\u5bfc\u81f4\u6a21\u578b\u8fc7\u62df\u5408(Overfitting)\u7684\u6f5c\u5728\u56e0\u7d20\uff1a<\/p>\n\n\n\n
\u566a\u58f0\u5bfc\u81f4\u7684\u8fc7\u62df\u5408<\/p>\n<\/li>
\u7f3a\u4e4f\u4ee3\u8868\u6027\u6837\u672c\u5bfc\u81f4\u7684\u8fc7\u5206\u62df\u5408<\/p>\n<\/li>
\u591a\u91cd\u6bd4\u8f83\u95ee\u9898(\u6709\u5f85\u89e3\u91ca\u6e05\u695a)\uff1a\u4e3b\u8981\u6307\u7684\u662f\uff0c\u5f53\u6211\u4eec\u5b58\u5728\u591a\u4e2a\u6807\u7b7e\u503c\u7684\u65f6\u5019\uff0c\u51b3\u7b56\u6811\u7b97\u6cd5\u8981\u9009\u62e9\u4e00\u4e2a\u6700\u4f73\u5c5e\u6027$x_{\\max}$ \u6765\u5212\u5206\u6570\u636e\uff0c\u7136\u800c\u8fd9\u591a\u4e2a\u6807\u7b7e\u5c5e\u6027\u968f\u7740\u5c5e\u6027\u7684\u6570\u91cf\u589e\u52a0\uff0c\u4e3a\u4e86\u5224\u65ad\u662f\u5426\u52a0\u5165\u5230\u521d\u59cb\u51b3\u7b56\u6811\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u5224\u65ad\u4ee5\u4e0b\u7b49\u5f0f\uff1a\n$$\n\\Delta(T_0,T_{x_{\\max}})>\\alpha\n$$\n\u5176\u4e2d$\\alpha$\u662f\u6211\u4eec\u786e\u5b9a\u7684\u9608\u503c\u3002$k$\u7684\u6570\u91cf\u589e\u52a0\u5c31\u4f1a\u5bfc\u81f4\u8fd9\u4e2a\u7b49\u5f0f\u6210\u7acb\u7684\u53ef\u80fd\u6027\u8fdb\u4e00\u6b65\u52a0\u5927\uff0c\u8fd9\u5bfc\u81f4\u4e86\u6211\u4eec\u53ef\u80fd\u5728\u4e0d\u7ecf\u610f\u95f4\u52a0\u5165\u4e86\u4e00\u4e9b\u6b3a\u9a97\u6027\u7684\u7ed3\u70b9\u5bfc\u81f4\u4e86\u6a21\u578b\u7684\u8fc7\u5206\u62df\u5408\u3002<\/p>\n<\/li>
\u6cdb\u5316\u8bef\u5dee\u4f30\u8ba1\u3002\u63d0\u4f9b\u90e8\u5206\u4f30\u8ba1\u6cdb\u5316\u8bef\u5dee\u7684\u65b9\u6cd5\u3002<\/p>\n
- \n
\u4f7f\u7528\u518d\u4ee3\u5165\u4f30\u8ba1\u3002\u8fd9\u79cd\u65b9\u6cd5\u5c31\u662f\u6cdb\u5316\u8bef\u5dee\u7684\u4e50\u89c2\u4f30\u8ba1<\/strong>\uff0c\u8003\u8651\u6700\u4f4e\u7684\u8bad\u7ec3\u8bef\u5dee\uff0c\u4e3a\u6211\u4eec\u7684\u6700\u7ec8\u6a21\u578b\u3002<\/p>\n<\/li>\n
\u7ed3\u5408\u6a21\u578b\u590d\u6742\u5ea6\u3002\u4e00\u822c\u6211\u4eec\u8003\u8651\u5965\u5361\u59c6\u5243\u5200(Occam’s razor)\u6216\u8005\u8282\u4fed\u539f\u5219(principle of parsimony)\u3002\u4e5f\u5c31\u662f\u5c3d\u53ef\u80fd\u7684\u9009\u62e9\u7b80\u5355\u7684\u6a21\u578b\u3002\u7c7b\u4f3c\u4e8e$BIC$\u548c$AIC$\u90a3\u6837\u5b50\uff0c\u6211\u4eec\u540c\u6837\u79f0\u8fd9\u4e2a\u53eb \u60b2\u89c2\u8bef\u5dee\u4f30\u8ba1<\/strong>\uff1a\u51b3\u7b56\u6811$T$\u7684\u60b2\u89c2\u4f30\u8ba1$e_g(T)$\u53ef\u4ee5\u7528\u4e0b\u5f0f\u8ba1\u7b97\uff1a\n$$\ne_g(T) = \\frac{\\sum_{i = 1}^k[e(t_i)+\\Omega(t_i)]}{\\sum_{i = 1}^kn(t_i)} = \\frac{e(T)+\\Omega(T)}{N_t}\n$$\n\u5176\u4e2d\uff0c$k$ \u662f\u51b3\u7b56\u6811\u7684\u53f6\u7ed3\u70b9\u6570\uff0c$e(T)$\u51b3\u7b56\u6811\u7684\u603b\u8bad\u7ec3\u8bef\u5dee\uff0c$N_t$\u662f\u8bad\u7ec3\u8bb0\u5f55\u6570\uff0c$\\Omega(t_i)$\u662f\u6bcf\u4e2a\u7ed3\u70b9$t_i$\u5bf9\u5e94\u7684\u60e9\u7f5a\u9879(\u7c7b\u4f3c\u4e8e$-2\\log n$\u4e00\u6837\u3002<\/p>\n<\/li>\n
\u6700\u5c0f\u63cf\u8ff0\u957f\u5ea6\u539f\u5219\u3002MDL<\/p>\n<\/li>\n<\/ol>\n<\/li>
\u5148\u526a\u679d\u540e\u526a\u679d\u3002\u4e00\u4e2a\u662f\u63d0\u524d\u7ec8\u6b62\uff0c\u53e6\u4e00\u4e2a\u662f\u5b50\u6811\u63d0\u5347\u6216\u5b50\u6811\u66ff\u6362\u3002<\/p>\n<\/li><\/ol>\n\n\n\n
\u6bd4\u8f83\u4e24\u4e2a\u6a21\u578b\u7684\u6027\u80fd<\/h4>\n\n\n\n
\u7c7b\u4f3c\u4e8e\u6570\u7406\u7edf\u8ba1\u4e2d\u7684\u4e8c\u9879\u5206\u5e03\u68c0\u9a8c\uff0c\u68c0\u9a8c\u8bef\u5dee\u662f\u5426\u663e\u8457\u3002$p$\u5c31\u662f\u8bef\u5dee\u7387$n$\u5c31\u662f\u6837\u672c\u6570\u3002\u76ee\u7684\u662f\uff0c\u4e3a\u4e86\u8bef\u5dee\u7387\u8de8\u8fc70%\uff0c\u4e5f\u5c31\u662f\u7f6e\u4fe1\u533a\u95f4\u8981\u8de8\u8fc70\uff0c\u5373\u8bef\u5dee\u7387\u4e3a0\u3002<\/p>\n\n\n\n
\u6bd4\u8f83\u4e24\u79cd\u5206\u7c7b\u6cd5\u7684\u6027\u80fd<\/h4>\n\n\n\n
\u4e00\u6837\u7684\u662f\u5047\u8bbe\u8bef\u5dee\u6765\u81ea\u4e8e\u6b63\u6001\u5206\u5e03\uff0c\u7136\u540e\u5229\u7528$t$\u68c0\u9a8c\u6765\u68c0\u9a8c\u4e8c\u8005\u662f\u5426\u76f8\u540c\u3002<\/p>\n\n\n\n
\u4e00\u4e9b\u5176\u4ed6\u7684\u51b3\u7b56\u6811<\/h3>\n\n\n\n
GBDT<\/h4>\n\n\n\n
GBDT\u7b97\u6cd5\u539f\u7406\u53ca\u5e94\u7528<\/a><\/p>\n\n\n\n
