- \n
- 1.\u8f93\u51651\u00f7(1+e^-x) (e^\u5728shift+LN\uff1bx\u5728alpha+))<\/li>\n\n\n\n
- 2.\u6309 =<\/li>\n\n\n\n
- 3.\u6309CALC<\/li>\n\n\n\n
- 4.\u8f93\u5165x<\/li>\n\n\n\n
- 5.\u8fde\u6309\u4e24\u4e0b=<\/li>\n\n\n\n
- 6.\u91cd\u590d3-5 <\/li>\n<\/ul>\n\n\n\n
y=sigmoid(x)\uff1b\u5219y’=y(1-y)\uff1b\u03b4x=\u03b4y*y(1-y)<\/p>\n\n\n\n
\u7cfb\u7edf\u8bbe\u8ba1<\/strong><\/p>\n\n\n\n
\u4e00\u3001\u76d1\u7763\u5b66\u4e60\uff08\u6709\u6807\u7b7e\u6570\u636e\uff09<\/p>\n\n\n\n
\u56de\u5f52\u4efb\u52a1\uff08\u9884\u6d4b\u8fde\u7eed\u503c\uff09\uff1a<\/p>\n\n\n\n
- \n
- \u7ebf\u6027\u56de\u5f52 LR\uff08\u7b80\u5355\uff09<\/li>\n\n\n\n
- \u591a\u5c42\u611f\u77e5\u673a MLP\uff08\u590d\u6742\uff09<\/li>\n<\/ul>\n\n\n\n
\u5206\u7c7b\u4efb\u52a1\uff08\u9884\u6d4b\u79bb\u6563\u6807\u7b7e\uff09\uff1a<\/p>\n\n\n\n
- \n
- \u903b\u8f91\u56de\u5f52 LR<\/li>\n\n\n\n
- \u51b3\u7b56\u6811\uff08Decision Tree\uff09<\/li>\n\n\n\n
- K-\u8fd1\u90bb KNN<\/li>\n\n\n\n
- \u8d1d\u53f6\u65af\u5206\u7c7b\uff08Naive Bayes\uff09<\/li>\n\n\n\n
- \u652f\u6301\u5411\u91cf\u673a SVM<\/li>\n\n\n\n
- \u591a\u5c42\u611f\u77e5\u673a MLP<\/li>\n<\/ul>\n\n\n\n
\u4e8c\u3001\u65e0\u76d1\u7763\u5b66\u4e60\uff08\u65e0\u6807\u7b7e\u6570\u636e\uff09<\/p>\n\n\n\n
\u805a\u7c7b\u4efb\u52a1\uff1a<\/p>\n\n\n\n
- \n
- \u805a\u7c7b\uff08Clustering\uff09\uff08K-Means\uff09<\/li>\n<\/ul>\n\n\n\n
\u964d\u7ef4\u4efb\u52a1\uff1a<\/p>\n\n\n\n
- \n
- \u964d\u7ef4\uff08Dimensionality Reduction\uff09\n
- \n
- PCA\u4e3b\u6210\u5206\u5206\u6790\uff08\u7ebf\u6027\uff09Autoencoder\u81ea\u7f16\u7801\u5668\uff08\u975e\u7ebf\u6027\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
\u4e09\u3001\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\uff08\u4ee5\u795e\u7ecf\u7f51\u7edc\u4e3a\u57fa\u7840\uff09<\/p>\n\n\n\n
\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\uff1a<\/p>\n\n\n\n
- \n
- \u5377\u79ef\u795e\u7ecf\u7f51\u7edc CNN\uff1a\u4e3b\u8981\u7528\u4e8e\u56fe\u50cf\u8bc6\u522b\uff08\u673a\u5668\u89c6\u89c9\uff09<\/li>\n\n\n\n
- \u591a\u5c42\u611f\u77e5\u673a MLP\uff1a\u57fa\u7840\u795e\u7ecf\u7f51\u7edc\uff0c\u53ef\u7528\u4e8e\u591a\u79cd\u4efb\u52a1<\/li>\n\n\n\n
- Transformer\uff1a\u5e8f\u5217\u5efa\u6a21\u7ed3\u6784\uff0c\u5e7f\u6cdb\u7528\u4e8e NLP \u548c\u56fe\u50cf\u7b49\u4efb\u52a1<\/li>\n\n\n\n
- \u5927\u8bed\u8a00\u6a21\u578b LLM\uff1a\u4ee5 Transformer \u4e3a\u57fa\u7840\u7684\u9884\u8bad\u7ec3\u8bed\u8a00\u6a21\u578b\uff08\u5982 GPT\u3001BERT\uff09<\/li>\n<\/ul>\n\n\n\n
\u56db\u3001\u81ea\u7136\u8bed\u8a00\u5904\u7406\uff08NLP\uff09\u76f8\u5173<\/p>\n\n\n\n
- \n
- Word2Vector\uff1a\u5c06\u81ea\u7136\u8bed\u8a00\u8f6c\u6210\u8bcd\u5411\u91cf<\/li>\n\n\n\n
- \u8bed\u8a00\u6a21\u578b\uff1aRNN\u3001Transformer \uff0c\u7528\u4e8e\u5efa\u6a21\u81ea\u7136\u8bed\u8a00\u7684\u6982\u7387\u5206\u5e03<\/li>\n\n\n\n
- Transformer\uff1a\u73b0\u4ee3 NLP \u7684\u4e3b\u529b\u6a21\u578b\uff08\u5982 BERT\u3001GPT\uff09<\/li>\n\n\n\n
- \u5927\u8bed\u8a00\u6a21\u578b LLM\uff1a\u5fae\u8c03\u3001\u53c2\u6570\u5316\u5fae\u8c03\u3001\u63d0\u793a\u8bcd\u5de5\u7a0b\u3001RAG\u68c0\u7d22\u589e\u52a0\u751f\u6210<\/li>\n\n\n\n
- CNN\uff1a\u5bf9\u8bcd\u5411\u91cf\u5c42\u5c42\u5377\u79ef\uff0c\u63d0\u53d6\u7279\u5f81<\/li>\n<\/ul>\n\n\n\n
\u4e94\u3001\u751f\u6210\u5f0f\u6a21\u578b\uff08Generative Models\uff09<\/p>\n\n\n\n
- \n
- \u751f\u6210\u5f0f\u6a21\u578b\uff1a\u5b66\u4e60\u6570\u636e\u7684\u5206\u5e03\u4ee5\u751f\u6210\u65b0\u6837\u672c\uff0c\u4f8b\u5982\uff1a\n
- \n
- \u5404\u79cdGAN\uff08\u751f\u6210\u5bf9\u6297\u7f51\u7edc\uff09<\/li>\n\n\n\n
- VAE\uff08\u53d8\u5206\u81ea\u7f16\u7801\u5668\uff09<\/li>\n\n\n\n
- \u53bb\u566a\u6269\u6563\u6a21\u578b<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
\u516d\u3001\u5f3a\u5316\u5b66\u4e60\uff08Reinforcement Learning\uff09<\/p>\n\n\n\n
- \n
- \u5f3a\u5316\u5b66\u4e60 RL\uff1aQ-Learning\u53caDQN<\/li>\n<\/ul>\n\n\n\n
\u4e03\u3001\u673a\u5668\u89c6\u89c9<\/p>\n\n\n\n
- \n
- \u56fe\u7247\u5206\u5272\uff1a\u5377\u79ef+\u9006\u5377\u79ef<\/li>\n\n\n\n
- \u7269\u4f53\u8bc6\u522b=\u5212\u5206+\u5206\u7c7b\uff1b\u5212\u5206\uff1afast\/faster R-CNN<\/li>\n\n\n\n
- \u6587\u56fe\u4e92\u8f6c\uff1a\u89c6\u89c9\u8bed\u8a00\u6a21\u578bVLM<\/li>\n<\/ul>\n\n\n\n
\u516b\u3001\u7b54\u9898\u6a21\u677f<\/p>\n\n\n\n
\u672c\u7cfb\u7edf\u65e8\u5728\u89e3\u51b3\u3010\u4efb\u52a1\u63cf\u8ff0\uff0c\u4f8b\u5982\uff1a\u56fe\u50cf\u4e2d\u7684\u4eba\u8138\u8bc6\u522b\u3001\u6587\u672c\u60c5\u611f\u5206\u7c7b\u3001\u7528\u6237\u8d2d\u4e70\u884c\u4e3a\u9884\u6d4b\u3011\u95ee\u9898\u3002\u8be5\u95ee\u9898\u53ef\u4ee5\u89c6\u4e3a\u4e00\u4e2a\u3010\u5206\u7c7b \/ \u56de\u5f52 \/ \u751f\u6210 \/ \u5f3a\u5316\u5b66\u4e60\u3011\u4efb\u52a1\u3002<\/p>\n\n\n\n
- \n
- \u6570\u636e\u6536\u96c6\u4e0e\u9884\u5904\u7406
\u9996\u5148\u91c7\u96c6\u5305\u542b\u3010\u63cf\u8ff0\u6570\u636e\u6765\u6e90\uff0c\u4f8b\u5982\uff1a\u56fe\u7247\u3001\u6587\u672c\u3001\u4f20\u611f\u5668\u6570\u636e\u7b49\u3011\u7684\u6570\u636e\u96c6\uff0c\u5bf9\u6570\u636e\u8fdb\u884c\u6e05\u6d17\u3001\u7f3a\u5931\u503c\u5904\u7406\u3001\u5f52\u4e00\u5316\uff08\u6216\u5206\u8bcd\u3001\u7f16\u7801\uff09\u7b49\u9884\u5904\u7406\u64cd\u4f5c\uff0c\u4ee5\u4fbf\u6a21\u578b\u6709\u6548\u5b66\u4e60\u3002<\/li>\n\n\n\n - \u7279\u5f81\u5de5\u7a0b
