{"id":3341,"date":"2022-02-27T15:13:24","date_gmt":"2022-02-27T07:13:24","guid":{"rendered":"https:\/\/egonlin.com\/?p=3341"},"modified":"2022-02-27T15:13:24","modified_gmt":"2022-02-27T07:13:24","slug":"%e7%ac%ac%e4%b8%83%e7%af%87%ef%bc%9a%e5%89%8d%e5%90%91%e5%88%86%e6%ad%a5%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3341","title":{"rendered":"\u7b2c\u4e03\u7bc7\uff1a\u524d\u5411\u5206\u6b65\u7b97\u6cd5"},"content":{"rendered":"

\u524d\u5411\u5206\u6b65\u7b97\u6cd5<\/h1>\n

\u524d\u5411\u5206\u6b65\u7b97\u6cd5\u5f15\u5165<\/h1>\n

  \u5047\u8bbeNick\u7684\u5e74\u9f84\u662f25\u5c81\u3002<\/p>\n

    \n
  1. \u7b2c1\u68f5\u51b3\u7b56\u6811<\/li>\n<\/ol>\n

    \u628aNick\u7684\u5e74\u9f84\u8bbe\u7f6e\u6210\u521d\u59cb\u503c0\u5c81\u53bb\u5b66\u4e60\uff0c\u5982\u679c\u7b2c1\u68f5\u51b3\u7b56\u6811\u9884\u6d4bNick\u7684\u5e74\u9f84\u662f12\u5c81\uff0c\u5373\u6b8b\u5dee\u503c\u4e3a$25-12=13$<\/p>\n

      \n
    1. \u7b2c2\u8bfe\u51b3\u7b56\u6811\n
        \n
      1. \u628aNick\u7684\u5e74\u9f84\u8bbe\u7f6e\u6210\u6b8b\u5dee\u503c13\u5c81\u53bb\u5b66\u4e60\uff0c\u5982\u679c\u7b2c2\u68f5\u51b3\u7b56\u6811\u80fd\u628aNick\u5206\u523013\u5c81\u7684\u53f6\u5b50\u8282\u70b9\uff0c\u7d2f\u52a0\u4e24\u68f5\u51b3\u7b56\u6811\u7684\u9884\u6d4b\u503c\u52a0\u548c$12+13=25$\uff0c\u5c31\u662fNick\u7684\u771f\u5b9e\u5e74\u9f8425\u5c81<\/li>\n
      2. \u5982\u679c\u7b2c2\u68f5\u51b3\u7b56\u6811\u7684\u5f97\u5230\u7684\u662f10\u5c81\uff0c\u6b8b\u5dee\u503c\u4e3a$25-12-10=3$<\/li>\n<\/ol>\n<\/li>\n
      3. \u7b2c3\u8bfe\u51b3\u7b56\u6811<\/li>\n<\/ol>\n

        \u628aNick\u7684\u5e74\u9f84\u8bbe\u7f6e\u6210\u6b8b\u5dee\u503c3\u5c81\u53bb\u5b66\u4e60\u2026\u2026<\/p>\n

          \n
        1. \u7ee7\u7eed\u91cd\u590d\u4e0a\u8ff0\u8fc7\u7a0b\u5b66\u4e60\uff0c\u4e0d\u65ad\u903c\u8fd1Nick\u7684\u771f\u5b9e\u5e74\u9f84<\/li>\n<\/ol>\n

          \u524d\u5411\u5206\u6b65\u7b97\u6cd5\u8be6\u89e3<\/h1>\n

          \u52a0\u6cd5\u6a21\u578b<\/h2>\n

            \u52a0\u6cd5\u6a21\u578b(additive model)\u4e00\u822c\u8868\u793a\u4e3a\u5f31\u5b66\u4e60\u5668\u52a0\u548c
          \n$$
          \nf(x) = \\sum_{t=1}^T\\theta_tb(x;\\gamma_t)
          \n$$
          \n\u5176\u4e2d$b(x;\\gamma_t)$\u4e3a\u5f31\u5b66\u4e60\u5668\uff0c$\\gamma_t$\u4e3a\u5f31\u5b66\u4e60\u5668\u7684\u53c2\u6570\uff0c$\\theta_t$\u4e3a\u5f31\u5b66\u4e60\u5668\u7684\u7cfb\u6570\u3002<\/p>\n

