{"id":3337,"date":"2022-02-27T15:11:59","date_gmt":"2022-02-27T07:11:59","guid":{"rendered":"https:\/\/egonlin.com\/?p=3337"},"modified":"2022-02-27T15:12:24","modified_gmt":"2022-02-27T07:12:24","slug":"%e7%ac%ac%e5%85%ad%e7%af%87%ef%bc%9a%e6%9c%80%e5%b0%8f%e8%a7%92%e5%9b%9e%e5%bd%92%e6%b3%95","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3337","title":{"rendered":"\u7b2c\u516d\u7bc7\uff1a\u6700\u5c0f\u89d2\u56de\u5f52\u6cd5"},"content":{"rendered":"

\u6700\u5c0f\u89d2\u56de\u5f52\u6cd5<\/h1>\n

  \u6700\u5c0f\u89d2\u56de\u5f52\u76f8\u5f53\u4e8e\u524d\u5411\u9009\u62e9\u6cd5\u548c\u524d\u5411\u68af\u5ea6\u6cd5\u7684\u4e00\u4e2a\u6298\u4e2d\u7b97\u6cd5\uff0c\u7b80\u5316\u4e86\u524d\u9879\u68af\u5ea6\u6cd5\u56e0$\\epsilon$\u7684\u8fed\u4ee3\u8fc7\u7a0b\uff0c\u5e76\u5728\u4e00\u5b9a\u7a0b\u5ea6\u7684\u4fdd\u8bc1\u4e86\u524d\u5411\u68af\u5ea6\u6cd5\u7684\u7cbe\u51c6\u5ea6\u3002<\/p>\n

  \u901a\u5e38\u7528\u6700\u5c0f\u89d2\u56de\u5f52\u6cd5\u89e3\u51b3\u7ebf\u6027\u6a21\u578b\u7684\u56de\u5f52\u7cfb\u6570\u3002\u5bf9\u4e8e\u4e00\u4e2a\u6709$m$\u4e2a\u6837\u672c\uff0c\u6bcf\u4e2a\u6837\u672c\u6709$n$\u4e2a\u7279\u5f81\u7684\u8bad\u7ec3\u96c6\u800c\u8a00\uff0c\u5047\u8bbe\u53ef\u4ee5\u62df\u5408\u4e00\u4e2a\u7ebf\u6027\u6a21\u578b$Y=\\omega^TX$\uff0c\u5176\u4e2d$Y$\u662f$m1$\u7684\u5411\u91cf\uff0c$X$\u662f$m<\/em>n$\u7684\u77e9\u9635\uff0c$\\omega$\u662f$n*1$\u7684\u5411\u91cf\u3002\u5373\u53ef\u901a\u8fc7\u6700\u5c0f\u89d2\u56de\u5f52\u6cd5\u6c42\u5f97\u6700\u5c0f\u5316\u8be5\u6a21\u578b\u7684\u53c2\u6570$\\omega$\u3002<\/p>\n

