u9650\u5236\u6cdb\u5316\u8bef\u5dee\u3002<\/p>\n<\/li>\n

          2. \n

            \u7834\u788e\u7cfb\u6570<\/strong>\uff1a\u4e00\u4e2a\u5047\u8bbe\u7c7b\u7684\u7834\u788e\u7cfb\u6570\u5ea6\u91cf\u4e86\u6700\u591a\u53ef\u4ee5\u88ab\u7834\u788e\u7684\u70b9\u6570\uff0c\u7c7b\u4f3c\u4e8eVC\u7ef4\u6570\u3002<\/p>\n<\/li>\n

          3. \n

            PAC \u5b66\u4e60<\/strong>\uff1aPAC\u5b66\u4e60\u662f\u4e00\u79cd\u673a\u5668\u5b66\u4e60\u6846\u67b6\uff0c\u4e3b\u8981\u5173\u6ce8\u5b66\u4e60\u7b97\u6cd5\u7684\u6709\u6548\u6837\u672c\u590d\u6742\u5ea6\u3002VC\u7ef4\u5728\u5206\u6790PAC\u5b66\u4e60\u7684\u6837\u672c\u590d\u6742\u5ea6\u4e2d\u8d77\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\u3002<\/p>\n<\/li>\n<\/ol>\n

            \u4e0e Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u76f8\u5173\u7684\u672a\u6765\u524d\u666f\u548c\u6280\u672f<\/h2>\n

            Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u5c06\u7ee7\u7eed\u6210\u4e3a\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u548c\u7edf\u8ba1\u5b66\u4e60\u7406\u8bba\u53d1\u5c55\u7684\u6838\u5fc3\u6982\u5ff5\u3002\u968f\u7740\u6570\u636e\u96c6\u53d8\u5f97\u8d8a\u6765\u8d8a\u5927\u3001\u8d8a\u6765\u8d8a\u590d\u6742\uff0c\u7406\u89e3\u548c\u5229\u7528 VC \u7ef4\u5ea6\u5bf9\u4e8e\u6784\u5efa\u5177\u6709\u826f\u597d\u6cdb\u5316\u7684\u6a21\u578b\u5c06\u53d8\u5f97\u8d8a\u6765\u8d8a\u91cd\u8981\u3002<\/p>\n

            VC \u7ef4\u4f30\u8ba1\u7684\u8fdb\u6b65\u53ca\u5176\u4e0e\u5404\u79cd\u5b66\u4e60\u6846\u67b6\u7684\u96c6\u6210\u53ef\u80fd\u4f1a\u5e26\u6765\u66f4\u9ad8\u6548\u3001\u66f4\u51c6\u786e\u7684\u5b66\u4e60\u7b97\u6cd5\u3002\u6b64\u5916\uff0cVC \u7ef4\u4e0e\u6df1\u5ea6\u5b66\u4e60\u548c\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u7684\u7ed3\u5408\u53ef\u80fd\u4f1a\u4ea7\u751f\u66f4\u7a33\u5065\u3001\u66f4\u6613\u4e8e\u89e3\u91ca\u7684\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u3002<\/p>\n

            \u5982\u4f55\u4f7f\u7528\u4ee3\u7406\u670d\u52a1\u5668\u6216\u5c06\u5176\u4e0e Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u5173\u8054<\/h2>\n

            \u4ee3\u7406\u670d\u52a1\u5668\uff08\u4f8b\u5982 OneProxy (oneproxy.pro) \u63d0\u4f9b\u7684\u4ee3\u7406\u670d\u52a1\u5668\uff09\u5728\u8bbf\u95ee\u4e92\u8054\u7f51\u65f6\u5bf9\u7ef4\u62a4\u9690\u79c1\u548c\u5b89\u5168\u8d77\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\u3002\u5b83\u4eec\u5145\u5f53\u7528\u6237\u548c\u7f51\u7edc\u670d\u52a1\u5668\u4e4b\u95f4\u7684\u4e2d\u4ecb\uff0c\u5141\u8bb8\u7528\u6237\u9690\u85cf\u5176 IP \u5730\u5740\u5e76\u4ece\u4e0d\u540c\u7684\u5730\u7406\u4f4d\u7f6e\u8bbf\u95ee\u5185\u5bb9\u3002<\/p>\n

