{"id":2977,"date":"2022-02-20T20:52:50","date_gmt":"2022-02-20T12:52:50","guid":{"rendered":"https:\/\/egonlin.com\/?p=2977"},"modified":"2023-02-01T12:36:36","modified_gmt":"2023-02-01T04:36:36","slug":"%e7%ac%ac%e4%b8%80%e8%8a%82%ef%bc%9a%e7%ba%bf%e6%80%a7%e5%9b%9e%e5%bd%92%e5%bc%95%e5%85%a5","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=2977","title":{"rendered":"\u7b2c\u4e00\u8282\uff1a\u7ebf\u6027\u56de\u5f52\u5f15\u5165"},"content":{"rendered":"

\u7ebf\u6027\u56de\u5f52<\/h1>\n

  \u7ebf\u6027\u56de\u5f52\u662f\u6bd4\u8f83\u7ecf\u5178\u7684\u7ebf\u6027\u6a21\u578b\uff0c\u5c5e\u4e8e\u76d1\u7763\u5b66\u4e60\u4e2d\u9884\u6d4b\u503c\u4e3a\u8fde\u7eed\u503c\u7684\u56de\u5f52\u95ee\u9898\u3002<\/p>\n

  \u7ebf\u6027\u56de\u5f52\u9488\u5bf9\u7684\u662f\u4e00\u4e2a\u6216\u591a\u4e2a\u7279\u5f81\u4e0e\u8fde\u7eed\u76ee\u6807\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u5efa\u6a21\uff0c\u5373\u7ebf\u6027\u56de\u5f52\u5206\u6790\u7684\u4e3b\u8981\u76ee\u6807\u662f\u5728\u8fde\u7eed\u5c3a\u5ea6\u4e0a\u9884\u6d4b\u8f93\u51fa\uff0c\u800c\u975e\u5206\u7c7b\u6807\u7b7e\uff0c\u5373\u9884\u6d4b\u503c\u4e3a\u8fde\u7eed\u503c\u3002<\/p>\n

\u7ebf\u6027\u56de\u5f52\u5b66\u4e60\u76ee\u6807<\/h1>\n
    \n
  1. \u7ebf\u6027\u6a21\u578b<\/li>\n
  2. \u4e00\u5143\u7ebf\u6027\u56de\u5f52\u548c\u591a\u5143\u7ebf\u6027\u56de\u5f52<\/li>\n
  3. \u591a\u9879\u5f0f\u56de\u5f52\u548c\u5bf9\u6570\u7ebf\u6027\u56de\u5f52<\/li>\n
  4. \u7ebf\u6027\u56de\u5f52\u7684L1\u6b63\u5219\u5316\u548cL2\u6b63\u5219\u5316<\/li>\n
  5. \u7ebf\u6027\u56de\u5f52\u6d41\u7a0b<\/li>\n
  6. \u7ebf\u6027\u56de\u5f52\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n

    \u7ebf\u6027\u56de\u5f52\u5f15\u5165<\/h1>\n

    \"\"<\/div>
    \n  \u76f8\u4fe1\u6211\u4eec\u5f88\u591a\u4eba\u53ef\u80fd\u90fd\u6709\u53bb\u552e\u697c\u5904\u4e70\u623f\u800c\u65e0\u5948\u56de\u5bb6\u7684\u884c\u4e3a\uff0c\u5c31\u7b97\u4f60\u6ca1\u53bb\u8fc7\u552e\u697c\u5904\uff0c\u76f8\u4fe1\u4f60\u4e5f\u5e94\u8be5\u542c\u8bf4\u8fc7\u90a3\u4ee4\u4eba\u53f9\u800c\u60ca\u6b62\u7684\u623f\u4ef7\u5427\uff1f\u5bf9\u4e8e\u9ad8\u623f\u4ef7\u4f60\u6ca1\u6709\u60f3\u8fc7\u8fd9\u623f\u4ef7\u662f\u600e\u4e48\u7b97\u51fa\u6765\u7684\u5462\uff1f\u96be\u9053\u5c31\u662f\u623f\u5730\u4ea7\u5546\u62cd\u62cd\u8111\u95e8\uff0c\u5317\u4eac\u7684\u4e00\u69821000\u4e07\uff0c\u4e0a\u6d77\u7684\u4e00\u6982800\u4e07\uff0c\u676d\u5dde\u7684\u4e00\u6982600\u4e07\u5417\uff1f\u770b\u5230\u8fd9\u76f8\u4fe1\u4f60\u5e94\u8be5\u6709\u52a8\u529b\u60f3\u8981\u5b66\u597d\u673a\u5668\u5b66\u4e60\u8d70\u5411\u4eba\u751f\u5dc5\u5cf0\u4e86\u3002<\/p>\n

      \u5176\u5b9e\u4ed4\u7ec6\u60f3\u60f3\u8fd9\u623f\u4ef7\u5927\u6709\u6765\u5934\uff0c\u9996\u5148\u623f\u4ef7\u4e0d\u53ef\u80fd\u53ea\u548c\u5730\u533a\u6709\u5173\uff0c\u5317\u4eac\u67091000\u4e07\u7684\u623f\u5b50\uff0c\u53c8\u4f1a\u6709800\u4e07\u3001600\u4e07\u7684\u623f\u5b50\uff0c\u90a3\u8fd9\u4e9b\u623f\u4ef7\u4e0d\u548c\u5730\u533a\u6709\u5173\u8fd8\u548c\u4ec0\u4e48\u6709\u5173\u5462\uff1f\u5982\u679c\u4f60\u771f\u7684\u4e70\u8fc7\u623f\u5c31\u77e5\u9053\uff0c\u623f\u5b50\u7684\u4ef7\u683c\u9996\u5148\u548c\u5730\u533a\u662f\u6709\u7740\u6bd4\u8f83\u5927\u7684\u8054\u7cfb\u7684\uff0c\u5317\u4eac\u4e94\u73af\u5916\u7684\u623f\u5b50\u53ef\u80fd\u90fd\u9ad8\u4e8e\u676d\u5dde\u4efb\u4f55\u5730\u533a\u7684\u623f\u5b50\uff0c\u5728\u540c\u4e00\u4e2a\u5730\u533a\u5185\uff0c\u623f\u5b50\u7684\u4ef7\u683c\u5927\u591a\u548c\u623f\u5b50\u7684\u5360\u5730\u9762\u79ef\u3001\u6237\u578b\u3001\u91c7\u5149\u5ea6\u7b49\u7b49\u56e0\u7d20\u6709\u5173\u7cfb\u3002<\/p>\n