\u63d0\u53d6\u5e76\u6784\u9020\u5173\u952e\u7279\u5f81\uff0c\u5982\u3010\u793a\u4f8b\u7279\u5f81\uff0c\u5982\uff1a\u56fe\u50cf\u7684\u8fb9\u7f18\u7279\u5f81\u3001\u6587\u672c\u7684TF-IDF\u5411\u91cf\u3001\u7528\u6237\u884c\u4e3a\u7edf\u8ba1\u7279\u5f81\u7b49\u3011\uff0c\u5fc5\u8981\u65f6\u8fdb\u884c\u964d\u7ef4\u4ee5\u63d0\u9ad8\u8bad\u7ec3\u6548\u7387\u3002<\/li>\n\n\n\n - \u6a21\u578b\u9009\u62e9
\u9009\u62e9\u9002\u7528\u4e8e\u672c\u4efb\u52a1\u7684\u6a21\u578b\uff1a\u5982\u4e3a\u5206\u7c7b\u4efb\u52a1\uff0c\u53ef\u9009\u62e9\u903b\u8f91\u56de\u5f52\u3001\u51b3\u7b56\u6811\u3001SVM\u3001MLP\u7b49\uff1b\u5982\u4e3a\u56de\u5f52\u4efb\u52a1\uff0c\u53ef\u9009\u7528\u7ebf\u6027\u56de\u5f52\u3001MLP\u3001SVR\uff1b\u5982\u4e3a\u751f\u6210\u4efb\u52a1\uff0c\u53ef\u9009\u7528\u751f\u6210\u5f0f\u6a21\u578b\uff08GAN\u3001VAE\uff09\u6216\u5927\u8bed\u8a00\u6a21\u578b\uff1b\u5982\u4e3a\u51b3\u7b56\u63a7\u5236\u4efb\u52a1\uff0c\u53ef\u4f7f\u7528\u5f3a\u5316\u5b66\u4e60\uff08\u5982Q-Learning\u3001DQN\u7b49\uff09\u3002<\/li>\n\n\n\n - \u8bad\u7ec3\u4e0e\u8bc4\u4f30
\u4f7f\u7528\u8bad\u7ec3\u96c6\u8fdb\u884c\u6a21\u578b\u8bad\u7ec3\uff0c\u91c7\u7528\u4ea4\u53c9\u9a8c\u8bc1\u9632\u6b62\u8fc7\u62df\u5408\uff0c\u5e76\u7528\u9a8c\u8bc1\u96c6\/\u6d4b\u8bd5\u96c6\u8bc4\u4f30\u6a21\u578b\u6027\u80fd\uff0c\u6307\u6807\u5305\u62ec\u51c6\u786e\u7387\u3001F1\u5206\u6570\u3001\u5747\u65b9\u8bef\u5dee\u6216\u7d2f\u8ba1\u5956\u52b1\u7b49\u3002<\/li>\n<\/ol>\n\n\n\nIntro<\/h2>\n\n\n\n
\u6cdb\u5316\u6027\u4e0e\u8fc7\u62df\u5408<\/strong><\/p>\n\n\n\n
\u5b66\u4e60\u7684\u6cdb\u5316\u6027\u95ee\u9898:\u6a21\u578b\u5e94\u8be5\u5b66\u4e60\u666e\u904d\u7684\u89c4\u5f8b\u8fd8\u662f\u8bb0\u4f4f\u7279\u5b9a\u7ec6\u8282<\/p>\n\n\n\n
![\"\"](\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\")
<\/div><\/figure>\n\n\n\n\u6b20\u62df\u5408\u2013\u56e0\u6a21\u578b\u4e0d\u591f\u590d\u6742\u65e0\u6cd5\u523b\u753b\u771f\u5b9e\u89c4\u5f8b\uff0c\u6a21\u578b\u5047\u8bbe\u53ef\u80fd\u4e0d\u6210\u7acb
\u8fc7\u62df\u5408\u2013\u56e0\u6a21\u578b\u8fc7\u4e8e\u590d\u6742\u5bfc\u81f4\u8bb0\u4f4f\u6570\u636e\u7684\u7ec6\u8282(\u5982\u968f\u673a\u566a\u58f0)\u800c\u4e0d\u662f\u6f5c\u5728\u7684\u89c4\u5f8b<\/p>\n\n\n\n<\/div><\/figure>\n\n\n\n\u907f\u514d\u8fc7\u62df\u5408\u7684\u65b9\u6cd5\uff1a<\/p>\n\n\n\n
- \n
- \u589e\u52a0\u8bad\u7ec3\u6570\u636e<\/li>\n\n\n\n
- \u6b63\u5219\u5316\uff08\u6a21\u578b\u8fc7\u4e8e\u590d\u6742\u65f6\u7ed9\u4e88\u60e9\u7f5a\uff09<\/li>\n\n\n\n
- \u6570\u636e\u5212\u5206&\u4ea4\u53c9\u9a8c\u8bc1\uff08\u8bad\u7ec3\u65f6\u4fdd\u7559\u90e8\u5206\u672a\u77e5\u6570\u636e\u7528\u4e8e\u6d4b\u8bd5\uff0c\u4ee5\u68c0\u9a8c\u6cdb\u5316\u80fd\u529b\uff09<\/li>\n\n\n\n
- \u65e9\u505c<\/li>\n\n\n\n
- \u5f15\u5165\u5148\u9a8c\u77e5\u8bc6\uff08\u5982\u8d1d\u53f6\u65af\u5148\u9a8c\uff09<\/li>\n<\/ul>\n\n\n\n
\u7ebf\u6027\u56de\u5f52<\/h2>\n\n\n\n
\u7528\u7ebf\u6027\u51fd\u6570\u62df\u5408\u6570\u636e\uff0c\u6839\u636e\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7ed9\u51fa\u7ed3\u679c\u3002<\/p>\n\n\n\n
\u7ebf\u6027\u51fd\u6570\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n\n
\u5bf9\u4e8e\u4e00\u4e2a\u8f93\u5165\u6837\u672cx\uff0c\u6a21\u578b\u8f93\u51fay\uff0c\u771f\u5b9e\u503cr\uff0c\u5219\u5c06\u5e73\u65b9\u8bef\u5dee\u5b9a\u4e49\u4e3a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u5bf9\u4e8e\u5b8c\u6574\u6570\u636e\u96c6D={(x(1)<\/sup>,r(1)<\/sup>),…,(x(n)<\/sup>,r(n)<\/sup>)}\u635f\u5931\u51fd\u6570\u5b9a\u4e49\u4e3a\u5747\u65b9\u8bef\u5deeMSE\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5\u4f18\u5316\u635f\u5931\u51fd\u6570<\/p>\n\n\n\n
\u4f18\u5316\u76ee\u6807\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u8fed\u4ee3\u6b65\u9aa4\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u5176\u4e2d<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u4f46\u662f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5\u6c42\u7ebf\u6027\u56de\u5f52\u5b9e\u9645\u4e0a\u8d70\u4e86\u5f2f\u8def\uff0c\u56e0\u4e3a\u7ebf\u6027\u56de\u5f52\u53ef\u4ee5\u7528\u6570\u5b66\u65b9\u6cd5\u5f97\u51fa\u6700\u4f18\u89e3\u3002\u6211\u4eec\u501f\u52a9\u77e9\u9635\u5f62\u5f0f\u7684\u7ebf\u6027\u56de\u5f52\u6765\u8bf4\u660e\u8fd9\u4e2a\u95ee\u9898\u3002\u4ee4\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u9884\u6d4b\u503c\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u68af\u5ea6\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u6700\u4f18\u53c2\u6570w*\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u5bf9\u5e94\u7684\u6700\u4f18\u7ebf\u6027\u51fd\u6570\u4e3a\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u6211\u4eec\u53ea\u9700\u7b97\u51faH\u5373\u53ef<\/p>\n\n\n\n
\u95ee\u9898\uff1aXT<\/sup>X\u53ef\u80fd\u4e0d\u53ef\u9006\uff0c\u5bfc\u81f4\u6211\u4eec\u8fd8\u662f\u53ea\u80fd\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5<\/p>\n\n\n\n
\u89e3\u51b3\uff1a\u4f7f\u7528\u6b63\u5219\u5316\uff0c\u5bf9\u635f\u5931\u51fd\u6570\u5f15\u5165\u60e9\u7f5a\u9879<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u65b0\u7684\u6700\u4f18\u89e3\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\nXT<\/sup>X + \u03bbI\u4e00\u5b9a\u662f\u6ee1\u79e9\u7684\uff0c\u6240\u4ee5\u4e00\u5b9a\u53ef\u9006<\/p>\n\n\n\n
\u51b3\u7b56\u6811<\/h2>\n\n\n\n
\u5206\u7c7b\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u53ef\u80fd\u9047\u5230\u4e0d\u7ebf\u6027\u53ef\u5206\u7684\u793a\u4f8b\uff0c\u6216\u662f\u5c5e\u6027\u503c\u4e0d\u662f\u6570\u5b57\uff0c\u4f46\u662f\u6cbf\u67d0\u4e9b\u7ef4\u5ea6\u5c40\u90e8\u7ebf\u6027\u53ef\u5206<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u51b3\u7b56\u6811\u7684\u57fa\u672c\u601d\u60f3\uff1a\u5206\u800c\u6cbb\u4e4b