  \u9996\u5148\u628a\u77e9\u9635$X$\u770b\u6210$n$\u4e2a$m*1$\u7684\u5411\u91cf$X_i \\quad(i=1,2,\\cdots,n)$\uff0c\u4e4b\u540e\u9009\u62e9\u4e0e\u5411\u91cf$Y$\u4f59\u5f26\u76f8\u4f3c\u5ea6\u6700\u5927\uff0c\u5373\u4e0e$Y$\u6700\u4e3a\u63a5\u8fd1\u7684\u4e00\u4e2a\u53d8\u91cf$Xi$\uff0c\u4f7f\u7528\u7c7b\u4f3c\u4e8e\u524d\u5411\u9009\u62e9\u6cd5\u4e2d\u7684\u6b8b\u5dee\u8ba1\u7b97\u65b9\u6cd5\u5f97\u5230\u65b0\u7684\u76ee\u6807$Y<\/em>{err}$\uff0c\u6b64\u65f6\u4e0d\u540c\u4e8e\u524d\u5411\u68af\u5ea6\u6cd5\u7684\u4e00\u5c0f\u6b65\u4e00\u5c0f\u6b65\u8d70\uff0c\u800c\u662f\u8d70\u5230\u51fa\u73b0\u4e00\u4e2a$X_j\\quad(j=1,2,i-1,i+1,\\cdots,n)$\u7684\u65f6\u5019\uff0c\u6b64\u65f6$Xi$\u548c$Y<\/em>{err}$\u7684\u4f59\u5f26\u76f8\u4f3c\u5ea6\u7b49\u4e8e$Xj$\u548c$Y<\/em>{err}$\u7684\u4f59\u5f26\u76f8\u4f3c\u5ea6\uff0c\u8fd9\u4e2a\u65f6\u5019\u6b8b\u5dee$Y_{err}$\u6cbf\u7740$X_i$\u548c$X_j$\u7684\u89d2\u5e73\u5206\u7ebf\u65b9\u5411\u8d70\uff0c\u77e5\u9053\u51fa\u73b0\u7b2c\u4e09\u4e2a\u7279\u5f81$Xk$\u548c$Y<\/em>{err}$\u7684\u76f8\u5173\u5ea6\u7b49\u4e8e$Xi$\u548c$Y<\/em>{err}$\u7684\u4f59\u5f26\u76f8\u4f3c\u5ea6\u7b49\u4e8e$Xj$\u548c$Y<\/em>{err}$\u7684\u4f59\u5f26\u76f8\u4f3c\u5ea6\u7684\u65f6\u5019\uff0c\u4f7f\u7528\u8fd9\u4e09\u8005\u7684\u5171\u540c\u89d2\u5e73\u5206\u7ebf\uff0c\u4f5c\u4e3a\u6b8b\u5dee$Y_{err}$\u7684\u8def\u5f84\u65b9\u5411\uff0c\u76f4\u5230\u6240\u6709\u53d8\u91cf\u53d6\u5b8c\u4e86\uff0c\u505c\u6b62\u7b97\u6cd5\uff0c\u5373\u53ef\u5f97\u5230$\\omega$\u3002<\/p>\n