Gradient Boosting Decision Tree\uff08GBDT\uff09\u662f\u68af\u5ea6\u63d0\u5347\u51b3\u7b56\u6811\u3002GBDT\u6a21\u578b\u6240\u8f93\u51fa\u7684\u7ed3\u679c\u662f\u7531\u5176\u5305\u542b\u7684\u82e5\u5e72\u68f5\u51b3\u7b56\u6811\u7d2f\u52a0\u800c\u6210\uff0c\u6bcf\u4e00\u68f5\u51b3\u7b56\u6811\u90fd\u662f\u5bf9\u4e4b\u524d\u51b3\u7b56\u6811\u7ec4\u5408\u9884\u6d4b\u6b8b\u5dee\u7684\u62df\u5408\uff0c\u662f\u5bf9\u4e4b\u524d\u6a21\u578b\u7ed3\u679c\u7684\u4e00\u79cd\u201c\u4fee\u6b63\u201d\u3002\u68af\u5ea6\u63d0\u5347\u6811\u65e2\u53ef\u4ee5\u7528\u4e8e\u56de\u5f52\u95ee\u9898\uff08\u6b64\u65f6\u88ab\u79f0\u4e3aCART\u56de\u5f52\u6811\uff09\uff0c\u4e5f\u53ef\u4ee5\u88ab\u7528\u4e8e\u89e3\u51b3\u5206\u7c7b\u95ee\u9898\uff08\u6b64\u65f6\u88ab\u79f0\u4e3a\u5206\u7c7b\u6811\uff09\u3002<\/p>\n\n\n\n
\u535a\u5f08\u6811<\/h4>\n\n\n\n
\u3010Python\u6570\u636e\u6316\u6398\u8bfe\u7a0b\u3011\u56db.\u51b3\u7b56\u6811DTC\u6570\u636e\u5206\u6790\u53ca\u9e22\u5c3e\u6570\u636e\u96c6\u5206\u6790<\/a>\u8fd9\u4e2a\u9644\u4ee3\u7801\uff0c\u633a\u7ed9\u529b\u7684\u3002<\/p>\n\n\n\n
\u5176\u4ed6\u5206\u7c7b\u6280\u672f<\/h2>\n\n\n\n
\u57fa\u4e8e\u89c4\u5219\u7684\u5206\u7c7b\u5668<\/h3>\n\n\n\n
P127<\/p>\n\n\n\n
\u6700\u8fd1\u90bb\u5206\u7c7b\u5668(Nearest Neighbor)<\/h3>\n\n\n\n
\u79ef\u6781\u5b66\u4e60\u65b9\u6cd5\u4e0e\u6d88\u6781\u5b66\u4e60\u65b9\u6cd5\uff1a<\/p>\n\n\n\n
- \u79ef\u6781\u5b66\u4e60\u65b9\u6cd5(Eager Learner)<\/strong>: \u51b3\u7b56\u6811<\/strong>\u548c\u57fa\u4e8e\u89c4\u5219\u7684\u5206\u7c7b\u5668<\/strong>\u3002\u5982\u679c\u8bad\u7ec3\u6570\u636e\u53ef\u7528\uff0c\u5b83\u4eec\u5c31\u5f00\u59cb\u5b66\u4e60\u4ece\u8f93\u5165\u5c5e\u6027\u5230\u7c7b\u6807\u53f7\u7684\u6620\u5c04\u6a21\u578b\u3002<\/li>
- \u6d88\u6781\u5b66\u4e60\u65b9\u6cd5(Lazy Learner):<\/strong> \u4f8b\u5b50\u6709 Rote<\/strong> **\u5206\u7c7b\u5668(Rote Classifier)**\u3002\u91c7\u53d6\u4e0e\u4e4b\u76f8\u53cd\u7684\u7b56\u7565\uff0c\u63a8\u8fdf\u5bf9\u8bad\u7ec3\u6570\u636e\u7684\u5efa\u6a21\uff0c\u76f4\u5230\u9700\u8981\u5206\u7c7b\u6d4b\u8bd5\u6837\u4f8b\u65f6\u518d\u8fdb\u884c\u3002<\/li><\/ol>\n\n\n\n
\u7b97\u6cd5\uff1a\u68c0\u6d4b\u9700\u8981\u9884\u6d4b\u70b9\u5468\u56f4\u6700\u8fd1\u7684k\u4e2a\u70b9\uff0c\u7136\u540e\u8003\u8651\u6700\u591a\u7684\u7c7b\u522b\u7684\u70b9\u3002<\/p>\n\n\n\n
\u8d1d\u53f6\u65af\u5206\u7c7b\u5668<\/h3>\n\n\n\n
\u91cd\u6e29\u8d1d\u53f6\u65af\u5b9a\u7406\uff1abalabala<\/p>\n\n\n\n
\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u5668(Naive Bayes classifier)<\/h4>\n\n\n\n
\u4e3b\u8981\u6709\u4ee5\u4e0b\u5047\u8bbe\uff0c\u5728\u4f30\u8ba1\u7c7b\u6761\u4ef6\u6982\u7387\u7684\u65f6\u5019\u5047\u8bbe\u5c5e\u6027\u4e4b\u95f4\u6761\u4ef6\u72ec\u7acb<\/strong>\uff0c\u4e5f\u5c31\u662f\n$$\nP(\\textbf X|Y = y) = \\prod_{i = 1}^dP(X_i|Y=y)\n$$\n\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u8fd9\u6837\u8ba1\u7b97\u540e\u9a8c\u6982\u7387\uff1a\n$$\nP(Y|\\textbf X) = \\frac{P(Y)\\cdot\\prod_{i = 1}^dP(X_i|Y)}{P(\\textbf X)}\n$$\n\u7531\u4e8e$P(\\textbf X)$(\u7ed9\u5b9a\u4e86$Y$)\u90fd\u662f\u56fa\u5b9a\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u8981\u8003\u8651\u5206\u5b50\u3002\u7c7b\u4f3c\u4e8e\u8d1d\u53f6\u65af\u7edf\u8ba1\u4e2d\u7684\u6b63\u6bd4\u4e8e$\\propto$ .<\/p>\n\n\n\n
\u79bb\u6563\u60c5\u51b5<\/h5>\n\n\n\n
\u5982\u679c\u662f\u79bb\u6563\u60c5\u51b5\u7684\u8bdd\uff0c\u90a3\u4e48\u6761\u4ef6\u5206\u5e03\u5f88\u5bb9\u6613\u8ba1\u7b97\uff0c\u53ea\u9700\u8981\u8ba1\u7b97\u4ed6\u4eec\u5404\u81ea\u5728\u5bf9\u5e94$Y$\u4e0b\u7684\u4e2a\u6570\u518d\u9664\u4ee5\u603b\u6570\u5373\u53ef\u3002<\/p>\n\n\n\n
\u8fde\u7eed\u60c5\u51b5\u7684\u6761\u4ef6\u6982\u7387<\/h5>\n\n\n\n
\u6211\u4eec\u6709\u4e24\u79cd\u65b9\u6cd5\u6765\u4f30\u8ba1\u8fde\u7eed\u5c5e\u6027\u7684\u7c7b\u6761\u4ef6\u6982\u7387\u3002<\/p>\n\n\n\n
- \u6bcf\u4e00\u4e2a\u8fde\u7eed\u5c5e\u6027\u79bb\u6563\u5316\uff0c\u7136\u540e\u7528\u76f8\u5e94\u7684\u79bb\u6563\u533a\u95f4<\/strong>\u66ff\u6362\u8fde\u7eed\u5c5e\u6027\u503c\u3002<\/li>
- \u5229\u7528\u6b63\u6001\u5206\u5e03\u3002\u5047\u8bbe\u8fde\u7eed\u53d8\u91cf\u670d\u4ece\u67d0\u79cd\u6982\u7387\u5206\u5e03\uff0c\u4e00\u822c\u53d6\u6b63\u6001\u5206\u5e03\uff0c\u7136\u540e\u5229\u7528\u6837\u672c\u5747\u503c\u548c\u6837\u672c\u65b9\u5dee\u6765\u4f30\u8ba1\u6b63\u6001\u5206\u5e03\uff0c\u4e5f\u5c31\u662f$X\\sim N(\\bar{x},s^2)$\u3002\u8fd9\u5c31\u662f\u7c7b\u4f3c\u4e8e\u6211\u4eec\u5728MVA\u5b66\u4e60\u7684Bayes Classification Rule\u3002<\/li><\/ol>\n\n\n\n