\u5728\u5c0f\u8303\u56f4\u5185\u6309\u7ebf\u6027\u5206\u7c7b<\/p>\n\n\n\n<\/div><\/figure>\n\n\n\n\u6784\u9020\u51b3\u7b56\u6811\u7684\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n
- \n
- \u6784\u9020\u4e00\u4e2a\u6839\u8282\u70b9\uff0c\u5305\u542b\u6574\u4e2a\u6570\u636e\u96c6<\/li>\n\n\n\n
- \u9009\u62e9\u4e00\u4e2a\u6700\u5408\u9002\u7684\u5c5e\u6027<\/li>\n\n\n\n
- \u6839\u636e\u9009\u62e9\u5c5e\u6027\u7684\u4e0d\u540c\u53d6\u503c\uff0c\u5c06\u5f53\u524d\u8282\u70b9\u7684\u6837\u672c\u5212\u5206\u6210\u82e5\u5e72\u5b50\u96c6<\/li>\n\n\n\n
- \u5bf9\u6bcf\u4e2a\u5212\u5206\u540e\u7684\u5b50\u96c6\u521b\u5efa\u4e00\u4e2a\u5b69\u5b50\u8282\u70b9\uff0c\u5e76\u5c06\u5b50\u96c6\u7684\u6570\u636e\u4f20\u7ed9\u8be5\u5b69\u5b50\u8282\u70b9<\/li>\n\n\n\n
- \u9012\u5f52\u91cd\u590d2~4\u76f4\u5230\u6ee1\u8db3\u505c\u6b62\u6761\u4ef6<\/li>\n<\/ul>\n\n\n\n
\u5173\u952e\u95ee\u9898\uff1a<\/p>\n\n\n\n
\u5982\u4f55\u9ad8\u6548\u7387\u7684\u6784\u5efa\u51b3\u7b56\u6811?
\u2014\u2014\u9009\u62e9\u6bcf\u4e2a\u5c5e\u6027X\u7684\u65f6\u5019\uff0c\u5c3d\u53ef\u80fd\u6700\u5927\u5316\u6807\u7b7eY\u7684\u7eaf\u5ea6<\/p>\n\n\n\n\u5982\u4f55\u9009\u62e9\u5c5e\u6027\u4ee5\u6700\u5927\u5316\u6807\u7b7e\u7684\u7eaf\u5ea6?
\u2014\u2014\u9009\u62e9X\u4ee5\u6700\u5927\u5316\u4fe1\u606f\u589e\u76ca\u3001Gini\u7cfb\u6570\u7b49<\/p>\n\n\n\nID3\u7b97\u6cd5\u5373\u6839\u636e\u4fe1\u606f\u589e\u76ca\u8fdb\u884c\u5212\u5206<\/p>\n\n\n\n
\u5b9a\u4e49\u71b5\u2014\u2014\u523b\u753b\u4e00\u4e2a\u6570\u636e\u96c6\u5408\u7684\u4e0d\u7eaf\u51c0\u5ea6
\u5047\u8bbe\u6570\u636e\u96c6D\u4e2d\u6709K\u79cd\u4e0d\u540c\u7684\u5206\u7c7b\uff0c\u5b9a\u4e49\u4e3a{C1<\/sub>,…,Ck<\/sub>}\uff0c\u5219\uff1a<\/p>\n\n\n\n<\/div><\/p>\n\n\n\n\u5047\u8bbe\u6211\u4eec\u9009\u5b9a\u5c5e\u6027A\u4f5c\u4e3a\u4e00\u4e2a\u5206\u7c7b\uff0c\u5c5e\u6027A\u5c06D\u5206\u6210n\u7c7b\uff0c\u5b9a\u4e49\u4e3a{D1<\/sub>,…,Dk<\/sub>}\uff0c\u5219\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u4fe1\u606f\u589e\u76ca\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u5047\u5b9a\u6211\u4eec\u5e0c\u671b\u5c0610\u4e2a\u6837\u672c\u5206\u7c7b\uff0c\u76ee\u6807\u4e3a\u533a\u5206\u9ad8\/\u4f4e\u6536\u5165\uff0855\u5f00\uff09\uff1b\u6211\u4eec\u9996\u5148\u6309\u5b66\u5386\u8fdb\u884c\u5206\u7c7b\uff08\u8282\u70b9D\uff09\uff0c\u5176\u4e2d\u9ad8\u5b66\u5386\u4e2d\u6536\u51654\u9ad82\u4f4e\uff08\u5b50\u8282\u70b9D1<\/sub>\uff09\uff0c\u4f4e\u5b66\u5386\u4e2d\u6536\u51651\u9ad83\u4f4e\uff08\u5b50\u8282\u70b9D2<\/sub>\uff09\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u7b97\u6cd5\u4f18\u7f3a\u70b9\uff1a<\/p>\n\n\n\n
\u4f18\u70b9\uff1a<\/p>\n\n\n\n
- \n
- \u6613\u7406\u89e3, \u53ef\u89e3\u91ca\u6027, \u4fbf\u4e8e\u53ef\u89c6\u5316\u5206\u6790<\/li>\n\n\n\n
- \u6570\u636e\u9884\u5904\u7406\u8981\u6c42\u4f4e<\/li>\n\n\n\n
- \u53ef\u4ee5\u8f7b\u6613\u5904\u7406\u975e\u7ebf\u6027\u8fb9\u754c<\/li>\n\n\n\n
- \u6570\u636e\u9a71\u52a8\uff0c\u53ef\u4ee5\u4ee5\u4efb\u610f\u7cbe\u5ea6\u62df\u5408\u8bad\u7ec3\u96c6<\/li>\n<\/ul>\n\n\n\n
\u7f3a\u70b9\uff1a\u5bb9\u6613\u8fc7\u62df\u5408\uff08\u566a\u58f0\u6837\u4f8b\u4e5f\u4f1a\u88ab\u5b66\u4e60\uff09<\/p>\n\n\n\n
\u89e3\u51b3\uff1a<\/p>\n\n\n\n
\u968f\u673a\u68ee\u6797\uff1a\u5c06\u6570\u636e\u968f\u673a\u5212\u5206\u5b50\u96c6\uff0c\u5404\u81ea\u6784\u5efa\u51b3\u7b56\u6811\uff0c\u6309\u591a\u4e2a\u51b3\u7b56\u6811\u7684\u7ed3\u679c\u6295\u7968\u51b3\u5b9a\u3002<\/p>\n\n\n\n
\u968f\u673a\u68ee\u6797\u7684\u4f18\u70b9\uff1a<\/p>\n\n\n\n
- \n
- \u5f80\u5f80\u6bd4\u51b3\u7b56\u6811\u66f4\u51c6\u786e<\/li>\n\n\n\n
- \u8bad\u7ec3\u901f\u5ea6\u5feb, \u5bb9\u6613\u5e76\u884c\u5316 (\u8bad\u7ec3\u65f6\u6811\u4e0e\u6811\u4e4b\u95f4\u662f\u76f8\u4e92\u72ec\u7acb\u7684)<\/li>\n\n\n\n
- \u53ef\u4ee5\u5904\u7406\u9ad8\u7ef4(feature\u5f88\u591a)\u6570\u636e\uff0c\u5e76\u4e14\u4e0d\u7528\u505a\u7279\u5f81\u9009\u62e9 (\u56e0\u4e3a\u7279\u5f81\u5b50\u96c6\u662f\u968f\u673a\u9009\u62e9\u7684)<\/li>\n\n\n\n
- \u53ef\u4ee5\u5904\u7406\u7f3a\u5931\u5c5e\u6027<\/li>\n\n\n\n
- \u7ed3\u679c\u6613\u89e3\u91ca (i.e.,\u5728\u8bad\u7ec3\u5b8c\u540e\uff0c\u80fd\u591f\u7ed9\u51fa\u54ea\u4e9bfeature\u6bd4\u8f83\u91cd\u8981)<\/li>\n\n\n\n
- \u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u80fd\u591f\u68c0\u6d4b\u5230feature\u95f4\u7684\u4e92\u76f8\u5f71\u54cd<\/li>\n\n\n\n
- \u5bf9\u4e8e\u4e0d\u5e73\u8861\u7684\u6570\u636e\u96c6\u6765\u8bf4\uff0c\u5b83\u53ef\u4ee5\u5e73\u8861\u8bef\u5dee<\/li>\n<\/ul>\n\n\n\n
\u8d1d\u53f6\u65af\u5206\u7c7b<\/h2>\n\n\n\n
\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u4e0d\u540c\u7c7b\u578b\u7684\u6570\u636e\u4ea4\u878d\u5728\u4e00\u8d77\uff0c\u51b3\u7b56\u6811\u7b97\u6cd5\u5c31\u65e0\u6cd5\u51c6\u786e\u533a\u5206<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u6211\u4eec\u901a\u8fc7\u8ba1\u7b97\u67d0\u4e2a\u4f4d\u7f6e\u7684\u70b9\u5c5e\u4e8e\u67d0\u4e00\u7c7b\u7684\u6982\u7387\uff0c\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898<\/p>\n\n\n\n