          \u52a0\u6cd5\u6a21\u578b\u76ee\u6807\u51fd\u6570\u4f18\u5316\u95ee\u9898<\/h2>\n

            \u7ed9\u5b9a\u8bad\u7ec3\u6570\u636e\u4ee5\u53ca\u76ee\u6807\u51fd\u6570$L(y,f(x))$\uff0c\u52a0\u6cd5\u6a21\u578b\u7684\u7ecf\u9a8c\u98ce\u9669\u6700\u5c0f\u5316\u95ee\u9898\u65e2\u53ef\u4ee5\u53d8\u4e3a\u76ee\u6807\u51fd\u6570\u6700\u5c0f\u5316\u95ee\u9898
          \n$$
          \n\\underbrace{min}_{\\theta_t,\\gammat}\\sum<\/em>{i=1}^mL(yi,\\sum<\/em>{t=1}^T\\theta_tb(x_i;\\gammat))
          \n$$
          \n  \u4e0a\u8ff0\u52a0\u6cd5\u6a21\u578b\u7684\u76ee\u6807\u51fd\u6570\u4f18\u5316\u95ee\u9898\u662f\u4e00\u4e2a\u5f88\u590d\u6742\u7684\u4f18\u5316\u95ee\u9898\uff0c\u4f46\u662f\u901a\u8fc7\u524d\u5411\u5206\u5e03\u7b97\u6cd5(forward stagewise algorithm)\u53ef\u4ee5\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0c\u5b83\u7684\u601d\u60f3\u662f\uff1a\u56e0\u4e3a\u5b66\u4e60\u95ee\u9898\u662f\u52a0\u6cd5\u6a21\u578b\uff0c\u6240\u4ee5\u6bcf\u4e00\u6b65\u53ea\u5b66\u4e60\u4e00\u4e2a\u5f31\u5b66\u4e60\u5668\u53ca\u5176\u7cfb\u6570\uff0c\u7136\u540e\u9010\u6b65\u903c\u8fd1\u4f18\u5316\u76ee\u6807\u51fd\u6570\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6bcf\u4e00\u6b65\u53ea\u9700\u8981\u4f18\u5316\u5982\u4e0b\u6240\u793a\u7684\u76ee\u6807\u51fd\u6570
          \n$$
          \n\\underbrace{min}<\/em>{\\theta,\\gamma}\\sum_{i=1}^mL(y_i,\\theta{b(x_i;\\gamma)})
          \n$$<\/p>\n

          \u524d\u5411\u5206\u6b65\u7b97\u6cd5\u6d41\u7a0b<\/h1>\n

          \u8f93\u5165<\/h2>\n

            \u6709$m$\u4e2a\u6570\u636e$n$\u4e2a\u7279\u5f81\u7684\u8bad\u7ec3\u6570\u636e\u96c6$T={(x_1,y_1),(x_2,y_2),\\cdots,(x_m,y_m)}$\uff1b\u76ee\u6807\u51fd\u6570$L(y,f(x))$\uff1b\u5f31\u5b66\u4e60\u6a21\u578b\u96c6${b(x;\\gamma_t)},\\quad(t=1,2,\\cdots,T)$\uff0c\u5728Boosting\u7b97\u6cd5\u4e2d$T$\u76f8\u5f53\u4e8e\u5f31\u5b66\u4e60\u5668\u7684\u4e2a\u6570\u3002<\/p>\n

          \u8f93\u51fa<\/h2>\n

            \u52a0\u6cd5\u6a21\u578b$f(x)$\u3002<\/p>\n

          \u6d41\u7a0b<\/h2>\n
            \n
          1. \u521d\u59cb\u5316$f_0(x)=0$<\/li>\n
          2. \u5bf9$t=1,2,\\cdots,T$\n
              \n
            1. \u6781\u5c0f\u5316\u76ee\u6807\u51fd\u6570
              \n$$
              \n(\\theta_t,\\gammat)=\\underbrace{arg\\,min}<\/em>{\\theta,\\gamma}\\sum_{i=1}^mL(yi,f<\/em>{t-1}(x_i)+\\theta{b(x_i;\\gamma)})
              \n$$
              \n\u5f97\u5230\u53c2\u6570$\\theta_t,\\gamma_t$<\/li>\n
            2. \u66f4\u65b0
              \n$$
              \nft(x)=f<\/em>{t-1}(x)+\\theta_tb(x;\\gamma_t)
              \n$$<\/li>\n<\/ol>\n<\/li>\n
            3. \u5f97\u5230\u52a0\u6cd5\u6a21\u578b<\/li>\n<\/ol>\n

              $$
              \nf(x)=fT(x)=\\sum<\/em>{t=1}^T\\theta_tb(x;\\gamma_t)
              \n$$<\/p>\n","protected":false},"excerpt":{"rendered":"

              \u524d\u5411\u5206\u6b65\u7b97\u6cd5 \u524d\u5411\u5206\u6b65\u7b97\u6cd5\u5f15\u5165   \u5047\u8bbeNick\u7684\u5e74\u9f84\u662f25\u5c81\u3002 \u7b2c1\u68f5\u51b3\u7b56\u6811 \u628aNick […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,303,304],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3341"}],"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=3341"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3341\/revisions"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3341"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3341"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}