\u6700\u7ec8\u6211\u4eec\u8003\u8651\u540e\u9a8c\u6982\u7387\u6700\u5927\u7684\u4e3a\u6211\u4eec\u7684\u5206\u7c7b\u7c7b\u522b\u3002<\/p>\n\n\n\n
\u8fd9\u4e0e\u6211\u4eec\u5728MVA\u5b66\u5230\u7684\u7c7b\u4f3c\u3002\u56de\u987eMVA\uff0c\u82e5\u662f\u4e24\u7ec4\u7684\u60c5\u51b5\uff0c\u5219\u8003\u8651\u7684\u662f\uff0c\n$$\n\\frac{f_1(\\textbf X)}{f_2(\\textbf X)}\\leq \\left(\\frac{c(1|2)}{c(2|1)}\\right)\\left(\\frac{p_2}{p_1}\\right)\n$$<\/p>\n\n\n\n
\u6761\u4ef6\u6982\u7387\u7684$\\boldsymbol m$\u4f30\u8ba1<\/h5>\n\n\n\n
\u5982\u679c\u4e00\u4e2a\u5c5e\u6027\u7684\u7c7b\u6761\u4ef6\u6982\u7387\u7b49\u4e8e0\uff0c\u5219\u6574\u4e2a\u7c7b\u7684\u540e\u9a8c\u6982\u7387\u5c31\u7b49\u4e8e0\u3002\u56e0\u6b64\u6211\u4eec\u63d0\u51fa\u4e86$m$\u4f30\u8ba1(m-estimate)\u65b9\u6cd5\u6765\u4f30\u8ba1\u6761\u4ef6\u6982\u7387\uff1a\n$$\np(x_i|y_j) = \\frac{n_c + mp}{n+m}\n$$\n\u5176\u4e2d$n$\u662f\u7c7b$y_j$\u4e2d\u7684\u5b9e\u4f8b\u603b\u6570\uff0c$n_c$\u662f\u7c7b$y_j$\u7684\u8bad\u7ec3\u6837\u4f8b\u4e2d\u53d6\u503c$x_i$\u7684\u6837\u4f8b\u6570\uff0c$m$\u662f\u79f0\u4e3a\u7b49\u4ef7\u6837\u672c\u5927\u5c0f\u7684\u53c2\u6570\uff0c\u800c$p$\u662f\u7528\u6237\u6307\u5b9a\u7684\u53c2\u6570\u3002<\/p>\n\n\n\n
- $p$\u7684\u53d6\u503c\uff1a$p$\u53ef\u4ee5\u770b\u4f5c\u662f\u5728\u7c7b$y_j$\u7684\u8bb0\u5f55\u4e2d\u89c2\u5bdf\u5c5e\u6027\u503c$x_i$\u7684\u5148\u9a8c\u6982\u7387\u3002\u7b49\u4ef7\u6837\u672c\u5927\u5c0f\u51b3\u5b9a\u5148\u9a8c\u6982\u7387$p$\u548c\u89c2\u6d4b\u6982\u7387$n_C\/n$\u4e4b\u95f4\u7684\u5e73\u8861\u3002<\/li>
- $m$\u7684\u53d6\u503c\uff1f\uff1f<\/li><\/ol>\n\n\n\n
\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u7684\u7279\u5f81<\/h5>\n\n\n\n
- \u9762\u5bf9\u5b64\u7acb\u7684\u566a\u58f0\u70b9\uff0c\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u4ecd\u7136\u662f\u5065\u58ee(Robust)\u7684\u3002<\/li>
- \u9762\u5bf9\u65e0\u5173\u5c5e\u6027\uff0c\u4e5f\u662f\u5065\u58ee\u7684\u3002<\/li>
- \u76f8\u5173\u5c5e\u6027\u4f1a\u964d\u4f4e\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u7684\u6027\u80fd\u3002\u6761\u4ef6\u72ec\u7acb\u5047\u8bbe\u4e0d\u6210\u7acb\u3002<\/li><\/ol>\n\n\n\n
\u8d1d\u53f6\u65af\u7684\u8bef\u5dee\u7387<\/h5>\n\n\n\n
\u4e8b\u5b9e\u4e0a\u4e5f\u5c31\u662f\u8bef\u5206\u7684\u6982\u7387\u3002\u4f8b\u5982\u5728MVA\u4e2d\u5b66\u4e60\u5230\u7684ECM(Expected cost of misclassification)\u3002\n$$\nECM = c(2|1)P(2|1)p_1 + c(1|2)P(1|2)p_2\n$$\n$(2|1)$\u8868\u793a\u5b9e\u9645\u4e0a\u662fGroup 1 \u4f46\u88ab\u5206\u5230Group2\u3002<\/p>\n\n\n\n
\u5728\u8fd9\u91cc\u6211\u4eec\u8bb0\u8d1d\u53f6\u65af\u8bef\u5dee\u7387\u4e3a\n$$\n\\mbox{Error} = \\int_{R_1}f_2(\\textbf X)\\mathrm{d}\\textbf X + \\int_{R_2}f_1(\\textbf X)\\mathrm{d}\\textbf X\n$$<\/p>\n\n\n\n
\u8d1d\u53f6\u65af\u4fe1\u5ff5\u7f51\u7edc<\/h4>\n\n\n\n
\u4e5f\u5c31\u662fBayesian Belief Networks<\/strong>(\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u5c06Belief\u7406\u89e3\u4e3a\u6982\u7387), BNN\uff0c\u7b80\u79f0\u8d1d\u53f6\u65af\u7f51\u7edc\u3002\u7528\u56fe\u5f62\u6765\u8868\u793a\u4e00\u7ec4\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u7684\u6982\u7387\u5173\u7cfb\u3002\u8d1d\u53f6\u65af\u7f51\u7edc\u6709\u4e24\u4e2a\u4e3b\u8981\u6210\u5206\uff0c<\/p>\n\n\n\n
- \u4e00\u4e2a\u6709\u5411\u65e0\u73af\u56fe(dag)\uff0c\u8868\u793a\u53d8\u91cf\u4e4b\u95f4\u7684\u4f9d\u8d56\u5173\u7cfb\u3002<\/li>
- \u4e00\u4e2a\u6982\u7387\u8868\uff0c\u628a\u5404\u7ed3\u70b9\u548c\u5b83\u7684\u76f4\u63a5\u7236\u7ed3\u70b9\u5173\u8054\u8d77\u6765\u3002<\/li><\/ol>\n\n\n\n
\u8f93\u5165\uff1a\u5df2\u77e5\u4e4b\u524d\u6761\u4ef6\uff0c\u53d1\u751f\u4e0b\u4e00\u4e2a\u7ed3\u70b9\u7684\u6982\u7387\u3002<\/p>\n\n\n\n
\u8f93\u51fa\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u6761\u4ef6\uff0c\u8f93\u51fa\u67d0\u4e00\u9879\u7684\u6982\u7387\u3002\u8fd9\u4e2a\u6982\u7387\u662f\u53ef\u4ee5\u5c42\u5c42\u63a8\u8fdb\u8ba1\u7b97\u51fa\u6765\u7684\u3002<\/p>\n\n\n\n
\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc<\/h3>\n\n\n\n
\u7406\u89e3\u6240\u9700\u7684\u4e00\u4e9b\u77e5\u8bc6<\/h4>\n\n\n\n
\u77e9\u9635\u3001\u5411\u91cf\u5fae\u5206\u8ba1\u7b97<\/a><\/p>\n\n\n\n
\u77e9\u9635\u6c42\u5bfc\u3001\u51e0\u79cd\u91cd\u8981\u7684\u77e9\u9635\u53ca\u5e38\u7528\u7684\u77e9\u9635\u6c42\u5bfc\u516c\u5f0f<\/a><\/p>\n\n\n\n