\u8d1d\u53f6\u65af\u516c\u5f0f\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\nP(Ci<\/sub>)\u5148\u9a8c\u6982\u7387\uff1a\u5728\u6ca1\u6709\u89c2\u5bdf\u5230\u6570\u636e\u4e4b\u524d\uff0c\u6211\u4eec\u5bf9\u67d0\u4e2a\u4e8b\u4ef6\uff08\u5982\u67d0\u4e2a\u7c7b\u522b\uff09\u7684\u539f\u59cb\u4f30\u8ba1\u3002\u8868\u793a\u6211\u4eec\u5728\u6ca1\u6709\u4efb\u4f55\u7279\u5f81\u4fe1\u606f\u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u4e2a\u6837\u672c\u5c5e\u4e8e\u7c7b\u522bCi<\/sub>\u7684\u53ef\u80fd\u6027\u3002
p(x | Ci<\/sub>)\u4f3c\u7136\uff08likelihood\uff09\uff1a\u5728\u7c7b\u522b\u4e3a Ci<\/sub> \u7684\u524d\u63d0\u4e0b\uff0c\u89c2\u5bdf\u5230\u7279\u5f81 x \u7684\u6982\u7387\uff1b
p(x)\u8bc1\u636e\uff08evidence\uff09\uff1a\u662f\u6240\u6709\u7c7b\u522b\u4e0b\u751f\u6210\u7279\u5f81 x \u7684\u603b\u6982\u7387\uff0c\u7528\u4e8e\u5f52\u4e00\u5316\u3002
P(Ci<\/sub> | x)\u540e\u9a8c\u6982\u7387\uff1a\u8868\u793a\u5728\u89c2\u5bdf\u5230\u7279\u5f81 x \u540e\uff0c\u6837\u672c\u5c5e\u4e8e\u7c7b\u522b Ci<\/sub>\u200b \u7684\u6982\u7387<\/p>\n\n\n\n\u5728\u590d\u6742\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u4e0d\u53ea\u8003\u8651\u4e00\u4e2a\u7279\u5f81x\uff0c\u56e0\u6b64\u4e0a\u5f0f\u4f1a\u53d8\u4e3a\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u7531\u4e8e\u6211\u4eec\u6700\u7ec8\u53ea\u5173\u6ce8\u6982\u7387\u7684\u76f8\u5bf9\u5927\u5c0f\uff0c\u800c\u5206\u6bcd\uff08evidence\uff09\u662f\u7edf\u4e00\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u8ba1\u7b97\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u72ec\u7acb\u6027\u5047\u8bbe\uff08\u6734\u7d20\u8d1d\u53f6\u65af\u5047\u8bbe\uff09\uff1a\u5982\u679c\u6211\u4eec\u5047\u8bbe\u5404\u4e2ax\u95f4\u662f\u72ec\u7acb\u7684\uff0c\u5219\u4e0a\u9762\u7684\u7ea6\u7b49\u4e8e\u662f\u6210\u7acb\u7684<\/p>\n\n\n\n
\u8d1d\u53f6\u65af\u5206\u7c7b\u7684\u8bad\u7ec3\u8fc7\u7a0b\u4e5f\u5c31\u662f\u8ba1\u6570\uff0c\u7edf\u8ba1\u51fa\u6240\u6709\u7684P(xj<\/sub> | Ci<\/sub>)\uff0c\u6709\u65f6\u53ef\u80fd\u51fa\u73b0\u503c\u4e3a0\u7684\u60c5\u51b5\uff0c\u53ef\u4ee5\u901a\u8fc7\u865a\u62df\u8ba1\u6570\u7684\u65b9\u5f0f\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u4f18\u70b9\uff1a<\/p>\n\n\n\n
- \n
- \u8bad\u7ec3\u3001\u6d4b\u8bd5\u8fc7\u7a0b\u901f\u5ea6\u5feb<\/li>\n\n\n\n
- \u8868\u73b0\u597d\uff1a\u5f53\u72ec\u7acb\u6027\u5047\u8bbe\u6210\u7acb\u65f6\uff0c\u6548\u679c\u597d\uff1b\u9762\u5bf9\u591a\u5206\u7c7b\u95ee\u9898\u4e5f\u8868\u73b0\u826f\u597d<\/li>\n\n\n\n
- \u6613\u4e8e\u5728\u6570\u636e\u96c6\u66f4\u65b0\u65f6\u8fdb\u884c\u8bad\u7ec3\uff0c\u7b97\u6cd5\u6613\u7ef4\u62a4<\/li>\n<\/ul>\n\n\n\n
\u7f3a\u70b9\uff1a<\/p>\n\n\n\n
- \n
- \u4f9d\u8d56\u4e8e\u72ec\u7acb\u6027\u5047\u8bbe<\/li>\n\n\n\n
- \u5bb9\u6613\u6b20\u62df\u5408<\/li>\n<\/ul>\n\n\n\n
K-\u8fd1\u90bb KNN<\/h2>\n\n\n\n
\u57fa\u672c\u601d\u60f3\uff1a\u6839\u636e\u8ddd\u79bb\u81ea\u5df1\u6700\u8fd1\u7684\u51e0\u4e2a\u70b9\u7684\u6240\u5c5e\u7c7b\u522b\u8fdb\u884c\u6295\u7968<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u8ddd\u79bb\u6307\u6807\u7684\u9009\u53d6\uff1a<\/p>\n\n\n\n
- \n
- \u6b27\u6c0f\u8ddd\u79bb\uff08\u53d7\u7ef4\u5ea6\u5f71\u54cd\u8f83\u5927\uff09<\/li>\n\n\n\n
- \u66fc\u54c8\u987f\u8ddd\u79bb<\/li>\n\n\n\n
- \u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb<\/li>\n<\/ul>\n\n\n\n
\u7531\u4e8e\u5404\u4e2a\u5c5e\u6027\u7684\u5c3a\u5ea6\u4e0d\u4e00\u5b9a\u4e00\u81f4\uff0c\u56e0\u6b64\u9700\u8981\u5bf9\u6bcf\u4e2a\u5c5e\u6027\u5206\u522b\u8fdb\u884c\u5f52\u4e00\u5316<\/p>\n\n\n\n
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K\u7684\u9009\u53d6\uff1a<\/p>\n\n\n\n
\u7ef4\u8bfa\u56fe\uff1a<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\nk\u8d8a\u5c0f\uff1a\u66f4\u80fd\u53cd\u6620\u5c40\u90e8\u7ec6\u8282\uff0c\u4f46\u4f1a\u5bfc\u81f4\u8fc7\u62df\u5408
k\u8d8a\u5927\uff1a\u8fb9\u754c\u66f4\u52a0\u5e73\u6ed1\uff0c\u4e5f\u53ef\u80fd\u5bfc\u81f4\u6b20\u62df\u5408<\/p>\n\n\n\n\u4f18\u70b9\uff1a<\/p>\n\n\n\n
- \n
- \u6613\u4e8e\u7406\u89e3\u3001\u89e3\u91ca\u548c\u5b9e\u73b0<\/li>\n\n\n\n
- \u8bad\u7ec3\u96be\u5ea6\u4f4e<\/li>\n\n\n\n
- \u53ef\u4ee5\u65e0\u7f1d\u6dfb\u52a0\u65b0\u6570\u636e\uff0c\u800c\u4e0d\u4f1a\u5f71\u54cd\u6a21\u578b\u7684\u51c6\u786e\u6027<\/li>\n<\/ul>\n\n\n\n
\u7f3a\u70b9\uff1a<\/p>\n\n\n\n
- \n
- \u4e0d\u9002\u7528\u4e8e\u5927\u578b\u6570\u636e\u96c6\uff08\u8ba1\u7b97\u8ddd\u79bb\u7684\u8ba1\u7b97\u6210\u672c\u5f88\u9ad8\uff09<\/li>\n\n\n\n
- \u6781\u6613\u53d7\u5230\u7ef4\u5ea6\u7684\u5f71\u54cd<\/li>\n\n\n\n
- \u9700\u8981\u5927\u91cf\u5b58\u50a8<\/li>\n\n\n\n
- \u9700\u8981\u6570\u636e\u5f52\u4e00\u5316<\/li>\n<\/ul>\n\n\n\n
\u903b\u8f91\u56de\u5f52LR<\/h2>\n\n\n\n
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\u611f\u77e5\u673a\u7684\u7ed3\u6784\u975e\u5e38\u7b80\u5355\uff0c\u5176\u8f93\u51fag(x)\u53ea\u6709{1,0}\uff0c\u6839\u636e\u5224\u522b\u51fd\u6570\u7684\u7b26\u53f7\u51b3\u5b9a<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u8bad\u7ec3\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n
\u89c4\u5b9a\u6570\u636e\u96c6D={(x(1)<\/sup>,r(1)<\/sup>),...,x(d)<\/sup>r(d)<\/sup>};\nfor (x(l)<\/sup>,r(l)<\/sup>) in D:\n| if r(l)<\/sup>g(x(l)<\/sup>)\u22640:\uff08\u9884\u6d4b\u4e0e\u5b9e\u9645\u4e0d\u4e00\u81f4\uff09\n| | w=w+\u03b7r(l)<\/sup>x(l)<\/sup>\uff08\u5c06\u8d85\u5e73\u9762\u5411\u88ab\u9519\u8bef\u5206\u7c7b\u7684\u70b9\u79fb\u52a8\uff0c\u03b7\u4e3a\u5b66\u4e60\u7387\uff09\n\u91cd\u590d\u4e0a\u8ff0\u8fc7\u7a0b\uff0c\u76f4\u81f3\u5168\u90e8\u6570\u636e\u96c6\u90fd\u88ab\u6b63\u786e\u5206\u7c7b<\/code><\/pre>\n\n\n\n\u611f\u77e5\u673a\u7684\u95ee\u9898\uff1a<\/p>\n\n\n\n