      \u8fd9\u4e2a\u65f6\u5019\u5c31\u6709\u67d0\u4f4d\u806a\u660e\u7684\u6295\u673a\u8005\u60f3\u5230\u4e86\uff0c\u6211\u662f\u4e0d\u662f\u53ef\u4ee5\u627e\u5230\u4e00\u4e2a\u65b9\u6cd5\u6765\u9884\u6d4b\u623f\u4ef7\u5462\uff1f\u5982\u679c\u8fd9\u4e2a\u623f\u5b50\u7684\u623f\u4ef7\u660e\u663e\u5c0f\u4e8e\u8fd9\u6240\u623f\u5b50\u8be5\u6709\u7684\u623f\u4ef7(\u6ce8\uff1a\u623f\u4ef7\u53ef\u80fd\u5728\u67d0\u6bb5\u65f6\u95f4\u7531\u4e8e\u67d0\u79cd\u4e0d\u4e3a\u4eba\u77e5\u7684\u56e0\u7d20\u6709\u5c0f\u5e45\u6ce2\u52a8)\uff0c\u5c31\u628a\u90a3\u6240\u4e70\u8fc7\u6765\u4e86\uff0c\u7b49\u623f\u4ef7\u6da8\u56de\u53bb\u4e86\u518d\u5356\u51fa\u53bb\uff0c\u8fd9\u6837\u770b\u8d77\u6765\u4e5f\u662f\u751f\u8d22\u4e4b\u9053\u3002(\u6ce8\uff1a\u7eaf\u5c5e\u865a\u6784)<\/p>\n

      \u53ef\u662f\u5982\u679c\u53bb\u9884\u6d4b\u623f\u4ef7\u5462\uff1f\u4e0a\u9762\u8bb2\u5230\u4e86\u623f\u4ef7\u548c\u623f\u5b50\u6240\u5728\u5730\u533a$x_1$\u3001\u5360\u5730\u9762\u79ef$x_2$\u3001\u6237\u578b$x_3$\u548c\u91c7\u5149\u5ea6$x_4$\u6709\u5173\uff0c\u90a3\u4e48\u6211\u662f\u4e0d\u662f\u53ef\u4ee5\u628a\u8fd9\u4e9b\u56e0\u7d20\u5047\u60f3\u6210\u623f\u5b50\u7684\u7279\u5f81\uff0c\u7136\u540e\u7ed9\u8fd9\u4e9b\u6bcf\u4e2a\u7279\u5f81\u90fd\u52a0\u4e0a\u4e00\u4e2a\u76f8\u5e94\u7684\u6743\u91cd$\\omega$\uff0c\u65e2\u53ef\u4ee5\u5f97\u5230\u5982\u4e0b\u7684\u51b3\u7b56\u51fd\u6570
    \n

    \"file\"<\/div>
    \n\u5176\u4e2d$b$\u53ef\u4ee5\u7406\u89e3\u4e3a\u504f\u5dee\uff0c\u4f60\u4e5f\u53ef\u4ee5\u60f3\u6210\u623f\u5b50\u7684\u8fd9\u4e9b\u7279\u5f81\u518d\u5dee\u4e5f\u53ef\u80fd\u4f1a\u6709\u4e00\u4e2a\u5e95\u4ef7\u3002<\/p>\n

      \u57fa\u4e8e\u4e0a\u8ff0\u7ed9\u51fa\u623f\u4ef7\u7684\u51b3\u7b56\u51fd\u6570\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5bf9\u4e00\u4e2a\u67d0\u4e2a\u4e0d\u77e5\u540d\u7684\u623f\u5b50\u8f93\u5165\u5b83\u7684\u8fd9\u4e9b\u7279\u5f81\uff0c\u7136\u540e\u5c31\u53ef\u4ee5\u5f97\u5230\u8fd9\u6240\u623f\u5b50\u7684\u9884\u6d4b\u4ef7\u683c\u4e86\u3002<\/p>\n

      \u7406\u60f3\u603b\u662f\u7f8e\u597d\u7684\uff0c\u5373\u4e00\u6761\u751f\u8d22\u4e4b\u9053\u5c31\u5728\u773c\u524d\uff0c\u4f46\u662f\u6211\u4eec\u5982\u4f55\u53bb\u5f97\u5230\u8fd9\u4e2a\u51b3\u7b56\u51fd\u6570\u5462\uff1f\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e2a\u7279\u5f81\u503c\uff0c\u4f46\u662f\u8fd9\u4e2a$\\omega$\u600e\u4e48\u5f97\u5230\u5462\uff1f\u8fd9\u5c31\u662f\u6211\u4eec\u7684\u7ebf\u6027\u56de\u5f52\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u4e0b\u9762\u8ba9\u6211\u4eec\u4e00\u8d77\u8d70\u5411\u8fd9\u6761\u751f\u8d22\u4e4b\u9053\u5427\uff01<\/p>\n

    \u7ebf\u6027\u56de\u5f52\u8be6\u89e3<\/h1>\n

    \u7ebf\u6027\u6a21\u578b<\/h2>\n

      \u7ed9\u5b9a\u6709$n$\u5c5e\u6027\u7684\u6837\u672c$x=(x_1,x_2,\\ldots,x_n)$\uff0c\u5176\u4e2d$x_i$\u662f$x$\u5728\u7b2c$i$\u4e2a\u5c5e\u6027\u4e0a\u7684\u53d6\u503c\uff0c\u7ebf\u6027\u6a21\u578b(linear model)\u5219\u662f\u8bd5\u56fe\u5b66\u5f97\u4e00\u4e2a\u901a\u8fc7\u7ebf\u6027\u7ec4\u5408\u9884\u6d4b\u7684\u51fd\u6570\u3002\u8be5\u7ebf\u6027\u7ec4\u5408\u53ef\u4ee5\u8868\u793a\u4e3a
    \n

    \"file\"<\/div>
    \n\u7ebf\u6027\u7ec4\u5408\u7528\u5411\u91cf\u53ef\u4ee5\u8868\u793a\u4e3a
    \n
    \"file\"<\/div>
    \n  \u5982\u679c$\\omega$\u548c$b$\u88ab\u786e\u5b9a\u4e4b\u540e\uff0c\u6a21\u578b\u5c31\u53ef\u4ee5\u786e\u5b9a\u3002<\/p>\n

    \u4e00\u5143\u7ebf\u6027\u56de\u5f52<\/h2>\n

    \u4e00\u5143\u7ebf\u6027\u56de\u5f52\u7684\u76ee\u6807\u51fd\u6570<\/h3>\n

      \u7ed9\u5b9a\u6709$m$\u4e2a\u6837\u672c\u7684\u6570\u636e\u96c6$D={(x_1,y_1),(x_2,y_2),\\ldots,(x_m,y_m)}$\uff0c\u5047\u8bbe\u6bcf\u4e2a\u6837\u672c\u53ea\u6709$1$\u4e2a\u7279\u5f81\u4e3a$x_i$\u3002<\/p>\n