Denominator Layout \u5206\u6bcd\u5e03\u5c40<\/p>\n\n\n\n
Nominator Layout \u5206\u5b50\u5e03\u5c40<\/p>\n\n\n\n
\u8bbe$f(\\textbf x)$\u662f$\\textbf x$\u7684\u6807\u91cf\u51fd\u6570\uff0c\u6b63\u5e38\u7684\u68af\u5ea6\uff1a\n$$\n\\frac{\\partial f(\\textbf x)}{\\partial \\textbf x} = \\begin{pmatrix}\n\\frac{\\partial f(\\textbf x)}{\\partial x_1}\\\\\n\\frac{\\partial f(\\textbf x)}{\\partial x_2}\\\\\n\\vdots\\\\\n\\frac{\\partial f(\\textbf x)}{\\partial x_n}\\end{pmatrix}\n$$\n\u800c\u8f6c\u7f6e\u7684\u68af\u5ea6\uff1a\n$$\n\\left(\\frac{\\partial f(\\textbf x)}{\\partial \\textbf x}\\right)^T =\\frac{\\partial f(\\textbf x)}{\\partial\\textbf x^T}=\\begin{pmatrix}\n\\frac{\\partial f(\\textbf x)}{\\partial x_1}&\n\\frac{\\partial f(\\textbf x)}{\\partial x_2}&\n\\cdots&\n\\frac{\\partial f(\\textbf x)}{\\partial x_n}\\end{pmatrix}\n$$<\/p>\n\n\n\n
\u611f\u77e5\u5668Perceptron<\/h4>\n\n\n\n
\u7b80\u5355\u7684\u5355\u5c42\u795e\u7ecf\u7f51\u7edc\u2014\u2014\u611f\u77e5\u5668\u3002<\/p>\n\n\n\n
![\"img\"\/](\"https:\/\/upload-images.jianshu.io\/upload_images\/11345863-4feca33b55dd2350.png?imageMogr2\/auto-orient\/strip%7CimageView2\/2\/w\/397\/format\/webp\")
<\/figure>\n\n\n\n\u7ed9\u5b9a\u6743\u91cd\uff0c\u7136\u540e\u83b7\u5f97\u4e00\u4e2a\u6700\u7ec8\u7684\u52a0\u6743\u548c\uff0c\u7136\u540e\u5229\u7528\u6fc0\u6d3b\u51fd\u6570Activiation function\u5f97\u5230\u6700\u540e\u7684\u7ed3\u679c\u3002<\/p>\n\n\n\n
\u51e0\u4e2a\u6559\u7a0b\uff1a<\/h5>\n\n\n\n
- CSDN\u6559\u7a0b<\/a><\/li>
- \u7b80\u4e66\u6559\u7a0b<\/a><\/li><\/ol>\n\n\n\n
\u4e00\u4e2a\u524d\u7f6e\u77e5\u8bc6\uff1a<\/h5>\n\n\n\n
\u7a7a\u95f4\u4efb\u4e00\u70b9\u5230\u8d85\u5e73\u9762\u7684\u8ddd\u79bb\u516c\u5f0f\u7684\u63a8\u5bfc\u8fc7\u7a0b<\/a><\/p>\n\n\n\n
<\/figure>\n\n\n\n
\u6c42\u89e3\u8ddd\u79bb$d$\u548c\u4e3a\u4ec0\u4e48$w$\u662f\u6cd5\u5411\u91cf\u8fd8\u6709\u53e6\u5916\u7684\u89e3\u6cd5\u3002<\/p>\n\n\n\n
$w$\u662f\u6cd5\u5411\u91cf\u53ef\u4ee5\u7528\u5411\u91cf\u79ef\u70b9\u4e58\u63a8\u51fa\u6765\uff1a\u9009\u53d6\u4e24\u4e2a\u5728$\\textbf w\\cdot\\textbf x + b = 0$\u4e0a\u7684\u70b9$x_1,x_2$\uff0c\u6211\u4eec\u77e5\u9053$\\textbf x_1 – \\textbf x_2$\u4e00\u5b9a\u662f\u5728\u8fd9\u6761\u76f4\u7ebf\u4e0a\u7684\uff0c\u56e0\u6b64\u6709\n$$\n\\textbf w(\\textbf x_1-\\textbf x_2) = 0\n$$\n\u6240\u4ee5$\\textbf w$\u4e0e\u5728\u8fd9\u6761\u76f4\u7ebf\u4e0a\u7684\u5411\u91cf\u5185\u79ef\u4e3a0\uff0c\u56e0\u6b64$\\textbf w$\u4e00\u5b9a\u662f\u8be5\u76f4\u7ebf\u7684\u6cd5\u5411\u91cf\u3002<\/p>\n\n\n\n
\u8ddd\u79bb$d$\u89c1\u5e95\u4e0b\u7684\u63a8\u5bfc(SVM\u7684)\u3002<\/p>\n\n\n\n
\u611f\u77e5\u5668\uff1a<\/h5>\n\n\n\n
\u611f\u77e5\u5668\u662f\u5178\u578b\u7684\u7ebf\u6027\u5206\u7c7b\u5b66\u4e60\u7b97\u6cd5\u3002\u7ed9\u5b9a$N$\u4e2a\u6837\u672c\u7684\u8bad\u7ec3\u96c6\uff1a$(x^{(n)},y^{(n)})^{N}{n=1}$\uff0c\u5176\u4e2d$y^{(n)}\\in\\lbrace+1,-1\\rbrace$\uff0c\u8bd5\u56fe\u627e\u5230\u4e00\u7ec4\u53c2\u6570$w^*, b^*$\uff0c\u4f7f\u5f97\u6bcf\u4e2a\u6837\u672c$(x^{(n)},y^{(n)})^{N}<\/em>{n=1}$\uff0c\u6709\n$$\ny^{(n)}(w^{T}x^{(n)} + b^<\/em>)>0,\\quad\\forall n\\in[1,N]\n$$\n\u5176\u5b9e\u4e5f\u5c31\u662f\u6b63\u786e\u7387\u3002\u5176\u4e2d$\\hat{y} = w^{T}x^{(n)} + b^<\/em>$\u3002\u56e0\u6b64\uff0c\u53ea\u8981\u9884\u6d4b\u6b63\u786e\uff0c\u5176\u503c\u5c31\u4f1a\u5927\u4e8e0\u3002<\/p>\n\n\n\n
\u6fc0\u6d3b\u51fd\u6570(Activiation Function)<\/h5>\n\n\n\n
\u5728\u8fd9\u91cc\u6211\u4eec\u5229\u7528\u7684\u662fSign\u51fd\u6570\n$$\n\\mbox{Sign}(x) = \\begin{cases}\n-1, &x0\\\\\n\\end{cases}\n$$\n\u4e00\u822c\u6211\u4eec\u820d\u5f03\u6389$x=0$\u7684\u90e8\u5206\uff0c\u4e5f\u5c31\u662f\u53ea\u6709$x>0, y= 1$\u548c$x\\leq0,y=-1$\u3002<\/p>\n\n\n\n
\u76ee\u6807<\/h5>\n\n\n\n
\u6700\u5c0f\u5316loss function, $M$\u4e3a\u8bef\u5206\u7c7b\u7684\u6837\u672c\n$$\n\\min_{w,b} L(w,b) = -\\sum_{x_i\\in M} y_i(w\\cdot x_i + b)\n$$\n\u635f\u5931\u51fd\u6570\u7684\u68af\u5ea6\u4e3a\uff1a\n$$\n\\nabla_wL(w,b) = -\\sum_{x_i\\in M}y_ix_i\n$$<\/p>\n\n\n\n
$$\n\\nabla_bL(w,b) = -\\sum_{x_i\\in M}y_i\n$$<\/p>\n\n\n\n
\u7136\u540e\u9009\u53d6\u4e00\u4e2a\u5b66\u4e60\u6b65\u957f\uff0c\u4e5f\u5c31\u662f\u5b66\u4e60\u7387$\\eta$\u3002<\/p>\n\n\n\n
\u66f4\u65b0\u65b9\u5f0f(\u5b66\u4e60\u65b9\u5f0f)<\/h5>\n\n\n\n