\u8f93\u51fa\u53ea\u67090\u548c1\uff0c\u8fc7\u4e8e\u751f\u786c\uff0c\u96be\u4ee5\u4f18\u5316<\/p>\n\n\n\n
\u4f7f\u7528sigmoid<\/strong><\/p>\n\n\n\n
\u6211\u4eec\u9996\u5148\u5b9a\u4e49y\u4e3a\u6570\u636e\u70b9x\u5c5e\u4e8e\u7c7b\u522bC1<\/sub>\u7684\u6982\u7387\uff0c\u76f8\u5e94\u7684\uff0c\u5c5e\u4e8eC2<\/sub>\u7684\u6982\u7387\u5c31\u662f1-y\uff0c\u7136\u540e\u6839\u636e<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u662f\u5426\u5927\u4e8e\u96f6\uff0c\u6765\u5224\u65ad\u5e94\u8be5\u5c5e\u4e8e\u54ea\u4e00\u7c7b<\/p>\n\n\n\n
\u5982\u679c\u6570\u636e\u6ee1\u8db3\u6b63\u6001\u5206\u5e03\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a\uff08\u63a8\u5bfc\u7701\u7565\uff09<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n<\/div><\/figure>\n\n\n\n\u6211\u4eec\u5c06\u635f\u5931\u51fd\u6570\u5b9a\u4e49\u4e3a\uff0c\u6216\u79f0\u4e3a\u4ea4\u53c9\u71b5\u635f\u5931CE\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u7b49\u4ef7\u4e8e\u6700\u5927\u5316\u4f3c\u7136\uff08likelihood\uff09<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u8bad\u7ec3\u8fc7\u7a0b\uff1a\u901a\u8fc7\u68af\u5ea6\u4e0b\u964d\u6cd5\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u5bf9\u4e8e\u6574\u4e2a\u6570\u636e\u96c6D\u800c\u8a00\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u6211\u4eec\u5b9a\u4e49<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u5219\u6709<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u591a\u5206\u7c7b\u95ee\u9898<\/strong><\/p>\n\n\n\n
\u6709\u65f6\u6211\u4eec\u9700\u8981\u9884\u6d4b\u591a\u4e2a\u7c7b\uff0c\u5982\u679c\u6211\u4eec\u60f3\u7edf\u4e00\u5904\u7406\u6240\u6709\u7c7b\u800c\u4e0d\u5fc5\u9009\u62e9\u53c2\u8003\u7c7b\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 softmax \u51fd\u6570\u6765\u4ee3\u66ff\u540e\u9a8c\u7c7b\u6982\u7387y<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u5176\u4e2d<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n<\/div><\/figure>\n\n\n\n<\/div><\/figure>\n\n\n\n\u4ea4\u53c9\u71b5\u635f\u5931\u51fd\u6570\u53ca\u68af\u5ea6\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u652f\u6301\u5411\u91cf\u673aSVM<\/h2>\n\n\n\n
\u5148\u524d\u7684\u5206\u7c7b\u65b9\u6cd5\u4e2d\uff0c\u6211\u4eec\u7684\u76ee\u6807\u53ea\u662f\u5f97\u51fa\u4e00\u4e2a\u6b63\u786e\u7684\u7ed3\u679c\uff0c\u7ed3\u679c\u548c\u7ed3\u679c\u95f4\u7684\u4f18\u52a3\u600e\u4e48\u8bc4\u4ef7\uff1f<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u6211\u4eec\u5e0c\u671b\u5206\u5272\u7ebf\u8ddd\u4e24\u8fb9\u7684\u95f4\u9694\u6700\u5927\uff0c\u6211\u4eec\u5b9a\u4e49\u4e24\u6761\u865a\u7ebf\uff0c\u95f4\u9694\u6700\u5927\u65f6\u4e24\u6761\u865a\u7ebf\u4f1a\u521a\u597d\u5361\u5728\u4e24\u4e2a\u7c7b\u7684\u8fb9\u754c\u4e0b<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u95f4\u9694:<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u6700\u5927\u5316margin\u7b49\u4ef7\u4e8e\u6700\u5c0f\u53160.5*||w||<\/p>\n\n\n\n
\u5199\u6210\u4e00\u4e2a\u4f18\u5316\u95ee\u9898\u7684\u5f62\u5f0f\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u56e0\u4e3ay\u7684\u53d6\u503c\u53ea\u6709\u00b11\uff0c\u6240\u4ee5\u4fdd\u8bc1\u4e86\u6240\u6709\u70b9\u5728\u4e24\u6761\u865a\u7ebf\u5916<\/p>\n\n\n\n
\u6211\u4eec\u8fd8\u662f\u91c7\u7528\u611f\u77e5\u673a\u4f5c\u4e3a\u6a21\u578b\uff1a<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n\n
\u6211\u4eec\u9996\u5148\u5e0c\u671by(wT<\/sup>x+w0<\/sub>)>1\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4f18\u5316\u5176\u4e2d\u6700\u5c0f\u7684\u503c\uff0c\u76f4\u81f3\u5176\u5927\u4e8e1
\u5f53\u6240\u6709\u70b9\u90fd\u5728\u865a\u7ebf\u4ee5\u5916\uff0c\u6211\u4eec\u5f00\u59cb\u8c03\u6574w\u4f7f\u865a\u7ebf\u5361\u5728\u8fb9\u754c\u4e0a\u3002<\/p>\n\n\n\n<\/div><\/p>\n\n\n\n\u53ef\u4ee5\u5f97\u51fa\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u591a\u5c42\u611f\u77e5\u673aMLP<\/h2>\n\n\n\n
\u6839\u636e\u4eba\u7c7b\u7684\u795e\u7ecf\u7ed3\u6784\uff0c\u79d1\u5b66\u5bb6\u6784\u5efa\u51fa\u4eba\u5de5\u795e\u7ecf\u7f51\u7edcANN\u3002\u6211\u4eec\u7c7b\u6bd4\u4eba\u7c7b\u7684\u795e\u7ecf\u5143\uff0c\u901a\u8fc7\u8ba1\u7b97\u673a\u6a21\u62df\u51fa\u795e\u7ecf\u5143\u7684\u529f\u80fd\uff1a<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u5982\u679c\u5176\u4e2d\u7684\u6fc0\u6d3b\u51fd\u6570\u03c3 ()\u662fsign()\u7b26\u53f7\u51fd\u6570\u7684\u8bdd\uff0c\u8fd9\u4e2a\u795e\u7ecf\u5143\u5c31\u662f\u4e4b\u524d\u5b66\u8fc7\u7684\u611f\u77e5\u673a\u3002<\/p>\n\n\n\n
\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u611f\u77e5\u673a\u6765\u6a21\u62df\u4e0e\u6216\u8fd0\u7b97\uff1a<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u540c\u65f6\uff0c\u5f53\u6211\u4eec\u6dfb\u52a0\u4e00\u4e2a\u201c\u9690\u85cf\u5c42\u201d\uff0c\u6211\u4eec\u5c31\u80fd\u6a21\u62df\u4e00\u4e9b\u975e\u7ebf\u6027\u64cd\u4f5c\uff0c\u6bd4\u5982\u5f02\u6216<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u9664\u4e86\u7b26\u53f7\u51fd\u6570\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u9009\u62e9\u5176\u4ed6\u7684\u975e\u7ebf\u6027\u7684\u6fc0\u6d3b\u51fd\u6570<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u7b80\u5355\u7684\u591a\u5c42\u611f\u77e5\u673a\u7ed3\u6784\uff1a<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u591a\u5c42\u611f\u77e5\u673a\u5728\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5\u8fdb\u884c\u53c2\u6570\u66f4\u65b0\u65f6\u91c7\u7528\u7684\u7b56\u7565\u53eb\u8bef\u5dee\u53cd\u5411\u4f20\u64ad<\/strong><\/p>\n\n\n\n