      \u7531\u4e8e\u7ebf\u6027\u56de\u5f52\u5c5e\u4e8e\u7ebf\u6027\u6a21\u578b\u7684\u4e00\u79cd\uff0c\u5219\u7ebf\u6027\u56de\u5f52\u4e5f\u53ef\u4ee5\u901a\u8fc7\u7ebf\u6027\u7ec4\u5408\u7684\u65b9\u5f0f\u5b66\u5f97\u5173\u4e8e\u9884\u6d4b\u503c\u7684\u516c\u5f0f
    \n

    \"file\"<\/div>
    \n  \u73b0\u5728\u7684\u95ee\u9898\u65f6\u5982\u4f55\u5b66\u5f97\u5e76\u786e\u5b9a$\\omega$\u548c$b$\u3002\u663e\u7136\uff0c\u5173\u952e\u5728\u4e8e\u8861\u91cf\u771f\u5b9e\u503c$y_i$\u548c\u9884\u6d4b\u503c$\\hat{y_i}$\u4e4b\u95f4\u7684\u5dee\u522b\u3002\u901a\u5e38\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u4f7f\u7528\u5747\u65b9\u8bef\u5dee\u4f5c\u4e3a\u56de\u5f52\u6a21\u578b\u7684\u6027\u80fd\u5ea6\u91cf\uff0c\u65e2\u53ef\u4ee5\u5f97\u5230\u7ebf\u6027\u56de\u5f52\u7684\u635f\u5931\u51fd\u6570
    \n
    \"file\"<\/div>
    \n\u901a\u8fc7\u635f\u5931\u51fd\u6570\u5219\u53ef\u4ee5\u5f97\u5230\u7ebf\u6027\u56de\u5f52\u7684\u76ee\u6807\u51fd\u6570
    \n
    \"file\"<\/div><\/p>\n

    \u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u5316\u2014\u2014\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/h3>\n

      \u5747\u65b9\u8bef\u5dee\u7684\u51e0\u4f55\u610f\u4e49\u5bf9\u5e94\u4e86\u6b27\u6c0f\u8ddd\u79bb(Euclidean distance)\uff0c\u57fa\u4e8e\u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u5316\u8fdb\u884c\u6a21\u578b\u6c42\u89e3\u7684\u65b9\u6cd5\u79f0\u4e3a\u6700\u5c0f\u4e8c\u4e58\u6cd5(least square method)\u3002\u5728\u7ebf\u6027\u56de\u5f52\u4e2d\uff0c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u8bd5\u56fe\u627e\u5230\u4e00\u6761\u76f4\u7ebf\uff0c\u4f7f\u6240\u6709\u6837\u672c\u7684\u6b27\u5f0f\u8ddd\u79bb\u4e4b\u548c\u6700\u5c0f\uff0c\u5373\u8bd5\u56fe\u8ba9\u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u5316\u3002<\/p>\n

      \u5728\u56de\u5f52\u95ee\u9898\u4e2d\u5bf9\u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u5316\u7684\u8fc7\u7a0b\u79f0\u4e3a\u7ebf\u6027\u56de\u5f52\u7684\u6700\u5c0f\u4e8c\u4e58\u53c2\u6570\u4f30\u8ba1(parameter estimation)\uff0c\u53ef\u4ee5\u5bf9\u5747\u65b9\u8bef\u5dee\u5206\u522b\u5bf9$\\omega$\u548c$b$\u6c42\u5bfc\u5f97
    \n

    \"file\"<\/div>
    \n  \u5229\u7528\u6570\u5b66\u4e2d\u6c42\u6781\u503c\u7684\u601d\u60f3\u5373\u53ef\u6c42\u5f97$\\omega$\u548c$b$\u7684\u6700\u4f18\u89e3
    \n
    \"file\"<\/div>
    \nb = {\\frac{1}{m}} \\sum_{i=1}^m (y_i – \\omega{xi})
    \n$$
    \n\u5176\u4e2d$\\overline{x} = {\\frac{1}{m}}\\sum<\/em>{i=1}^m x_i$\uff0c\u5373$x$\u7684\u5747\u503c<\/p>\n

    \u591a\u5143\u7ebf\u6027\u56de\u5f52<\/h2>\n

      \u4e00\u5143\u7ebf\u6027\u56de\u5f52\u66f4\u591a\u7684\u662f\u4e3a\u4e86\u5165\u95e8\uff0c\u901a\u5e38\u60c5\u51b5\u4e0b\u78b0\u5230\u7684\u95ee\u9898\u90fd\u662f\u7528\u591a\u5143\u7ebf\u6027\u56de\u5f52(multivariate linear regression)\u89e3\u51b3\u7684\uff0c\u5373\u6837\u672c\u901a\u5e38\u90fd\u6709$n, \\quad n>1$\u4e2a\u7279\u5f81\u3002<\/p>\n

      \u7ed9\u5b9a\u6570\u636e\u96c6$D={(x_1,y_1),(x_2,y_2),\\ldots,(x_m,y_m)}$\uff0c\u5047\u8bbe\u6bcf\u4e2a\u6837\u672c\u6709$n$\u4e2a\u7279\u5f81\u5219$xi = x<\/em>{i1},x{i2},\\ldots,x<\/em>{in}$\u3002\u7531\u6b64\u53ef\u4ee5\u5f97\u5230$n$\u4e2a\u7279\u5f81\u6837\u672c\u7684\u9884\u6d4b\u503c\u548c\u76ee\u6807\u51fd\u6570
    \n

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

    \u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u5316\u2014\u2014\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/h3>\n

      \u5982\u679c\u5bf9\u8be5\u76ee\u6807\u51fd\u6570\u76f4\u63a5\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u8fdb\u884c\u4f30\u8ba1\uff0c\u8ba1\u7b97\u4f1a\u5f88\u9ebb\u70e6\uff0c\u56e0\u6b64\u628a\u7279\u5f81\u548c\u6807\u8bb0\u90fd\u5199\u6210\u5411\u91cf\u7684\u5f62\u5f0f\u5e76\u547d\u540d\u4e3a$X$\u548c$Y$
    \n

    \"file\"<\/div>
    \n  \u901a\u8fc7\u4e0a\u8ff0\u5411\u91cf\u7684\u8f6c\u6362\u53ef\u4ee5\u628a\u76ee\u6807\u51fd\u6570\u8f6c\u6362\u6210
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d${\\frac{1}{2}}$\u662f\u4e3a\u4e86\u65b9\u4fbf\u8ba1\u7b97\u3002<\/p>\n

      \u540c\u4e00\u5143\u7ebf\u6027\u56de\u5f52\uff0c\u5bf9$\\omega$\u6c42\u5bfc\u627e\u5230\u6700\u4f18\u7684$\\omega$\uff0c\u5bf9$\\omega$\u6c42\u5bfc\u5f97
    \n