\u68af\u5ea6\u7684\u6027\u8d28<\/h6>\n\n\n\n
\u51fd\u6570$f(x)$\u5728\u70b9$x_0$\u5904\u7684\u8d1f\u68af\u5ea6$-\\nabla f(x_0)$\u662f$f(x)$\u5728\u70b9$x_0$\u5904\u6700\u5feb\u7684\u4e0b\u964d\u65b9\u5411\u3002<\/p>\n\n\n\n
\u8bc1\u660e<\/strong>\uff1a\u7531\u6cf0\u52d2\u516c\u5f0f\u77e5\uff1a\n$$\n\\begin{eqnarray}\nf(x_0 + \\lambda p) – f(x_0) &=& \\left(\\nabla f(x_0)\\right)^T\\cdot\\lambda p+o(\\|\\lambda p\\|)\\\\\n&=&\\lambda\\left(\\nabla f(x_0)\\right)^T\\cdot p +o(\\|\\lambda p\\|)\n\\end{eqnarray}\n$$\n\u56e0\u6b64\u7565\u53bb\u9ad8\u9636\u65e0\u7a77\u5c0f\u91cf$o(\\|\\lambda p\\|)$\u4e0d\u8ba1\uff0c\u53d6$p = -\\nabla f(x_0)$\u65f6\uff0c\u51fd\u6570$f(x)$\u4e0b\u964d\u6700\u5feb\u3002\u8fd9\u91cc$\\lambda$\u5c31\u662f\u6b65\u957f\u3002<\/p>\n\n\n\n
GD(Gradient Descent)<\/h6>\n\n\n\n
\u6b63\u5e38\u7684\u68af\u5ea6\u4e0b\u964d\u65b9\u5f0f\u3002\u4ee5Perceptron\u4e3a\u4f8b\uff0c\u6211\u4eec\u7684\u68af\u5ea6\u53ef\u4ee5\u8fd1\u4f3c\u7684\u770b\u4f5c\n$$\n\\begin{eqnarray}\n\\nabla_wL(w,b) &=& -\\sum_{x_i\\in M}y_ix_i\\\\\n\\frac{\\partial L(w,b)}{\\partial w} &=& -\\sum_{x_i\\in M}y_ix_i\\\\\n\\end{eqnarray}\n$$\n\u5176\u5b9e\u4e5f\u53ef\u4ee5\u8fd1\u4f3c\u770b\u4f5c\u662f($\\Delta w_t$\u5f88\u5c0f\u7684\u65f6\u5019)\n$$\n\\frac{L_{t+1} – L_t}{w_{t+1}-w_t} = -\\sum_{x_i\\in M}y_ix_i\n$$\n\u8fd9\u5176\u5b9e\u5c31\u662f\u635f\u5931\u51fd\u6570\u7684\u5728$w_t$\u7684\u5bfc\u6570\u3002\u4e3a\u4e86\u83b7\u5f97\u66f4\u5c0f\u7684\u635f\u5931\u51fd\u6570\u503c\uff0c\u6211\u4eec\u5f80\u635f\u5931\u51fd\u6570\u51cf\u5c0f\u7684\u65b9\u5411\u524d\u8fdb\uff0c\u4e5f\u5c31\u662f\u8981\u4f7f\n$$\n\\begin{eqnarray}\nL_{t+1} – L_t =-(w_{t+1}-w_t)\\cdot\\sum_{x_i\\in M}y_ix_i&\\leq&0\\\\\n(w_{t+1}-w_t)\\cdot\\sum_{x_i\\in M}y_ix_i&\\geq&0\n\\end{eqnarray}\n$$\n\u6211\u4eec\u4e0d\u59a8\u987a\u7740\u5207\u7ebf\u7684\u65b9\u5411\uff0c\u4ee5\u83b7\u5f97\u4e0b\u4e00\u4e2a\u4f7f\u635f\u5931\u51fd\u6570\u53d8\u5c0f\u7684$w_{t+1}$\u7684\u503c\uff0c\u4e5f\u5c31\u662f\uff0c\n$$\nw_{t+1} = w_t + \\eta\\cdot\\sum_{x_i\\in M}y_ix_i\n$$\n\u5176\u4e2d\u5b66\u4e60\u7387$\\eta$\u4e3a\u91cd\u8981\u7684\u8c03\u53c2\u53c2\u6570\u3002<\/p>\n\n\n\n
SGD(Stochastic Gradient Descent)<\/h6>\n\n\n\n
\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u3002\u4e0e\u7ecf\u5178\u68af\u5ea6\u4e0b\u964d\u51e0\u4e4e\u76f8\u540c\uff0c\u4f46\u6211\u4eec\u6bcf\u6b21\u4ec5\u5229\u7528\u4e00\u4e2a\u6837\u672c\u6570\u636e\u6765\u4f30\u8ba1\u4e0b\u4e00\u4e2a\u53ef\u80fd\u7684$w_{t+1}$\uff0c\u4e5f\u5c31\u662f\n$$\nw_{t+1} = w_t +\\eta\\cdot y_jx_j\n$$\n$j$\u4e3a\u6211\u4eec\u5728$M$\u4e2d\u968f\u673a\u6311\u9009\u7684\u4e00\u4e2a\u6837\u672c\u3002<\/p>\n\n\n\n
MBGD(Mini-Batch Gradient Descent)\u548cBGD(Batch Gradient Descent)<\/h6>\n\n\n\n
\u5c0f\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u548c\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u3002\u5c0f\u6279\u91cf\u5373\u9009\u53d6\u4e00\u90e8\u5206\u6837\u672c\u8fdb\u884c\u68af\u5ea6\u4e0b\u964d\u8ba1\u7b97\u3002\u8fd9\u79cd\u65b9\u6cd5\u8f83\u4e3a\u5e38\u7528\u3002\u6211\u4eec\u5229\u7528\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u6781\u5927\u5730\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002<\/p>\n\n\n\n
Advantages and Disadvantages<\/h5>\n\n\n\n
\u5728\u6570\u636e\u96c6\u7ebf\u6027\u53ef\u5206\u65f6\uff0c\u611f\u77e5\u5668\u867d\u7136\u53ef\u4ee5\u627e\u5230\u4e00\u4e2a\u8d85\u5e73\u9762\u628a\u4e24\u7c7b\u6570\u636e\u5206\u5f00\uff0c \u4f46\u5e76\u4e0d\u80fd\u4fdd\u8bc1\u80fd\u5176\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n<\/li>
\u611f\u77e5\u5668\u5bf9\u6837\u672c\u987a\u5e8f\u6bd4\u8f83\u654f\u611f\u3002\u6bcf\u6b21\u8fed\u4ee3\u7684\u987a\u5e8f\u4e0d\u4e00\u81f4\u65f6\uff0c\u627e\u5230\u7684\u5206\u5272\u8d85\u5e73\u9762\u4e5f\u5f80\u5f80\u4e0d\u4e00\u81f4\u3002<\/p>\n<\/li>
\u5982\u679c\u8bad\u7ec3\u96c6\u4e0d\u662f\u7ebf\u6027\u53ef\u5206\u7684\uff0c\u5c31\u6c38\u8fdc\u4e0d\u4f1a\u6536\u655b[Freund and Schapire, 1999]\u3002<\/p>\n<\/li><\/ol>\n\n\n\n
\u591a\u5c42\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc<\/h4>\n\n\n\n