\u5047\u5b9a\u6211\u4eec\u73b0\u5728\u6709\u5982\u4e0b\u795e\u7ecf\u7f51\u7edc\uff1a<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u5e76\u5bf9\u6bcf\u4e2a\u795e\u7ecf\u5143\uff08\u4f4d\u4e8eL\u5c42\u7b2cj\u4e2a\uff09\u505a\u5982\u4e0b\u62bd\u8c61\uff1a<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6240\u6709\u7684<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u6211\u4eec\u5148\u5173\u5fc3\u8f93\u51fa\u5c42\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6240\u6709\u7684<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u5bb9\u6613\u5f97\u5230<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u6211\u4eec\u518d\u8003\u8651\u4f4d\u4e8eL\u5c42\u7684\u7b2cj\u4e2a\u795e\u7ecf\u5143
\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6240\u6709\u7684<\/p>\n\n\n\n<\/div><\/p>\n\n\n\n\u53ef\u4ee5\u5f97\u5230<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u73b0\u5728\uff0c\u5982\u679c\u80fd\u8ba1\u7b97\u51fa\u2202L\/\u2202x\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u80fd\u8ba1\u7b97\u51fa\u6211\u4eec\u60f3\u5f97\u5230\u7684\u6240\u6709\u6570\u636e\u3002<\/p>\n\n\n\n
\u6211\u4eec\u8003\u8651\u8f93\u51fa\u5c42\u795e\u7ecf\u5143
\u6211\u4eec\u9700\u8981\u8ba1\u7b97\uff1a<\/p>\n\n\n\n<\/div><\/p>\n\n\n\n\u6ce8\u610f\u5230<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u6ce8\u610f\uff0c\u5982\u679c\u662f\u4e2d\u95f4\u5c42\uff0c\u5219\u6700\u540e\u662f\u6c42\u548c\u7684\u5f62\u5f0f\uff0c\u56e0\u4e3ax\u88ab\u4f7f\u7528n\u6b21<\/p>\n\n\n\n
\u4e0a\u9762\u7684\u63a8\u5bfc\u975e\u5e38\u590d\u6742\uff0c\u4f46\u6211\u4eec\u53ea\u9700\u8981\u77e5\u9053\uff1a<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u6211\u4eec\u5c06\u7b2c\u4e00\u90e8\u5206\u79f0\u4e3a\u8f93\u5165\uff0c\u540e\u4e00\u90e8\u5206\u79f0\u4e3a\u8bef\u5dee\uff1b\u8f93\u5165\u662fwi,j<\/sub>L<\/sup>\u4e0a\u5bf9\u5e94\u7684xi<\/sub>L<\/sup>\uff0c\u800c\u8bef\u5dee\u03b4j<\/sub>L<\/sup>\u53ef\u4ee5\u6839\u636e\u4e0b\u9762\u7684\u5f0f\u5b50\u9012\u5f52\u8ba1\u7b97<\/p>\n\n\n\n
<\/div><\/p>\n\n\n\n\u5728\u9012\u5f52\u8ba1\u7b97\u68af\u5ea6\u7684\u65f6\u5019\u4f1a\u7ecf\u5e38\u91cd\u590d\uff0c\u53ef\u4ee5\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u4f18\u5316<\/p>\n\n\n\n
\u6df1\u5ea6\u5b66\u4e60\u7684\u7279\u70b9\uff1a<\/p>\n\n\n\n
- \n
- \u81ea\u52a8\u5b66\u4e60\u6570\u636e\u8868\u5f81<\/li>\n\n\n\n
- \u5b66\u4e60\u5c42\u6b21\u5316\u8868\u5f81<\/li>\n\n\n\n
- \u7aef\u5230\u7aef\u5b66\u4e60<\/li>\n<\/ul>\n\n\n\n
\u8bed\u8a00\u6a21\u578b<\/h2>\n\n\n\n
Word to Vector<\/strong><\/p>\n\n\n\n
\u5355\u7eaf\u4f7f\u7528ASCII\u7801\uff0c\u673a\u5668\u65e0\u6cd5\u7406\u89e3\u6570\u5b57\u7684\u610f\u4e49\uff0c\u65e0\u6cd5\u7406\u89e3\u5355\u8bcd\u4e0e\u5355\u8bcd\u95f4\u7684\u5173\u7cfb<\/p>\n\n\n\n
one-hot\u7f16\u7801\uff1a\u6bcf\u4e2a\u5355\u8bcd\u5360\u6709\u5411\u91cf\u4e2d\u7684\u4e00\u4f4d\uff0c\u8fd9\u4e00\u4f4d\u4e3a1\uff0c\u5176\u4f59\u4e3a0\uff1b\u975e\u5e38\u5360\u7528\u7a7a\u95f4\uff0c\u5e76\u4e14\u4e0d\u80fd\u53cd\u6620\u8bcd\u95f4\u5173\u7cfb<\/p>\n\n\n\n
\u6211\u4eec\u5e0c\u671b\u4f7f\u7528\u4e00\u79cd\u538b\u7f29\u7684\u5411\u91cf\uff0c\u5e76\u4e14\u80fd\u591f\u53cd\u6620\u8bcd\u95f4\u5173\u7cfb<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u5982\u4f55\u83b7\u5f97\u5355\u8bcd\u7f16\u7801\uff1a<\/p>\n\n\n\n
\u57fa\u672c\u60f3\u6cd5\uff0c\u5982\u679c\u672a\u77e5\u5355\u8bcd\u548c\u5df2\u77e5\u5355\u8bcd\u5177\u6709\u76f8\u4f3c\u7684\u4e0a\u4e0b\u6587\uff0c\u90a3\u4e48\u8ba4\u4e3a\u8fd9\u4e2a\u672a\u77e5\u5355\u8bcd\u548c\u5df2\u77e5\u5355\u8bcd\u76f8\u4f3c<\/p>\n\n\n\n
\u7b97\u6cd5\uff1a<\/p>\n\n\n\n
- \n
- \u51c6\u5907\u4e00\u4e2a\u5927\u89c4\u6a21\u7684\u6587\u672c\u5e93<\/li>\n\n\n\n
- \u7ed9\u6bcf\u4e2a\u5355\u8bcd\u5206\u914d\u4e00\u4e2a\u8bcd\u5411\u91cf<\/li>\n\n\n\n
- \u904d\u5386\u6587\u672c\uff0c\u83b7\u53d6\u5355\u8bcdw\u53ca\u5176\u4e24\u8fb9\u7684\u8bcdc<\/li>\n\n\n\n
- \u6839\u636e\u5411\u91cf\u76f8\u4f3c\u5ea6\u8ba1\u7b97\u7ed9\u5b9ac\u540e\u4e2d\u95f4\u4e3aw\u7684\u6982\u7387<\/li>\n\n\n\n
- \u66f4\u65b0\u8bcd\u5411\u91cf\uff0c\u76f4\u81f3\u6982\u7387\u6700\u5927\u5316<\/li>\n<\/ul>\n\n\n\n
\u73b0\u5728\u6211\u4eec\u5f97\u5230\u4e86\u8bcd\u5411\u91cf\uff0c\u6211\u4eec\u5e94\u8be5\u600e\u4e48\u8ba9\u8ba1\u7b97\u673a\u8f93\u51fa\u53e5\u5b50\uff1f<\/p>\n\n\n\n
\u5b9a\u4e49\u4e00\u53e5\u8bddx\u7531w1<\/sub>,..,wn<\/sub>\u6784\u6210\u7684\u6982\u7387\u4e3ap(x)=p(w1<\/sub>,w2<\/sub>,…,wn<\/sub>)\uff0c\u6211\u4eec\u5982\u4f55\u8ba1\u7b97\u8fd9\u4e2a\u6982\u7387\uff1f<\/p>\n\n\n\n
\u57fa\u4e8e\u6761\u4ef6\u6982\u7387\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\uff1ap(w1<\/sub>,w2<\/sub>,…,wn<\/sub>)=p(w1<\/sub>)p(w2<\/sub>|w1<\/sub>)…p(wn<\/sub>|w1<\/sub>,w2<\/sub>…)\uff0c\u800c\u5355\u8bcd\u4e00\u822c\u53ea\u548c\u76f8\u8fd1\u7684\u5355\u8bcd\u6709\u5173\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5316\u7b80\u6210\u53ea\u8003\u8651\u524dk\u4e2a\u5355\u8bcd<\/p>\n\n\n\n
\u90a3\u4e48\u6211\u4eec\u5982\u4f55\u83b7\u5f97\u8fd9\u4e2a\u6761\u4ef6\u6982\u7387\uff1f