    \"file\"<\/div>
    \n  \u5f97\u5230\u76ee\u6807\u51fd\u6570\u5bf9$\\omega$\u6c42\u5bfc\u516c\u5f0f\u4e4b\u540e\uff0c\u7406\u5e94\u6c42$2X^T(X\\omega-Y)=0$\u65f6$\\omega$\u7684\u503c\uff0c\u4f46\u662f\u9700\u8981\u8003\u8651$X^TX$\u662f\u5426\u4e3a\u6ee1\u79e9\u77e9\u9635\u3002<\/p>\n

      \u5f53$X^TX$\u4e3a\u6ee1\u79e9\u77e9\u9635(full-rank matrix)\u6216\u6b63\u5b9a\u77e9\u9635(positive definite matrix)\u65f6\uff0c$2X^T(X\\omega-Y)=0$\u53ef\u5f97$\\omega$\u4e3a
    \n

    \"file\"<\/div>
    \n  \u7136\u800c\u73b0\u5b9e\u751f\u6d3b\u4e2d$X^TX$\u5f80\u5f80\u4e0d\u4e3a\u6ee1\u79e9\u77e9\u9635\uff0c\u4f8b\u5982\u751f\u7269\u4fe1\u606f\u5b66\u7684\u57fa\u56e0\u82af\u7247\u6570\u636e\u4e2d\u5e38\u6709\u6210\u5343\u4e07\u4e2a\u5c5e\u6027\uff0c\u4f46\u5f80\u5f80\u53ea\u6709\u51e0\u767e\u4e2a\u6837\u4f8b\u3002\u56e0\u6b64\u4f1a\u6709\u591a\u4e2a$\\omega$\u90fd\u80fd\u4f7f\u5f97$2X^T(X\\omega-Y)=0$\uff0c\u5373\u8fd9\u4e9b$\\omega$\u90fd\u80fd\u4f7f\u5f97\u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u5316\uff0c\u901a\u5e38\u60c5\u51b5\u4e0b\u4f1a\u5f15\u5165\u6b63\u5219\u5316(regularization)\u9879\u89e3\u51b3\u8be5\u95ee\u9898\u3002
    \n  $\\omega$\u52a0\u5165\u6b63\u5219\u5316\u9879\u5219\u53d8\u6210
    \n
    \"file\"<\/div>
    \n\u7531\u4e8e\u52a0\u4e0a\u6b63\u5219\u5316\u9879$\\lambda{I}$\u540e\uff0c\u5bf9\u4efb\u610f\u7684\u5b9e\u6570$\\lambda$\uff0c$X^TX+\\lambda{I}$\u4e00\u5b9a\u4e3a\u6ee1\u79e9\u77e9\u9635\u3002<\/p>\n

    \u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u5316\u2014\u2014\u725b\u987f\u6cd5<\/h3>\n

      \u4f7f\u7528\u4e8c\u9636\u7684\u6d77\u68ee\u77e9\u9635\u7684\u9006\u77e9\u9635\u6216\u4f2a\u9006\u77e9\u9635\u6c42\u89e3\uff0c\u76f8\u6bd4\u6bd4\u68af\u5ea6\u4e0b\u964d\u6cd5\u6536\u655b\u66f4\u5feb\uff0c\u4f46\u662f\u5f53\u7279\u5f81\u53c2\u6570\u5927\u65f6\uff0c\u8ba1\u7b97\u91cf\u5e9e\u5927\uff0c\u65f6\u95f4\u6162\u3002<\/p>\n

    \u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u5316\u2014\u2014\u62df\u725b\u987f\u6cd5<\/h3>\n

      \u725b\u987f\u6cd5\u5f97\u5230\u7684$f”(x)$\u662f\u4e00\u4e2a\u534a\u6b63\u5b9a\u77e9\u9635\uff0c\u62df\u725b\u987f\u6cd5\u5219\u5229\u7528\u4e00\u4e2a\u6b63\u5b9a\u77e9\u9635\u4ee3\u66ff\u8fd9\u4e2a\u534a\u6b63\u5b9a\u77e9\u9635\u3002<\/p>\n

    \u591a\u9879\u5f0f\u56de\u5f52<\/h2>\n

      \u524d\u9762\u8bf4\u5230\u7ebf\u6027\u6a21\u578b\u4e3a
    \n

    \"file\"<\/div>
    \n\u4f46\u662f\u5982\u679c\u5728\u8fd9\u4e2a\u5173\u7cfb\u5f0f\u4e2d\u4e0d\u4ec5\u7528\u5230\u7279\u5f81$x_i$\u7684\u4e00\u6b21\u65b9\uff0c\u800c\u662f\u589e\u52a0\u4e00\u4e2a\u5173\u4e8e$x_i$\u7684$n, \\quad n\\geq2$\u6b21\u65b9\uff0c\u90a3\u4e48\u6a21\u578b\u5c31\u53d8\u6210\u4e86\u591a\u9879\u5f0f\u56de\u5f52(polynomial regression)\u3002<\/p>\n

      \u5047\u8bbe\u4e00\u4e2a\u6b63\u65b9\u4f53\u7684\u623f\u5b50\u7684\u4ef7\u683c\u4e0e\u623f\u5b50\u7684\u8fb9\u957f\u3001\u623f\u5b50\u7684\u5360\u5730\u9762\u79ef\u548c\u623f\u5b50\u7684\u4f53\u79ef\u6709\u5173\u7cfb\uff0c\u7136\u800c\u73b0\u5728\u53ea\u6709\u623f\u5b50\u7684\u8fb9\u957f$x_1$\u4e00\u4e2a\u7279\u5f81\uff0c\u5982\u679c\u53ea\u62ff\u7279\u5f81\u53bb\u9884\u6d4b\u623f\u5b50\u7684\u4ef7\u683c\uff0c\u5219\u6709\u5f88\u5927\u53ef\u80fd\u4f1a\u6b20\u62df\u5408\uff0c\u56e0\u6b64\u9700\u8981\u589e\u52a0\u623f\u5b50\u7684\u5360\u5730\u9762\u79ef\u548c\u4f53\u79ef\u8fd9\u4e24\u4e2a\u7279\u5f81\uff0c\u5373
    \n