\u591a\u5c42\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4e5f\u5c31\u662f\u591a\u5c42\u611f\u77e5\u5668\u7ec4\u6210\u3002\u4e5f\u5c31\u662f\u4e00\u822c\u6211\u4eec\u9664\u4e86\u8f93\u5165\u5c42\u8f93\u51fa\u5c42\u4ee5\u5916\uff0c\u8fd8\u6709\u9690\u85cf\u5c42\u3002<\/p>\n\n\n\n
ANN<\/h5>\n\n\n\n
ANN\u662f\u591a\u5c42\u524d\u9988\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u3002\u524d\u9988\u6211\u4eec\u4e00\u822c\u53ebfeed-forward\u3002\u5728\u9012\u5f52(Recurrent)\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u5141\u8bb8\u540c\u4e00\u5c42\u7ed3\u70b9\u76f8\u8fde\u6216\u4e00\u5c42\u7684\u7ed3\u70b9\u8fde\u5230\u524d\u9762\u5404\u5c42\u4e2d\u7684\u7ed3\u70b9\u3002<\/p>\n\n\n\n
<\/figure>\n\n\n\n
\u6fc0\u6d3b\u51fd\u6570<\/h5>\n\n\n\n
\u5e38\u7528\u6fc0\u6d3b\u51fd\u6570\uff08\u6fc0\u52b1\u51fd\u6570\uff09\u7406\u89e3\u4e0e\u603b\u7ed3<\/a><\/p>\n\n\n\n
\u51e0\u79cd\u5e38\u89c1\u6fc0\u6d3b\u51fd\u6570(\u7b14\u8bb0\u6574\u7406)<\/a><\/p>\n\n\n\n
\u6211\u4eec\u6709\u8bb8\u591a\u6fc0\u6d3b\u51fd\u6570\u4e0e\u6fc0\u6d3b\u51fd\u6570\u7684\u53d8\u79cd\u3002<\/p>\n\n\n\n
Sigmoid<\/strong><\/p>\n\n\n\n
<\/figure>\n\n\n\n
Sign<\/h6>\n\n\n\n
$$\n\\mbox{Sign}(x) = \\begin{cases}\n-1, &x0\\\\\n\\end{cases}\n$$<\/p>\n\n\n\n
Sigmoid<\/h6>\n\n\n\n
$$\n\\mbox{Sigmoid}(x) = \\frac{1}{1+e^{-x}}\n$$<\/p>\n\n\n\n
\u5de6\u7aef\u8d8b\u8fd1\u4e8e0\uff0c\u53f3\u7aef\u8d8b\u8fd1\u4e8e1\uff0c\u4e14\u4e24\u7aef\u90fd\u8d8b\u4e8e\u9971\u548c<\/a>.<\/p>\n\n\n\n
\u5173\u4e8e\u51fd\u6570\u9971\u548c\u89e3\u91ca:\u53c2\u8003https:\/\/www.cnblogs.com\/tangjicheng\/p\/9323389.html<\/a><\/p>\n\n\n\n
![\"img\"\/](\"https:\/\/images2018.cnblogs.com\/blog\/1370487\/201807\/1370487-20180717145622000-773000260.png\")
<\/figure>\n\n\n\n\u5982\u679c\u6211\u4eec\u521d\u59cb\u5316\u795e\u7ecf\u7f51\u7edc\u7684\u6743\u503c\u4e3a [0,1] \u4e4b\u95f4\u7684\u968f\u673a\u503c\uff0c\u7531\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u7684\u6570\u5b66\u63a8\u5bfc\u53ef\u77e5\uff0c\u68af\u5ea6\u4ece\u540e\u5411\u524d\u4f20\u64ad\u65f6\uff0c\u6bcf\u4f20\u9012\u4e00\u5c42\u68af\u5ea6\u503c\u90fd\u4f1a\u51cf\u5c0f\u4e3a\u539f\u6765\u76840.25\u500d\uff0c\u5982\u679c\u795e\u7ecf\u7f51\u7edc\u9690\u5c42\u7279\u522b\u591a\uff0c\u90a3\u4e48\u68af\u5ea6\u5728\u7a7f\u8fc7\u591a\u5c42\u540e\u5c06\u53d8\u5f97\u975e\u5e38\u5c0f\u63a5\u8fd1\u4e8e0\uff0c\u5373\u51fa\u73b0\u68af\u5ea6\u6d88\u5931\u73b0\u8c61\uff1b\u5f53\u7f51\u7edc\u6743\u503c\u521d\u59cb\u5316\u4e3a (1,+\u221e) (1,+\u221e)(1,+\u221e) \u533a\u95f4\u5185\u7684\u503c\uff0c\u5219\u4f1a\u51fa\u73b0\u68af\u5ea6\u7206\u70b8\u60c5\u51b5\u3002\n\u6570\u5b66\u5206\u6790\u89c1\u6587\u7ae0:https:\/\/www.jianshu.com\/p\/917f71b06499<\/a><\/p>\n\n\n\n
Sigmoid \u7684 output \u4e0d\u662f0\u5747\u503c\uff08\u5373zero-centered\uff09\u3002\u8fd9\u4f1a\u5bfc\u81f4\u540e\u4e00\u5c42\u7684\u795e\u7ecf\u5143\u5c06\u5f97\u5230\u4e0a\u4e00\u5c42\u8f93\u51fa\u7684\u975e0\u5747\u503c\u7684\u4fe1\u53f7\u4f5c\u4e3a\u8f93\u5165\u3002\n\u5176\u89e3\u6790\u5f0f\u4e2d\u542b\u6709\u5e42\u8fd0\u7b97\uff0c\u8ba1\u7b97\u673a\u6c42\u89e3\u65f6\u76f8\u5bf9\u6765\u8bb2\u6bd4\u8f83\u8017\u65f6\u3002\u5bf9\u4e8e\u89c4\u6a21\u6bd4\u8f83\u5927\u7684\u6df1\u5ea6\u7f51\u7edc\uff0c\u8fd9\u4f1a\u8f83\u5927\u5730\u589e\u52a0\u8bad\u7ec3\u65f6\u95f4.<\/p>\n\n\n\n
Tanh<\/h6>\n\n\n\n
$$\n\\mbox{tanh}(x) = \\frac{2}{1+e^{-2x}}-1 = \\frac{e^x-e^{-x}}{e^x+e^{-x}}\n$$<\/p>\n\n\n\n
\u5b83\u89e3\u51b3\u4e86Sigmoid\u51fd\u6570\u7684\u4e0d\u662fzero-centered\u8f93\u51fa\u95ee\u9898\uff0c\u7136\u800c\uff0c\u68af\u5ea6\u6d88\u5931\uff08gradient vanishing\uff09\u7684\u95ee\u9898\u548c\u5e42\u8fd0\u7b97\u7684\u95ee\u9898\u4ecd\u7136\u5b58\u5728\u3002<\/p>\n\n\n\n
ReLu<\/h6>\n\n\n\n
$$\n\\mbox{ReLu}(x) = \\max(x,0)\n$$<\/p>\n\n\n\n
![\"\"](\"https:\/\/www.wennroy.com\/wp-content\/uploads\/2022\/07\/20180503231727530.png\")
<\/figure>\n\n\n\n\u662f\u4e2a\u5206\u6bb5\u7ebf\u6027\u51fd\u6570\uff0c\u663e\u7136\u5176\u5bfc\u6570\u5728\u6b63\u534a\u8f74\u4e3a1\uff0c\u8d1f\u534a\u8f74\u4e3a0\uff0c\u8fd9\u6837\u5b83\u5728\u6574\u4e2a\u5b9e\u6570\u57df\u4e0a\u6709\u4e00\u534a\u7684\u7a7a\u95f4\u662f\u4e0d\u9971\u548c\u7684\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0csigmoid\u51fd\u6570\u51e0\u4e4e\u5168\u90e8\u533a\u57df\u90fd\u662f\u9971\u548c\u7684.<\/p>\n\n\n\n