\u2014\u2014naive\u7684\u60f3\u6cd5\u662f\u8ba1\u6570\uff0c\u4f46\u662f\u4e00\u4e9b\u7ec6\u5fae\u7684\u53d8\u5316\u5c31\u4f1a\u5bfc\u81f4\u8ba1\u6570\u4e0d\u51c6\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8bcd\u5411\u91cf\u4ee3\u66ff\u5355\u8bcd\u3002\u8bcd\u5411\u91cf\u53ef\u4ee5\u53cd\u6620\u76f8\u4f3c\u5ea6\uff0c\u4f46\u662f\u8fd9\u79cd\u65b9\u5f0f\u8fd8\u4e0d\u80fd\u53cd\u6620\u8bcd\u4e0e\u8bcd\u95f4\u7684\u987a\u5e8f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06\u591a\u4e2a\u8bcd\u5411\u91cf\u8fdb\u884c\u62fc\u63a5\u3002\u8fd9\u79cd\u65b9\u5f0f\u7684\u95ee\u9898\u662f\u8f93\u5165\u7684\u957f\u5ea6\u4e0d\u53ef\u53d8\uff0c\u5e76\u4e14\u6807\u70b9\u7b26\u53f7\u7b49\u4f1a\u5bf9\u5176\u4ea7\u751f\u5f88\u5927\u5f71\u54cd\u3002<\/p>\n\n\n\n\u6211\u4eec\u7684\u8981\u6c42\uff1a<\/p>\n\n\n\n
- \n
- \u5904\u7406\u53d8\u957f\u5e8f\u5217<\/li>\n\n\n\n
- \u8ddf\u8e2a\u957f\u671f\u4f9d\u8d56\u5173\u7cfb<\/li>\n\n\n\n
- \u4fdd\u5b58\u6709\u5173\u987a\u5e8f\u7684\u4fe1\u606f\u4fe1\u606f<\/li>\n\n\n\n
- \u5728\u8bed\u53e5\u95f4\u5171\u4eab\u53c2\u6570<\/li>\n<\/ul>\n\n\n\n
\u5faa\u73af\u795e\u7ecf\u7f51\u7edcRNN<\/strong><\/p>\n\n\n\n
\u6bcf\u6b21\u8f93\u51fa\u4e00\u4e2a\u5355\u8bcd\uff0c\u5728\u8f93\u51fa\u4e0b\u4e2a\u5355\u8bcd\u65f6\uff0c\u5c06\u8fd9\u4e2a\u5355\u8bcd\u4e5f\u8f93\u5165\u5230\u6a21\u578b\u4e2d<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\u7684\u5e94\u7528\uff1a<\/p>\n\n\n\n
\u8bed\u53e5\u5206\u7c7b\uff1a<\/p>\n\n\n\n
<\/div><\/figure>\n\n\n\n\u6587\u672c\u751f\u6210\uff1a<\/p>\n\n\n\n
- \u6570\u636e\u6536\u96c6\u4e0e\u9884\u5904\u7406
- \u5f3a\u5316\u5b66\u4e60 RL\uff1aQ-Learning\u53caDQN<\/li>\n<\/ul>\n\n\n\n
- \u751f\u6210\u5f0f\u6a21\u578b\uff1a\u5b66\u4e60\u6570\u636e\u7684\u5206\u5e03\u4ee5\u751f\u6210\u65b0\u6837\u672c\uff0c\u4f8b\u5982\uff1a\n
- PCA\u4e3b\u6210\u5206\u5206\u6790\uff08\u7ebf\u6027\uff09Autoencoder\u81ea\u7f16\u7801\u5668\uff08\u975e\u7ebf\u6027\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
- \u964d\u7ef4\uff08Dimensionality Reduction\uff09\n
- \u805a\u7c7b\uff08Clustering\uff09\uff08K-Means\uff09<\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-19-1024x374.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-20.png\")
<\/div><\/figure>\n\n\n\n![\"y=f(x)=w^{T} x+w_0\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-0e7499c2094ac4e1c0c558395427f4b2_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"l(w,w_0 \mid x,r)=(r-y)^2\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-30edaeb2730d1b1a38d9dd2830530ade_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"L(w,w_0 \mid D)=\frac{1}{2N}\sum_{l=1}^{N}(r^{(l)}-y^{(l)})^2\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-80186d72e8e25697a20f8bcb7f1d5c7d_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"min_w L(w)\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-e35276b86b74caf642f01e959d350baa_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"w_{t+1}=w_{t}-\eta_{t}\frac{\partial L}{\partial w}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-f23c1f285a5f16ce11b7852c170bf7e8_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L}{\partial w_j}=-\frac{1}{N}\sum_{l}\left( r^{(l)}-y^{(l)}\right)\frac{\partial y^{(l)}}{\partial w_j}=-\frac{1}{N}\sum_{l}(r^{(l)}-y^{(l)})x^{(l)}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-59d01f48bf57a7cac8c062a437dde23f_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"X=\begin{bmatrix}x^{(1)} \\ x^{(2)} \\ \vdots \\ x^{(N)}}\end{bmatrix}=\begin{bmatrix}x_0^{(1)} & x_1^{(1)} & \cdots & x_d^{(1)}\\ x_0^{(2)} & x_1^{(2)} & \cdots & x_d^{(2)}\\ \vdots & \vdots & \ddots & \vdots \\ x_0^{(N)}} & x_1^{(N)}} & \cdots & x_d^{(N)}}\end{bmatrix}w=\begin{bmatrix}w_1 \\ w_2 \\ \vdots \\ w_d\end{bmatrix}r=\begin{bmatrix}r^{(1)} \\ r^{(2)} \\ \vdots \\ r^{(N)}\end{bmatrix}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-a54c5135ef06193658278673b985f094_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"y=Xw=\begin{bmatrix}x^{(1)}w \\ x^{(2)}w \\ \vdots \\ x^{(N)}w\end{bmatrix}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-c1b04040ad3f9b01c9af6c46f62c022d_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"L(w)=\frac{1}{2}(r-y)^T(r-y)=\frac{1}{2}(r-Xw)^T(r-Xw)\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-28f67e18a1c84d72d784c9fb22d38fe1_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L(w)}{\partial w}=-X^T(r-Xw)\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-0b78b28bdc8c20217993e0be547557d0_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L(w)}{\partial w}=0 \\X^T(r-Xw)=0 \\X^Tr=X^TXw \\w^*=(X^TX)^{-1}X^Tr\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-e43700314d345227574d707ca36febcd_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"y=Xw^*=X(X^TX)^{-1}X^Tr=Hr\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-5af7aabdcfe004f771ea9039caa84d02_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"L(w,w_0 \mid D)=\frac{1}{2N}\sum_{l=1}^{N}(r^{(l)}-y^{(l)})^2+\frac{\lambda}{2}\Vert w \Vert^2_2 \\\farc{\partial L(w)}{\partial w}=X^T(r-Xw)+\lambda w\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-ddb5f457cd5ce128f14318d0a496500d_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L(w)}{\partial w}=0 \\X^T(r-Xw)+\lambda w=0 \\X^Tr=(X^TX + \lambda I)w \\w^*=(X^TX + \lambda I)^{-1}X^Tr\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-23037e32acae1f8f56ba2338ae31ff15_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-21.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-22.png\")