    \"file\"<\/div>
    \n\u4ee4$x_1=x_1,x_2={x_1}^2,x_3={x_1}^3$\uff0c\u5219\u591a\u9879\u5f0f\u7684\u7ebf\u6027\u6a21\u578b\u53d8\u6210
    \n
    \"file\"<\/div>
    \n  \u901a\u8fc7\u4e0a\u8ff0\u8f6c\u6362\u591a\u9879\u5f0f\u7684\u7ebf\u6027\u6a21\u578b\u53d8\u6210\u4e86\u4e00\u4e2a\u591a(\u4e09)\u5143\u7ebf\u6027\u56de\u5f52\u7684\u95ee\u9898\uff0c\u53ef\u4ee5\u4f7f\u7528\u7ebf\u6027\u56de\u5f52\u7684\u65b9\u6cd5\u6765\u5b8c\u6210\u7b97\u6cd5\u3002\u5e76\u4e14\u5bf9\u4e8e\u6bcf\u4e2a\u8fb9\u957f\u8fd9\u4e2a\u7279\u5f81$(x_1)$\u5f97\u5230\u4e00\u4e2a\u4e09\u5143\u6837\u672c\u7279\u5f81$(x_1,{x_1}^2,{x_1}^3)$\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\u5bf9\u4e8e\u591a\u7ef4\u5ea6\u7279\u5f81\u65f6\uff0c\u4f7f\u7528\u591a\u9879\u5f0f\u56de\u5f52\u4f1a\u4f7f\u5f97\u7279\u5f81\u4e4b\u95f4\u7684\u5173\u8054\u5ea6\u589e\u52a0\uff0c\u4f8b\u5982\u8fd9\u4e09\u4e2a\u7279\u5f81$(x_1,{x_1}^2,{x_1}^3)$\u662f\u6709\u5f88\u9ad8\u7684\u76f8\u5173\u6027\u7684\u3002<\/p>\n

      \u62ff\u4e0a\u4e00\u4e2a\u4f8b\u5b50\u5047\u8bbe\uff0c\u5982\u679c\u623f\u5b50\u7684\u8fb9\u957f\u4e3a$10$\uff0c\u5219\u623f\u5b50\u7684\u5360\u5730\u9762\u79ef\u4e3a$100$\uff0c\u623f\u5b50\u7684\u4f53\u79ef\u4e3a$1000$\uff0c\u8fd9\u4e09\u4e2a\u7279\u5f81\u6709\u4e86\u6570\u91cf\u7ea7\u7684\u5dee\u8ddd\uff0c\u6240\u4ee5\u5728\u4f7f\u7528\u591a\u9879\u5f0f\u56de\u5f52\u7684\u65f6\u5019\u9700\u8981\u6ce8\u610f\u5bf9\u7279\u5f81\u8fdb\u884c\u7279\u5f81\u7edf\u4e00\u5c3a\u5ea6\u5904\u7406\u3002<\/p>\n

      \u5de5\u4e1a\u4e0a\u53ef\u80fd\u5e76\u4e0d\u50cf\u623f\u5b50\u7684\u9762\u79ef\u3001\u623f\u5b50\u7684\u4f53\u79ef\u4e00\u6837\u6709\u660e\u786e\u7684\u76ee\u6807\u52a0\u4e0a$2\u6b21\u65b9$\u6216\u8005$3\u6b21\u65b9$\uff0c\u800c\u53ef\u80fd\u662f\u52a0\u4e0a$2\u6b21\u65b9$\u6216\u8005$5\u6b21\u65b9$\u6a21\u578b\u5c31\u80fd\u53d8\u5f97\u66f4\u597d\uff0c\u4f46\u662f\u5e76\u4e0d\u77e5\u9053$2\u6b21\u65b9$\u548c$5\u6b21\u65b9$\u8868\u793a\u4ec0\u4e48\u610f\u601d\uff0c\u8fdb\u800c\u4f1a\u5bfc\u81f4\u6a21\u578b\u7684\u89e3\u91ca\u80fd\u529b\u53d8\u5dee\u3002<\/p>\n

    \u5bf9\u6570\u7ebf\u6027\u56de\u5f52<\/h2>\n

      \u5047\u8bbe\u73b0\u5728\u5f97\u5230\u4e86\u4e00\u4e2a\u7ebf\u6027\u56de\u5f52\u6a21\u578b$\\hat{y}=\\omega^Tx+b$\uff0c\u4f46\u662f\u8be5\u7ebf\u6027\u6a21\u578b\u65e0\u6cd5\u6ee1\u8db3\u8f93\u51fa$\\hat{y}$\u4e0e\u8f93\u5165$x$\u7684\u7ebf\u6027\u5173\u7cfb\uff0c\u4f46\u662f$\\ln\\hat{y}$\u548c$x$\u6ee1\u8db3\u7ebf\u6027\u5173\u7cfb\uff0c\u5219\u53ef\u4ee5\u5c06\u8f93\u51fa\u6807\u8bb0\u7684\u5bf9\u6570\u4f5c\u4e3a\u7ebf\u6027\u6a21\u578b\u903c\u8fd1\u7684\u76ee\u6807\uff0c\u5373\u6a21\u578b\u51fd\u6570\u5982\u4e0b
    \n

    \"file\"<\/div>
    \n\u8fd9\u5c31\u662f\u5bf9\u6570\u7ebf\u6027\u56de\u5f52(log-linear regression)\uff0c\u5b83\u5b9e\u9645\u4e0a\u662f\u5728\u89c6\u56fe\u8ba9$e^{\\omega^T+b}$\u903c\u8fd1$\\hat{y}$\uff0c\u4f46\u662f\u4ecd\u7136\u53ef\u4ee5\u4f7f\u7528\u7ebf\u6027\u56de\u5f52\u7684\u7b97\u6cd5\u53bb\u5904\u7406\u8be5\u95ee\u9898\u3002<\/p>\n

      \u5047\u8bbe\u51fd\u6570$g(\u00b7)$\u662f\u5355\u8c03\u53ef\u5fae\u7684\u51fd\u6570\uff0c\u5219\u4e00\u822c\u5316\u7684\u5e7f\u4e49\u7ebf\u6027\u6a21\u578b(generalized linear model)\u53ef\u4ee5\u8868\u793a\u4e3a
    \n

    \"file\"<\/div>
    \n\u5176\u4e2d$g(\u00b7)$\u79f0\u4e3a\u8054\u7cfb\u51fd\u6570(link function)\uff0c\u5e76\u4e14\u5bf9\u6570\u7ebf\u6027\u56de\u5f52\u662f\u5e7f\u4e49\u7ebf\u6027\u6a21\u578b\u5728$g(\u00b7)=ln(\u00b7)$\u65f6\u7684\u7279\u4f8b\u3002<\/p>\n

    \u5c40\u90e8\u52a0\u6743\u7ebf\u6027\u56de\u5f52<\/h2>\n

      \u7ebf\u6027\u56de\u5f52\u7684\u4e00\u4e2a\u5927\u95ee\u9898\u5c31\u662f\u5bb9\u6613\u6b20\u62df\u5408\uff0c\u4e0a\u6b21\u8bb2\u5230\u7684\u591a\u9879\u5f0f\u56de\u5f52\u5c5e\u4e8e\u89e3\u51b3\u6b20\u62df\u5408\u7684\u65b9\u6cd5\u4e4b\u4e00\uff0c\u4f46\u662f\u5b83\u4e5f\u589e\u52a0\u4e86\u6570\u636e\u7684\u7ef4\u5ea6\uff0c\u5982\u679c\u6570\u636e\u672c\u8eab\u6709\u5f88\u591a\u7ef4\u5ea6\uff0c\u5219\u4e0d\u9002\u5408\u4f7f\u7528\u591a\u9879\u5f0f\u56de\u5f52\u3002<\/p>\n