ReLU\u867d\u7136\u7b80\u5355\uff0c\u4f46\u5374\u662f\u8fd1\u51e0\u5e74\u7684\u91cd\u8981\u6210\u679c\uff0c\u6709\u4ee5\u4e0b\u51e0\u5927\u4f18\u70b9\uff1a
1\uff09 \u89e3\u51b3\u4e86gradient vanishing\u95ee\u9898 (\u5728\u6b63\u533a\u95f4)
2\uff09\u8ba1\u7b97\u901f\u5ea6\u975e\u5e38\u5feb\uff0c\u53ea\u9700\u8981\u5224\u65ad\u8f93\u5165\u662f\u5426\u5927\u4e8e0
3\uff09\u6536\u655b\u901f\u5ea6\u8fdc\u5feb\u4e8esigmoid\u548ctanh<\/p>\n\n\n\nReLu\u662f\u5206\u6bb5\u7ebf\u6027\u51fd\u6570\uff0c\u5b83\u7684\u975e\u7ebf\u6027\u6027\u5f88\u5f31\uff0c\u56e0\u6b64\u7f51\u7edc\u4e00\u822c\u8981\u505a\u5f97\u5f88\u6df1\u3002\u4f46\u8fd9\u6b63\u597d\u8fce\u5408\u4e86\u6211\u4eec\u7684\u9700\u6c42\uff0c\u56e0\u4e3a\u5728\u540c\u6837\u6548\u679c\u7684\u524d\u63d0\u4e0b\uff0c\u5f80\u5f80\u6df1\u5ea6\u6bd4\u5bbd\u5ea6\u66f4\u91cd\u8981\uff0c\u66f4\u6df1\u7684\u6a21\u578b\u6cdb\u5316\u80fd\u529b\u66f4\u597d\u3002\u6240\u4ee5\u81ea\u4ece\u6709\u4e86Relu\u6fc0\u6d3b\u51fd\u6570\uff0c\u5404\u79cd\u5f88\u6df1\u7684\u6a21\u578b\u90fd\u88ab\u63d0\u51fa\u6765\u4e86\uff0c\u4e00\u4e2a\u6807\u5fd7\u6027\u7684\u4e8b\u4ef6\u662f\u5e94\u8be5\u662fVGG\u6a21\u578b\u548c\u5b83\u5728ImageNet\u4e0a\u53d6\u5f97\u7684\u6210\u529f.<\/p>\n\n\n\n
ReLU\u4e5f\u6709\u51e0\u4e2a\u9700\u8981\u7279\u522b\u6ce8\u610f\u7684\u95ee\u9898\uff1a
1\uff09ReLU\u7684\u8f93\u51fa\u4e0d\u662fzero-centered
2\uff09\u67d0\u4e9b\u795e\u7ecf\u5143\u53ef\u80fd\u6c38\u8fdc\u4e0d\u4f1a\u88ab\u6fc0\u6d3b(Dead ReLU Problem)\uff0c\u5bfc\u81f4\u76f8\u5e94\u7684\u53c2\u6570\u6c38\u8fdc\u4e0d\u80fd\u88ab\u66f4\u65b0\u3002\u6709\u4e24\u4e2a\u4e3b\u8981\u539f\u56e0\u53ef\u80fd\u5bfc\u81f4\u8fd9\u79cd\u60c5\u51b5\u4ea7\u751f: (1) \u975e\u5e38\u4e0d\u5e78\u7684\u53c2\u6570\u521d\u59cb\u5316\uff0c\u8fd9\u79cd\u60c5\u51b5\u6bd4\u8f83\u5c11\u89c1 (2) learning rate\u592a\u9ad8\u5bfc\u81f4\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u53c2\u6570\u66f4\u65b0\u592a\u5927\uff0c\u4e0d\u5e78\u4f7f\u7f51\u7edc\u8fdb\u5165\u8fd9\u79cd\u72b6\u6001\u3002\u89e3\u51b3\u65b9\u6cd5\u662f\u53ef\u4ee5\u91c7\u7528Xavier\u521d\u59cb\u5316\u65b9\u6cd5\uff0c\u4ee5\u53ca\u907f\u514d\u5c06learning rate\u8bbe\u7f6e\u592a\u5927\u6216\u4f7f\u7528adagrad\u7b49\u81ea\u52a8\u8c03\u8282learning rate\u7684\u7b97\u6cd5\u3002<\/p>\n\n\n\n\u5c3d\u7ba1\u5b58\u5728\u8fd9\u4e24\u4e2a\u95ee\u9898\uff0cReLU\u76ee\u524d\u4ecd\u662f\u6700\u5e38\u7528\u7684activation function\uff0c\u5728\u642d\u5efa\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u65f6\u5019\u63a8\u8350\u4f18\u5148\u5c1d\u8bd5\uff01<\/strong><\/p>\n\n\n\n
Swish\u51fd\u6570(Google\u5927\u8111\u56e2\u961f)<\/h6>\n\n\n\n
$$
\\mbox{Swish}(x) = x\\cdot \\mbox{Sigmoid}(x)
$$<\/p>\n\n\n\n![\"Swish\"\/](\"https:\/\/spaces.ac.cn\/usr\/uploads\/2017\/10\/3233256886.png\")
<\/figure>\n\n\n\n\u4ece\u56fe\u50cf\u4e0a\u6765\u770b\uff0cSwish\u51fd\u6570\u8ddfReLu\u5dee\u4e0d\u591a\uff0c\u552f\u4e00\u533a\u522b\u8f83\u5927\u7684\u662f\u63a5\u8fd1\u4e8e0\u7684\u8d1f\u534a\u8f74\u533a\u57df, Google\u5927\u8111\u505a\u4e86\u5f88\u591a\u5b9e\u9a8c\uff0c\u7ed3\u679c\u90fd\u8868\u660eSwish\u4f18\u4e8eReLu<\/p>\n\n\n\n
Gated linear units(GLU)\u6fc0\u6d3b\u51fd\u6570(facebook\u63d0\u51fa)<\/h6>\n\n\n\n
https:\/\/blog.csdn.net\/qq_32458499\/article\/details\/81513720<\/a><\/p>\n\n\n\n
Leaky ReLU\u51fd\u6570\uff08PReLU\uff09<\/h6>\n\n\n\n
\u51fd\u6570\u8868\u8fbe\u5f0f
$$
f(x) = \\max(\\alpha x,x)
$$
<\/p>\n\n\n\n![\"\"](\"https:\/\/www.wennroy.com\/wp-content\/uploads\/2022\/07\/20180506142451567.png\")
<\/figure>\n\n\n\n\u4eba\u4eec\u4e3a\u4e86\u89e3\u51b3Dead ReLU Problem\uff0c\u63d0\u51fa\u4e86\u5c06ReLU\u7684\u524d\u534a\u6bb5\u8bbe\u4e3a$\\alpha x$\u800c\u975e0\uff0c\u901a\u5e38$\\alpha=0.01$\u3002\u53e6\u5916\u4e00\u79cd\u76f4\u89c2\u7684\u60f3\u6cd5\u662f\u57fa\u4e8e\u53c2\u6570\u7684\u65b9\u6cd5\uff0c\u5373Parametric ReLU:$f(x)=\\max(\\alpha x,x)$\uff0c\u5176\u4e2d$\\alpha$\u53ef\u7531\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5<\/strong>\u5b66\u51fa\u6765\u3002\u7406\u8bba\u4e0a\u6765\u8bb2\uff0cLeaky ReLU\u6709ReLU\u7684\u6240\u6709\u4f18\u70b9\uff0c\u5916\u52a0\u4e0d\u4f1a\u6709Dead ReLU\u95ee\u9898\uff0c\u4f46\u662f\u5728\u5b9e\u9645\u64cd\u4f5c\u5f53\u4e2d\uff0c\u5e76\u6ca1\u6709\u5b8c\u5168\u8bc1\u660eLeaky ReLU\u603b\u662f\u597d\u4e8eReLU\u3002<\/p>\n\n\n\n