            \u5728 Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u4e2d\uff0c\u4ee3\u7406\u670d\u52a1\u5668\u53ef\u4ee5\u6309\u4ee5\u4e0b\u65b9\u5f0f\u4f7f\u7528\uff1a<\/p>\n

              \n
            1. \n

              \u589e\u5f3a\u6570\u636e\u9690\u79c1<\/strong>\uff1a\u5728\u8fdb\u884c\u673a\u5668\u5b66\u4e60\u4efb\u52a1\u7684\u5b9e\u9a8c\u6216\u6570\u636e\u6536\u96c6\u65f6\uff0c\u7814\u7a76\u4eba\u5458\u53ef\u80fd\u4f1a\u4f7f\u7528\u4ee3\u7406\u670d\u52a1\u5668\u6765\u4fdd\u6301\u533f\u540d\u5e76\u4fdd\u62a4\u4ed6\u4eec\u7684\u8eab\u4efd\u3002<\/p>\n<\/li>\n

            2. \n

              \u907f\u514d\u8fc7\u5ea6\u62df\u5408<\/strong>\uff1a\u4ee3\u7406\u670d\u52a1\u5668\u53ef\u7528\u4e8e\u4ece\u4e0d\u540c\u4f4d\u7f6e\u8bbf\u95ee\u4e0d\u540c\u7684\u6570\u636e\u96c6\uff0c\u4ece\u800c\u63d0\u4f9b\u66f4\u591a\u6837\u5316\u7684\u8bad\u7ec3\u96c6\uff0c\u6709\u52a9\u4e8e\u51cf\u5c11\u8fc7\u5ea6\u62df\u5408\u3002<\/p>\n<\/li>\n

            3. \n

              \u8bbf\u95ee\u53d7\u5730\u7406\u9650\u5236\u7684\u5185\u5bb9<\/strong>\uff1a\u4ee3\u7406\u670d\u52a1\u5668\u5141\u8bb8\u7528\u6237\u8bbf\u95ee\u6765\u81ea\u4e0d\u540c\u5730\u533a\u7684\u5185\u5bb9\uff0c\u4ece\u800c\u80fd\u591f\u5728\u4e0d\u540c\u7684\u6570\u636e\u5206\u5e03\u4e0a\u6d4b\u8bd5\u673a\u5668\u5b66\u4e60\u6a21\u578b\u3002<\/p>\n<\/li>\n<\/ol>\n

              \u901a\u8fc7\u7b56\u7565\u6027\u5730\u4f7f\u7528\u4ee3\u7406\u670d\u52a1\u5668\uff0c\u7814\u7a76\u4eba\u5458\u548c\u5f00\u53d1\u4eba\u5458\u53ef\u4ee5\u6709\u6548\u5730\u7ba1\u7406\u6570\u636e\u6536\u96c6\uff0c\u63d0\u9ad8\u6a21\u578b\u6cdb\u5316\u80fd\u529b\uff0c\u5e76\u589e\u5f3a\u5176\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u7684\u6574\u4f53\u6027\u80fd\u3002<\/p>\n

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

              \u6709\u5173 Vapnik-Chervonenkis (VC) \u7ef4\u5ea6\u53ca\u76f8\u5173\u4e3b\u9898\u7684\u66f4\u591a\u4fe1\u606f\uff0c\u8bf7\u53c2\u9605\u4ee5\u4e0b\u8d44\u6e90\uff1a<\/p>\n

                \n
              1. \n

                Vapnik, V., & Chervonenkis, A. (1971). \u8bba\u4e8b\u4ef6\u76f8\u5bf9\u9891\u7387\u4e0e\u5176\u6982\u7387\u7684\u7edf\u4e00\u6536\u655b<\/a><\/p>\n<\/li>\n

              2. \n

                Vapnik, V., & Chervonenkis, A. (1974). \u6a21\u5f0f\u8bc6\u522b\u7406\u8bba<\/a><\/p>\n<\/li>\n

              3. \n

                Shalev-Shwartz, S., & Ben-David, S. (2014). \u7406\u89e3\u673a\u5668\u5b66\u4e60\uff1a\u4ece\u7406\u8bba\u5230\u7b97\u6cd5<\/a><\/p>\n<\/li>\n