      \u5c40\u90e8\u52a0\u6743\u7ebf\u6027\u56de\u5f52(locally weighted linear regression)\u4e5f\u53ef\u4ee5\u89e3\u51b3\u6570\u636e\u6b20\u62df\u5408\u7684\u95ee\u9898\uff0c\u5b83\u4e3b\u8981\u662f\u5728\u4f30\u8ba1\u4e2d\u5f15\u5165\u4e00\u4e9b\u504f\u5dee\uff0c\u4ece\u800c\u964d\u4f4e\u9884\u6d4b\u7684\u5747\u65b9\u8bef\u5dee\uff0c\u5b83\u7684\u76ee\u6807\u51fd\u6570\u4e3a
    \n

    \"file\"<\/div>
    \n\u5176\u4e2d$w_i$\u548c$W$\u90fd\u662f\u5bf9\u89d2\u77e9\u9635\uff0c\u7528\u6765\u7ed9\u6bcf\u4e2a\u6570\u636e\u70b9\u8d4b\u4e88\u6743\u91cd\u3002<\/p>\n

      \u76ee\u6807\u51fd\u6570\u5bf9$\\omega$\u6c42\u5bfc\u5f97
    \n

    \"file\"<\/div>
    \n  \u5c40\u90e8\u52a0\u6743\u7ebf\u6027\u56de\u5f52\u7ed9\u9884\u6d4b\u70b9\u9644\u8fd1\u7684\u6bcf\u4e2a\u70b9\u8d4b\u4e88\u4e00\u5b9a\u7684\u6743\u91cd\uff0c\u7136\u540e\u4e0e\u7ebf\u6027\u56de\u5f52\u7c7b\u4f3c\uff0c\u5728\u8fd9\u4e2a\u88ab\u8d4b\u4e88\u6743\u91cd\u7684\u6837\u672c\u7684\u5b50\u96c6\u4e0a\u57fa\u4e8e\u6700\u5c0f\u5747\u65b9\u8bef\u5dee\u6765\u8fdb\u884c\u666e\u901a\u7684\u56de\u5f52\uff0c\u5373$X^TWX\\omega-X^TWY=0$\u65f6\u53ef\u4ee5\u5f97\u5230\u6700\u4f18\u7684$\\omega$\u4e3a
    \n
    \"file\"<\/div>
    \n  \u5176\u4e2d\u5c40\u90e8\u52a0\u6743\u7ebf\u6027\u56de\u5f52\u4e0e\u652f\u6301\u5411\u91cf\u673a\u7c7b\u4f3c\uff0c\u4f7f\u7528\u6838\u51fd\u6570\u7ed9\u79bb\u9884\u6d4b\u70b9\u8d8a\u8fd1\u7684\u70b9\u8d4b\u4e88\u66f4\u9ad8\u7684\u6743\u91cd\uff1b\u79bb\u9884\u6d4b\u70b9\u8d8a\u8fdc\u7684\u70b9\u8d4b\u4e88\u66f4\u4f4e\u7684\u6743\u91cd\u3002\u6838\u7684\u7c7b\u578b\u4e00\u822c\u53ef\u4ee5\u81ea\u7531\u9009\u62e9\uff0c\u4e00\u822c\u60c5\u51b5\u4e0b\u4f7f\u7528\u9ad8\u65af\u6838\uff0c\u9ad8\u65af\u6838\u5bf9\u5e94\u7684\u6743\u91cd\u5982\u4e0b
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d$k$\u76f8\u5f53\u4e8e\u5b66\u4e60\u7387\uff0c\u5b83\u51b3\u5b9a\u4e86\u5bf9\u9644\u8fd1\u7684\u70b9\u8d4b\u4e88\u591a\u5927\u7684\u6743\u91cd\u3002<\/p>\n

      \u901a\u8fc7\u9ad8\u65af\u6838\u5373\u53ef\u6784\u9020\u4e00\u4e2a\u53ea\u542b\u5bf9\u89d2\u5143\u7d20\u7684\u77e9\u9635$W$\uff0c\u5e76\u4e14\u70b9$x$\u4e0e$x_i$\u8d8a\u8fd1\uff0c\u5219$|x^{(i)}-x|$\u8d8a\u63a5\u8fd11\uff0c$W(i,i)$\u5c06\u4f1a\u8d8a\u8d8b\u8fd1\u4e8e$1$\uff1b\u5982\u679c\u70b9$x$\u4e0e$x_i$\u8d8a\u8fdc\uff0c\u5219$|x^{(i)}-x|$\u8d8a\u63a5\u8fd10\uff0c$W(i,i)$\u5c06\u4f1a\u8d8a\u8d8b\u8fd1\u4e8e$0$\uff0c\u5373\u79bb\u9884\u6d4b\u70b9\u8d8a\u63a5\u8fd1\u7684\u70b9\u6743\u91cd\u8d8a\u9ad8\uff0c\u79bb\u9884\u6d4b\u70b9\u8d8a\u8fdc\u7684\u70b9\u6743\u91cd\u8d8a\u4f4e\uff0c\u8fd9\u4e5f\u662f\u5c40\u90e8\u52a0\u6743\u7ebf\u6027\u56de\u5f52\u53ea\u5173\u6ce8\u9644\u8fd1\u70b9\u7684\u539f\u56e0\u3002<\/p>\n

      \u5c40\u90e8\u52a0\u6743\u7ebf\u6027\u56de\u5f52\u867d\u7136\u89e3\u51b3\u4e86\u6b20\u62df\u5408\u7684\u95ee\u9898\uff0c\u4f46\u662f\u7531\u4e8e\u6bcf\u4e2a\u9884\u6d4b\u70b9\u90fd\u8981\u8fdb\u884c\u4e00\u6b21\u7ebf\u6027\u56de\u5f52\u7684\u8fd0\u7b97\uff0c\u56e0\u6b64\u6837\u672c\u6570\u8d8a\u591a\u5219\u8be5\u65b9\u6cd5\u7684\u8ba1\u7b97\u91cf\u5c06\u8d8a\u5927\u3002\u76f8\u6bd4\u8f83\u666e\u901a\u7684\u7ebf\u6027\u56de\u5f52\uff0c\u666e\u901a\u7684\u7ebf\u6027\u56de\u5f52\u5c5e\u4e8e\u53c2\u6570\u6a21\u578b\uff0c\u800c\u5c40\u90e8\u52a0\u6743\u7ebf\u6027\u56de\u5f52\u5c5e\u4e8e\u975e\u53c2\u6570\u6a21\u578b\uff0c\u6bcf\u6b21\u589e\u52a0\u65b0\u6570\u636e\u7684\u65f6\u5019\u90fd\u9700\u8981\u57fa\u4e8e\u6837\u672c\u91cd\u65b0\u8ba1\u7b97$\\omega$\u3002<\/p>\n