ELU (Exponential Linear Units) \u51fd\u6570<\/h6>\n\n\n\n
$$
f(x) = \\begin{cases}
x,\\quad &\\mbox{if }x>0\\
\\alpha(e^x-1),&\\mbox{otherwise}
\\end{cases}
$$<\/p>\n\n\n\n![\"\"](\"https:\/\/www.wennroy.com\/wp-content\/uploads\/2022\/07\/20180506142835140.png\")
<\/figure>\n\n\n\nELU\u4e5f\u662f\u4e3a\u89e3\u51b3ReLU\u5b58\u5728\u7684\u95ee\u9898\u800c\u63d0\u51fa\uff0c\u663e\u7136\uff0cELU\u6709ReLU\u7684\u57fa\u672c\u6240\u6709\u4f18\u70b9\uff0c\u4ee5\u53ca\uff1a<\/p>\n\n\n\n
- \u4e0d\u4f1a\u6709Dead ReLU\u95ee\u9898<\/li>
- \u8f93\u51fa\u7684\u5747\u503c\u63a5\u8fd10\uff0czero-centered<\/li><\/ol>\n\n\n\n
\u5b83\u7684\u4e00\u4e2a\u5c0f\u95ee\u9898\u5728\u4e8e\u8ba1\u7b97\u91cf\u7a0d\u5927\u3002\u7c7b\u4f3c\u4e8eLeaky ReLU\uff0c\u7406\u8bba\u4e0a\u867d\u7136\u597d\u4e8eReLU\uff0c\u4f46\u5728\u5b9e\u9645\u4f7f\u7528\u4e2d\u76ee\u524d\u5e76\u6ca1\u6709\u597d\u7684\u8bc1\u636eELU\u603b\u662f\u4f18\u4e8eReLU\u3002<\/p>\n\n\n\n
MaxOut\u51fd\u6570<\/h6>\n\n\n\n
\u8bba\u6587\u300amaxout networks\u300b<\/p>\n\n\n\n
Maxout\u662f\u6df1\u5ea6\u5b66\u4e60\u7f51\u7edc\u4e2d\u7684\u4e00\u5c42\u7f51\u7edc\uff0c\u5c31\u50cf\u6c60\u5316\u5c42\u3001\u5377\u79ef\u5c42\u4e00\u6837\u7b49\uff0c\u6211\u4eec\u53ef\u4ee5\u628amaxout \u770b\u6210\u662f\u7f51\u7edc\u7684\u6fc0\u6d3b\u51fd\u6570\u5c42\u3002\u5982\u679c\u6211\u4eec\u8f93\u5165\u7279\u5f81\u5411\u91cf\u4e3a\uff1a$X = (x_1,x_2,\\ldots,x_d)$\uff0c\u4e5f\u5c31\u662f\u8f93\u5165$d$\u4e2a\u795e\u7ecf\u5143\u3002Maxout\u5bf9\u4e8e\u6bcf\u4e2a\u9690\u85cf\u795e\u7ecf\u5143\u8ba1\u7b97\u5982\u4e0b\uff1a
$$
h_i(x) = \\max_{j\\in[1,k]}z_{ij}
$$
\u795e\u7ecf\u7f51\u7edc\u6fc0\u6d3b\u51fd\u6570\u6c47\u603b\uff08Sigmoid\u3001tanh\u3001ReLU\u3001LeakyReLU\u3001pReLU\u3001ELU\u3001maxout\uff09<\/a><\/p>\n\n\n\n\u5e94\u7528\u4e2d\u5982\u4f55\u9009\u62e9\u5408\u9002\u7684\u6fc0\u6d3b\u51fd\u6570\uff1f<\/h6>\n\n\n\n
\u8fd9\u4e2a\u95ee\u9898\u76ee\u524d\u6ca1\u6709\u786e\u5b9a\u7684\u65b9\u6cd5\uff0c\u51ed\u4e00\u4e9b\u7ecf\u9a8c\u5427\u3002
1\uff09\u6df1\u5ea6\u5b66\u4e60\u5f80\u5f80\u9700\u8981\u5927\u91cf\u65f6\u95f4\u6765\u5904\u7406\u5927\u91cf\u6570\u636e\uff0c\u6a21\u578b\u7684\u6536\u655b\u901f\u5ea6\u662f\u5c24\u4e3a\u91cd\u8981\u7684\u3002\u6240\u4ee5\uff0c\u603b\u4f53\u4e0a\u6765\u8bb2\uff0c\u8bad\u7ec3\u6df1\u5ea6\u5b66\u4e60\u7f51\u7edc\u5c3d\u91cf\u4f7f\u7528zero-centered\u6570\u636e (\u53ef\u4ee5\u7ecf\u8fc7\u6570\u636e\u9884\u5904\u7406\u5b9e\u73b0) \u548czero-centered\u8f93\u51fa\u3002\u6240\u4ee5\u8981\u5c3d\u91cf\u9009\u62e9\u8f93\u51fa\u5177\u6709zero-centered\u7279\u70b9\u7684\u6fc0\u6d3b\u51fd\u6570\u4ee5\u52a0\u5feb\u6a21\u578b\u7684\u6536\u655b\u901f\u5ea6\u3002
2\uff09\u5982\u679c\u4f7f\u7528 ReLU\uff0c\u90a3\u4e48\u4e00\u5b9a\u8981\u5c0f\u5fc3\u8bbe\u7f6e learning rate\uff0c\u800c\u4e14\u8981\u6ce8\u610f\u4e0d\u8981\u8ba9\u7f51\u7edc\u51fa\u73b0\u5f88\u591a \u201cdead\u201d \u795e\u7ecf\u5143\uff0c\u5982\u679c\u8fd9\u4e2a\u95ee\u9898\u4e0d\u597d\u89e3\u51b3\uff0c\u90a3\u4e48\u53ef\u4ee5\u8bd5\u8bd5 Leaky ReLU\u3001PReLU \u6216\u8005 Maxout.
3\uff09\u6700\u597d\u4e0d\u8981\u7528 sigmoid\uff0c\u4f60\u53ef\u4ee5\u8bd5\u8bd5 tanh\uff0c\u4e0d\u8fc7\u53ef\u4ee5\u9884\u671f\u5b83\u7684\u6548\u679c\u4f1a\u6bd4\u4e0d\u4e0a ReLU \u548c Maxout.<\/p>\n\n\n\n\u4e00\u4e9b\u6709\u610f\u601d\u7684\u5b9e\u4f8b<\/h5>\n\n\n\n
- \u7b80\u4e66\u6559\u7a0b<\/a><\/li><\/ol>\n\n\n\n
- CSDN\u6559\u7a0b<\/a><\/li>
- \u5229\u7528\u6b63\u6001\u5206\u5e03\u3002\u5047\u8bbe\u8fde\u7eed\u53d8\u91cf\u670d\u4ece\u67d0\u79cd\u6982\u7387\u5206\u5e03\uff0c\u4e00\u822c\u53d6\u6b63\u6001\u5206\u5e03\uff0c\u7136\u540e\u5229\u7528\u6837\u672c\u5747\u503c\u548c\u6837\u672c\u65b9\u5dee\u6765\u4f30\u8ba1\u6b63\u6001\u5206\u5e03\uff0c\u4e5f\u5c31\u662f$X\\sim N(\\bar{x},s^2)$\u3002\u8fd9\u5c31\u662f\u7c7b\u4f3c\u4e8e\u6211\u4eec\u5728MVA\u5b66\u4e60\u7684Bayes Classification Rule\u3002<\/li><\/ol>\n\n\n\n
- \u6d88\u6781\u5b66\u4e60\u65b9\u6cd5(Lazy Learner):<\/strong> \u4f8b\u5b50\u6709 Rote<\/strong> **\u5206\u7c7b\u5668(Rote Classifier)**\u3002\u91c7\u53d6\u4e0e\u4e4b\u76f8\u53cd\u7684\u7b56\u7565\uff0c\u63a8\u8fdf\u5bf9\u8bad\u7ec3\u6570\u636e\u7684\u5efa\u6a21\uff0c\u76f4\u5230\u9700\u8981\u5206\u7c7b\u6d4b\u8bd5\u6837\u4f8b\u65f6\u518d\u8fdb\u884c\u3002<\/li><\/ol>\n\n\n\n