\u4e3e\u4f8b<\/h1>\n
# \u4e3e\u4f8b\u56fe\u4f8b\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\n%matplotlib inline\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')\n\n# X1*w1\nplt.annotate(xytext=(2, 5), xy=(8, 5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(6, 4.5, s='$X_1*\\omega_1$', color='g')\n# X1\nplt.annotate(xytext=(2, 5), xy=(4, 5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(2.5, 4.5, s='$X_1$', color='g')\n# X2\nplt.annotate(xytext=(2, 5), xy=(3, 7), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(2, 6, s='$X_2$', color='g')\n# Y\nplt.annotate(xytext=(2, 5), xy=(12, 8), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(5, 7.5, s='$Y$', color='g')\n\n# X1\nplt.annotate(xytext=(8, 5), xy=(10, 5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(8.5, 4.5, s='$X_1$', color='g')\n# X2\nplt.annotate(xytext=(8, 5), xy=(9, 7), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(8, 6, s='$X_2$', color='g')\n# w2(X1+X2)\nplt.annotate(xytext=(8, 5), xy=(12, 8), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='gray'))\nplt.text(10.5, 6.3, s='$(X_1+X_2)\\omega_2$', color='g')\n\nplt.xlim(0, 13)\nplt.ylim(2, 13)\nplt.title('\u6700\u5c0f\u89d2\u56de\u5f52\u6cd5\u4e3e\u4f8b', fontproperties=font, fontsize=20)\nplt.show()<\/code><\/pre>\n
\"\"<\/div><\/p>\n
  \u4e0a\u56fe\u5047\u8bbe$X$\u4e3a$2$\u7ef4\uff0c\u9996\u5148\u53ef\u4ee5\u770b\u51fa\uff0c\u79bb$Y$\u6700\u63a5\u8fd1\u7684\u662f$X_1$\uff0c\u9996\u5148\u5728$X_1$\u4e0a\u8d70\u4e00\u6bb5\u8ddd\u79bb\uff0c\u77e5\u9053\u6b8b\u5dee\u548c$X_1$\u7684\u76f8\u5173\u5ea6\u7b49\u4e8e\u6b8b\u5dee\u548c$X_2$\u7684\u76f8\u5173\u5ea6\uff0c\u5373\u6b8b\u5dee\u5728$X_1$\u548c$X_2$\u7684\u89d2\u5e73\u5206\u7ebf\u4e0a\uff0c\u7531\u4e8e$X$\u4e3a$2$\u7ef4\uff0c\u6b64\u65f6\u6cbf\u7740\u89d2\u5e73\u5206\u7ebf\u8d70\uff0c\u76f4\u5230\u6b8b\u5dee\u8db3\u591f\u5c0f\u65f6\u505c\u6b62\uff0c\u5982\u679c\u6b64\u65f6$X$\u4e0d\u662f$2$\u7ef4\uff0c\u5219\u7ee7\u7eed\u9009\u62e9\u7b2c3\u4e2a\u3001\u7b2c4\u4e2a\u7279\u5f81\u8d70\u4e0b\u53bb\u3002<\/p>\n
\u6700\u5c0f\u89d2\u56de\u5f52\u6cd5\u4f18\u7f3a\u70b9<\/h1>\n
\u4f18\u70b9<\/h2>\n
    \n
  1. \u7279\u522b\u9002\u5408\u7279\u5f81\u7ef4\u5ea6\u9ad8\u4e8e\u6837\u672c\u6570\u7684\u60c5\u51b5<\/li>\n<\/ol>\n
    \u7f3a\u70b9<\/h2>\n
      \n
    1. \u8fed\u4ee3\u65b9\u5411\u662f\u6839\u636e\u76ee\u6807\u7684\u6b8b\u5dee\u5b9a\u7684\uff0c\u6240\u4ee5\u7b97\u6cd5\u5bf9\u8bad\u7ec3\u96c6\u4e2d\u7684\u566a\u58f0\u7279\u522b\u654f\u611f<\/li>\n<\/ol>\n
      \u5c0f\u7ed3<\/h1>\n
        \u524d\u5411\u9009\u62e9\u6cd5\u7531\u4e8e\u6d89\u53ca\u5230\u6295\u5f71\uff0c\u53ea\u80fd\u7ed9\u51fa\u4e00\u4e2a\u8fd1\u4f3c\u89e3\uff1b\u524d\u5411\u68af\u5ea6\u6cd5\u5219\u9700\u8981\u81ea\u5df1\u624b\u52a8\u8c03\u8bd5\u4e00\u4e2a\u5f88\u597d\u7684$\\epsilon$\u53c2\u6570\uff1b\u6700\u5c0f\u89d2\u56de\u5f52\u6cd5\u7ed3\u5408\u4e86\u4e24\u8005\u7684\u4f18\u70b9\uff0c\u4f46\u662f\u81f3\u4e8e\u7b97\u6cd5\u5177\u4f53\u597d\u574f\u5bb3\u7684\u53d6\u51b3\u4e8e\u8bad\u7ec3\u96c6\uff0c\u5373\u7b97\u6cd5\u7684\u7a33\u5b9a\u6027\u65e0\u6cd5\u4fdd\u8bc1\u3002<\/p>\n
        \u5bf9\u7b97\u6cd5\u5177\u4f53\u8ba1\u7b97\u6709\u5174\u8da3\u7684\u540c\u5b66\uff0c\u53ef\u4ee5\u53c2\u8003Bradley Efron\u7684\u8bba\u6587\u300aLeast Angle Regression\u300b\uff0chttps:\/\/pan.baidu.com\/s\/10if9FGdkwEZ4_BolzCGszA<\/a> \uff0c\u5982\u679c\u4f60\u4e0b\u8f7d\u770b\u4e86\uff0c\u606d\u559c\u4f60\u5165\u5751\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
      \u6700\u5c0f\u89d2\u56de\u5f52\u6cd5   \u6700\u5c0f\u89d2\u56de\u5f52\u76f8\u5f53\u4e8e\u524d\u5411\u9009\u62e9\u6cd5\u548c\u524d\u5411\u68af\u5ea6\u6cd5\u7684\u4e00\u4e2a\u6298\u4e2d\u7b97\u6cd5\uff0c\u7b80\u5316\u4e86\u524d\u9879\u68af\u5ea6\u6cd5\u56e0 […]<\/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\/3337"}],"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=3337"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3337\/revisions"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}