    \u6b63\u5219\u5316<\/h2>\n

      \u5728\u8fc7\u62df\u5408\u95ee\u9898\u7684\u65f6\u5019\u8bf4\u5230\u8fc7\uff0c\u4e3a\u4e86\u89e3\u51b3\u8fc7\u62df\u5408\u95ee\u9898\u65f6\uff0c\u53ef\u4ee5\u5728\u5efa\u7acb\u6a21\u578b\u7684\u65f6\u5019\u52a0\u4e0a\u6b63\u5219\u5316\u9879\u3002\u5bf9\u4e8e\u7ebf\u6027\u6a21\u578b\uff0c\u4e00\u822c\u6709L1\u6b63\u5219\u5316\u3001L2\u6b63\u5219\u5316\u548c\u5f39\u6027\u7f51\u7edc\u7b49\u3002<\/p>\n

    L1\u6b63\u5219\u5316<\/h3>\n

    \"\"<\/div>
    \n  \u7ebf\u6027\u56de\u5f52\u7684L1\u6b63\u5219\u5316\u901a\u5e38\u79f0\u4e3aLasso\u56de\u5f52\uff0c\u5b83\u548c\u666e\u901a\u7684\u7ebf\u6027\u56de\u5f52\u7684\u533a\u522b\u662f\u5b83\u5728\u76ee\u6807\u51fd\u6570\u4e0a\u589e\u52a0\u4e86\u4e00\u4e2aL1\u6b63\u5219\u5316\u9879\uff0cL1\u6b63\u5219\u5316\u9879\u6709\u4e00\u4e2a\u6b63\u5219\u5316\u53c2\u6570$\\lambda$\u8c03\u8282\u76ee\u6807\u51fd\u6570\u7684\u5747\u65b9\u8bef\u5dee\u9879\u548c\u6b63\u5219\u5316\u9879\u7684\u6743\u91cd\uff0cLasso\u56de\u5f52\u7684\u76ee\u6807\u51fd\u6570\u8868\u8fbe\u5f0f\u4e3a
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d${\\frac{1}{2}}$\u53ea\u662f\u4e3a\u4e86\u65b9\u4fbf\u8ba1\u7b97\uff0c$m$\u662f\u6837\u672c\u6570\u91cf\uff0c$||\\omega||_1$\u4e3aL1\u8303\u6570\u3002<\/p>\n

      \u7531\u4e8e\u76ee\u6807\u51fd\u6570\u4e2d\u7684L1\u8303\u6570\u7528\u7684\u662f\u7edd\u5bf9\u503c\u4e4b\u548c\uff0c\u5bfc\u81f4\u76ee\u6807\u51fd\u6570\u4e2d\u6709\u4e0d\u53ef\u5bfc\u7684\u70b9\uff0c\u5373\u65e0\u6cd5\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u3001\u68af\u5ea6\u4e0b\u964d\u6cd5\u3001\u725b\u987f\u6cd5\u6c42\u89e3\u4f7f\u5f97\u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u5316\u7684$\\omega$\uff0c\u56e0\u6b64\u53ef\u4ee5\u4f7f\u7528\u5168\u65b0\u7684\u65b9\u6cd5\u6c42\u89e3\u6700\u4f18$\\omega$\uff0c\u5373\u5750\u6807\u8f74\u4e0b\u964d\u6cd5(coordinate descent)\u548c\u6700\u5c0f\u89d2\u56de\u5f52\u6cd5(least angle regression)<\/p>\n

      \u5982\u679c\u4f60\u5bf9Lasso\u56de\u5f52\u7684\u6c42\u89e3\u8fc7\u7a0b\u719f\u6089\u4e86\uff0c\u4f1a\u53d1\u73b0Lasso\u56de\u5f52\u53ef\u4ee5\u4f7f\u5f97\u4e00\u4e9b\u7279\u5f81\u7684$\\omega$\u53d8\u5c0f\uff0c\u751a\u81f3\u8fd8\u80fd\u4f7f\u5f97\u4e00\u4e9b\u7edd\u5bf9\u503c\u8f83\u5c0f\u7684$\\omega$\u76f4\u63a5\u53d8\u6210$0$\uff0c\u8fdb\u800c\u4f7f\u5f97\u6570\u636e\u7684\u7279\u5f81\u53d8\u5f97\u7a00\u758f\uff0c\u589e\u5f3a\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n

    L2\u6b63\u5219\u5316<\/h3>\n

      \u7ebf\u6027\u56de\u5f52\u7684L2\u6b63\u5219\u5316\u901a\u5e38\u79f0\u4e3aRidge\u56de\u5f52\uff0c\u4e5f\u79f0\u4e3a\u5cad\u56de\u5f52\u3002\u5b83\u548c\u666e\u901a\u7684\u7ebf\u6027\u56de\u5f52\u7684\u533a\u522b\u662f\u5b83\u5728\u76ee\u6807\u51fd\u6570\u4e0a\u589e\u52a0\u4e86\u4e00\u4e2aL2\u6b63\u5219\u5316\u9879\uff0c\u800cRidge\u56de\u5f52\u4e0eLasso\u56de\u5f52\u7684\u533a\u522b\u5728\u4e8eLasso\u56de\u5f52\u7684\u6b63\u5219\u5316\u9879\u662fL1\u8303\u6570\uff0c\u800cRidge\u56de\u5f52\u7684\u6b63\u5219\u5316\u9879\u662fL2\u8303\u6570\uff0cRidge\u56de\u5f52\u7684\u76ee\u6807\u51fd\u6570\u8868\u8fbe\u5f0f\u4e3a
    \n

    \"file\"<\/div>
    \n\u5176\u4e2d${\\frac{1}{2}}$\u53ea\u662f\u4e3a\u4e86\u65b9\u4fbf\u8ba1\u7b97\uff0c$m$\u662f\u6837\u672c\u6570\u91cf\uff0c$||\\omega||_2$\u4e3aL2\u8303\u6570\u3002<\/p>\n

      Ridge\u56de\u5f52\u4e00\u822c\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u77e9\u9635\u63a8\u5bfc\u5f62\u5f0f\uff0c\u548c\u666e\u901a\u7684\u7ebf\u6027\u56de\u5f52\u7c7b\u4f3c\uff0c\u9996\u5148\u5bf9$\\omega$\u6c42\u5bfc\u5f97
    \n