              4. \n

                Vapnik, VN (1998). \u7edf\u8ba1\u5b66\u4e60\u7406\u8bba<\/a><\/p>\n<\/li>\n

              5. \n

                \u7ef4\u57fa\u767e\u79d1 \u2013 VC \u7ef4\u5ea6<\/a><\/p>\n<\/li>\n

              6. \n

                \u74e6\u666e\u5c3c\u514b-\u5207\u5c14\u6c83\u5e74\u57fa\u65af\u7ef4\u5ea6\u2014\u2014\u5eb7\u5948\u5c14\u5927\u5b66<\/a><\/p>\n<\/li>\n

              7. \n

                \u7ed3\u6784\u98ce\u9669\u6700\u5c0f\u5316 \u2013 \u795e\u7ecf\u4fe1\u606f\u5904\u7406\u7cfb\u7edf (NIPS)<\/a><\/p>\n<\/li>\n<\/ol>\n

                \u901a\u8fc7\u63a2\u7d22\u8fd9\u4e9b\u8d44\u6e90\uff0c\u8bfb\u8005\u53ef\u4ee5\u66f4\u6df1\u5165\u5730\u4e86\u89e3 Vapnik-Chervonenkis \u7ef4\u5ea6\u7684\u7406\u8bba\u57fa\u7840\u548c\u5b9e\u9645\u5e94\u7528\u3002<\/p>","protected":false},"featured_media":470805,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-479495","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about Vapnik-Chervonenkis (VC) Dimension: A Comprehensive Guide<\/mark>","faq_items":[{"question":"What is the Vapnik-Chervonenkis (VC) dimension?","answer":"

                The Vapnik-Chervonenkis (VC) dimension is a fundamental concept in computational learning theory and statistics. It measures the capacity of a hypothesis class or learning algorithm to shatter data points, enabling a deeper understanding of generalization ability in machine learning models.<\/p>"},{"question":"Who introduced the VC dimension, and when was it first mentioned?","answer":"

                The VC dimension was introduced by Vladimir Vapnik and Alexey Chervonenkis in the early 1970s. They first mentioned it in their 1971 paper titled \"On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities.\"<\/p>"},{"question":"How does the VC dimension work?","answer":"

                The VC dimension quantifies the maximum number of data points that a hypothesis class can shatter, meaning it can correctly classify any possible binary labeling of the data points. It plays a crucial role in determining a model's ability to generalize from training data to unseen data, helping to prevent overfitting.<\/p>"},{"question":"What are the key features of the VC dimension?","answer":"

                The VC dimension offers important insights, including its role as a capacity measure for hypothesis classes, its link to generalization error in learning algorithms, its significance in model selection, and its support for the principle of Occam's razor.<\/p>"},{"question":"What types of VC dimension exist?","answer":"

                The VC dimension can be categorized into shatterable sets, growth functions, and breakpoints. A set of data points is considered shatterable if all possible binary labelings can be realized by the hypothesis class.<\/p>"},{"question":"How can the VC dimension be used, and what problems can arise?","answer":"

                The VC dimension finds applications in model selection, bounding generalization error, structural risk minimization, and support vector machines (SVM). However, challenges include computational complexity, non-binary classification, and data dependency. Researchers have developed approximation algorithms and techniques to address these issues.<\/p>"},{"question":"What are the perspectives and future technologies related to the VC dimension?","answer":"

                The VC dimension will continue to play a central role in machine learning and statistical learning theory. As data sets grow larger and more complex, understanding and leveraging the VC dimension will be crucial in developing models that generalize well and achieve better performance.<\/p>"},{"question":"How can proxy servers be associated with the VC dimension?","answer":"

                Proxy servers, like those provided by OneProxy (oneproxy.pro), can enhance data privacy during experiments or data collection for machine learning tasks. They can also help access diverse datasets from different geographical locations, contributing to more robust and generalized models.<\/p>"},{"question":"Where can I find more information about the VC dimension?","answer":"

                For more information about the VC dimension and related topics, you can explore the provided links to resources, research papers, and books on statistical learning theory and machine learning algorithms.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/479495","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\/479495\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media\/470805"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media?parent=479495"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}