    \"file\"<\/div>
    \n\u4ee4$X^T(X\\omega-Y)+\\lambda\\omega=0$\u5373\u53ef\u5f97\u5230$\\omega$\u4e3a
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d$E$\u4e3a\u5355\u4f4d\u77e9\u9635\u3002<\/p>\n

    \u5f39\u6027\u7f51\u7edc<\/h3>\n

      \u5f39\u6027\u7f51\u7edc(elastic net)\u662f\u5bf9Ridge\u56de\u5f52\u548cLasso\u56de\u5f52\u7684\u6298\u4e2d\u5904\u7406\uff0c\u901a\u8fc7\u6df7\u5408\u6bd4$\\gamma$\u8fdb\u884c\u63a7\u5236\uff0c\u5373\u5b83\u7684\u76ee\u6807\u51fd\u6570\u4e3a
    \n

    \"file\"<\/div>
    \n\u5176\u4e2d$\\gamma$\u548c$\\lambda$\u90fd\u662f\u8d85\u53c2\u6570\uff0c\u5f53$\\gamma=1$\u7684\u65f6\u5019\u5f39\u6027\u7f51\u7edc\u4e3aRidge\u56de\u5f52\uff1b\u5f53$\\gamma=0$\u7684\u65f6\u5019\u5f39\u6027\u7f51\u7edc\u4e3aLasso\u56de\u5f52\uff0c\u81f3\u4e8e\u6df7\u5408\u6bd4$\\gamma$\u503c\u5177\u4f53\u60c5\u51b5\u5177\u4f53\u5206\u6790\u3002<\/p>\n

    \u7ebf\u6027\u56de\u5f52\u6d41\u7a0b<\/h1>\n

    \u8f93\u5165<\/h2>\n

      \u6709$m$\u4e2a\u5b9e\u4f8b$n$\u7ef4\u7279\u5f81\u7684\u6570\u636e\u96c6
    \n

    \"file\"<\/div>
    \n\u5176\u4e2d$x_i$\u662f\u5b9e\u4f8b\u7684\u7279\u5f81\u5411\u91cf\u5373$({x_i}^{(1)},{x_i}^{(2)},\\cdots,{x_i}^{(n)})$\u3002<\/p>\n

    \u8f93\u51fa<\/h2>\n

      $\\omega$\u548c\u7ebf\u6027\u56de\u5f52\u6a21\u578b$f(x)=\\omega^Tx$\u3002<\/p>\n

    \u6d41\u7a0b<\/h2>\n
      \n
    1. \u9009\u53d6\u521d\u503c$\\omega=0$<\/li>\n
    2. \u8bad\u7ec3\u96c6\u4e2d\u9009\u53d6\u6570\u636e$(x_i,y_i)$\uff0c\u5bf9$\\omega$\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u66f4\u65b0
      \n
      \"file\"<\/div><\/li>\n
    3. \u91cd\u590d\u6b65\u9aa42\uff0c\u76f4\u81f3$\\omega$\u6536\u655b\u505c\u6b62\u66f4\u65b0<\/li>\n
    4. \u5f97\u5230\u6700\u5c0f\u5316\u7684\u76ee\u6807\u51fd\u6570$J(\\omega)$\uff0c\u540c\u65f6\u53ef\u4ee5\u5f97\u5230\u6700\u4f18\u7684$\\omega^$\uff0c\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u4e3a$f(x)={w^<\/em>}^Tx$<\/li>\n<\/ol>\n

      \u7ebf\u6027\u56de\u5f52\u4f18\u7f3a\u70b9<\/h1>\n

      \u4f18\u70b9<\/h2>\n
        \n
      1. \u5efa\u7acb\u4e86\u591a\u7279\u5f81\u4e0e\u6807\u8bb0\u95f4\u7684\u7ebf\u6027\u56e0\u679c\u5173\u7cfb\u4fbf\u4e8e\u5206\u6790<\/li>\n
      2. \u53ef\u4ee5\u5f97\u5230\u6bcf\u4e2a\u7279\u5f81\u503c\u7684\u6743\u91cd\uff0c\u6709\u5f88\u597d\u7684\u89e3\u91ca\u578b<\/li>\n<\/ol>\n

        \u7f3a\u70b9<\/h2>\n
          \n
        1. \u666e\u901a\u7684\u7ebf\u6027\u56de\u5f52\u65e0\u6cd5\u5904\u7406\u654f\u611f\u503c\u95ee\u9898<\/li>\n
        2. \u65e0\u6cd5\u5904\u7406\u5206\u7c7b\u95ee\u9898<\/li>\n<\/ol>\n

          \u5c0f\u7ed3<\/h1>\n

            \u7ebf\u6027\u56de\u5f52\u53ef\u4ee5\u8bf4\u662f\u6211\u4eec\u5b66\u7684\u7b2c\u4e00\u4e2a\u5de5\u4e1a\u4e0a\u8fd8\u5728\u4f7f\u7528\u7684\u7b97\u6cd5\uff0c\u5bf9\u4e8e\u8fde\u7eed\u503c\u7684\u6d4b\u91cf\u7ebf\u6027\u56de\u5f52\u7684\u8868\u73b0\u8fd8\u662f\u633a\u4e0d\u9519\u7684\u3002\u4f46\u901a\u5e38\u60c5\u51b5\u4e0b\u8fd8\u662f\u9700\u8981\u591a\u591a\u5c1d\u8bd5\u7ebf\u6027\u56de\u5f52\u7684\u53d8\u79cd\uff0c\u5373\u5bf9\u6570\u7ebf\u6027\u56de\u5f52\u3001\u6b63\u5219\u5316\u7ebf\u6027\u56de\u5f52\uff0c\u4f7f\u7528\u5b83\u4eec\u80fd\u591f\u66f4\u7cbe\u51c6\u7684\u9884\u6d4b\u6570\u636e\uff0c\u89e3\u51b3\u8fc7\u62df\u5408\u95ee\u9898\uff0c\u4e5f\u53ef\u4ee5\u4e00\u5b9a\u7684\u7a0b\u5ea6\u8ba9\u7ebf\u6027\u56de\u5f52\u62df\u5408\u975e\u7ebf\u6027\u6570\u636e\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

          \u7ebf\u6027\u56de\u5f52   \u7ebf\u6027\u56de\u5f52\u662f\u6bd4\u8f83\u7ecf\u5178\u7684\u7ebf\u6027\u6a21\u578b\uff0c\u5c5e\u4e8e\u76d1\u7763\u5b66\u4e60\u4e2d\u9884\u6d4b\u503c\u4e3a\u8fde\u7eed\u503c\u7684\u56de\u5f52\u95ee\u9898\u3002 &e […]<\/p>\n","protected":false},"author":3,"featured_media":2968,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,286],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/2977"}],"collection":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2977"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/2977\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/media\/2968"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2977"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2977"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}