<\/div><\/figure>\n\n\n\n![\"H(D)=-\sum_{k=1}^{K}p_k \log p_k=-\sum_{k=1}^{K}\frac{\vert C_k\vert}{\vert D\vert} \log \frac{\vert C_k\vert}{\vert D\vert}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-89b01f7ae3f56cf64f713ff8448c77a7_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"H(D \mid A)=\sum_{i=1}^{n}\frac{\vert D_i\vert}{\vert D\vert}H(D_i)\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-43c475333a8231a7cfaac6e5b2abf637_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"IG(D \mid A)=Gain(D \mid A)=H(D)-H(D \mid A)\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-4fd33d72f6a21fbcc945e66f203d3832_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"H(D)=-0.5\log_{2}0.5-0.5\log_{2}0.5 \\H(D \mid A)=0.6*(-\frac{4}{6}\log_{2}\frac{4}{6}-\frac{2}{6}\log_{2}\frac{2}{6})+0.4*(-\frac{1}{4}\log_{2}\frac{1}{4}-\frac{3}{4}\log_{2}\frac{3}{4}) \\IG(D \mid A)=\cdots\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-8806008c0941b43a6505c76cfa459db6_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-23-1024x494.png\")
<\/div><\/figure>\n\n\n\n![\"P(c_i \mid x)=\frac{p(x \mid C_i)P(C_i)}{p(x)}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-fef4ca7c7a258139fa82f5ad24da8b26_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"P(c_i \mid x_1,x_2,\cdots,x_n)=\frac{p(x_1,x_2,\cdots,x_n \mid C_i)P(C_i)}{p(x_1,x_2,\cdots,x_n)}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-18728e4db5e168d9a37de6ce67ad4611_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"P(x_1, x_2, \cdots, x_n \mid C_i) \\=P(x_1 \mid C_i) P(x_2 \mid x_1,C_i) \cdots P(x_n\mid x_1, x_2, \cdots , x_{n-1}, C_i) \\\approx P(x_1 \mid C_i) P(x_2 \mid C_i) \cdots P(x_n \mid C_i)\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-0bc49199fc196269217256fb654e4790_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"P(x_j \mid C_i)=\frac{count(x_j,C_i)+1}{\sum_{x_k\in \vert x \vert}count(x_k,C_i)+1}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-f02989c95a70fba1501ded314f8d6bf1_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-24.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-25.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-26-1024x259.png\")
<\/div><\/figure>\n\n\n\n![\"\log \frac{y}{1-y}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-433528f5003c48cf86ac46ec4572374a_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\log \frac{y}{1-y}=w^Tx+w_0 \\y=\frac{e^{w^Tx+w_0}}{1+e^{w^Tx+w_0}} \\y=sigmoid(w^Tx+w_0)=\frac{1}{1+e^{-(w^Tx+w_0)}}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-b43368a5b47db91a81411ab6a4c2e7d0_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-27-1024x233.png\")
<\/div><\/figure>\n\n\n\n![\"l(w,w_0,\mid x,r)=-r\log y-(1-r)\log (1-y)\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-860cb51f7e09f641a8e934f3f5d9cae8_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"p(r\mid x)=\left\{\begin{array}{lr}y \\ 1-y \\ \end{array} \right. \begin{array}{lr}if\quad r=1 \\ if\quad r=0 \\ \end{array}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-4beb25911b2ab00b36928755b0dfca46_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"L(w,w_0\mid D)=-\sum_{l=1}^{N} r^{(l)}\log y^{(l)}+(1-r^{(l)})\log (1-y^{(l)})\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-95fda9e705cead9186e891589d016c17_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"a=w^Tx+w_0 \\which\ means: y=sigmoid(a) \\and\ \frac{\partial a^{(l)}}{\partial w_j}=x_j^{(l)}, \\\frac{dy}{da}=y(1-y)\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-9fd2e831b0339e6ce3976d4c734688b0_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L}{\partial w_j}=-\sum_{l} \left( \frac{\partial L}{\partial y^{(l)}} \frac{\partial y^{(l)}}{\partial a^{(l)}} \frac{\partial a^{(l)}}{\partial w_j} \right)\\=-\sum_{l} \left( \frac{r^{(l)}}{y^{(l)}}-\frac{1-r^{(l)}}{1-y^{(l)}}}\right)\frac{\partial y^{(l)}}{\partial a^{(l)}} \frac{\partial a^{(l)}}{\partial w_j} \\=-\sum_{l}(r^{(l)}-y^{(l)})x_j^{(l)}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-7fa0476c73328fa561b5563132890262_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"y_i=softmax(a_1, a_2, \cdots , a_k)=\frac{e^{a_i}}{\sum_{j=1}^{k}e^{a_j}}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-1350b59348b1e012263ee98c7470790e_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"a=w^Tx+w_0\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-e2fd6f29d0e3d837ab0196b01bc21690_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-28.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-29-1024x237.png\")
<\/div><\/figure>\n\n\n\n![\"L_{CE}(y,r)=-\sum_{i=1}^{k}r_i\log y_i =-r^T(\log y) \\\frac{\partial L}{\partial w_j}=-\sum_{l}(r_{j}^{(l)}-y_{j}^{(l)})x_j^{(l)}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-38bbe4705642071173469132af78b38b_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-30.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-31.png\")
<\/div><\/figure>\n\n\n\n![\"margin=\frac{2}{\Vert w \Vert}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-67e7df8ce4e4b4ba09e49f8766a95e43_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"minimize \ \frac{1}{2}\Vert w\Vert\\subject\ to \ y^{(l)}(w^Tx^{(l)}+w_0)\geq 1, l=1,2,\cdots,n\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-b5be7e1c5c7ac278c16de068c97228f8_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-33.png\")
<\/div><\/figure>\n\n\n\n![\"L(w,w_0\mid D)=\frac{1}{N} \sum_{l=1}^{N} max(0,1-y^{(l)}(w^Tx^{(l)}+w_0))+\frac{\lambda}{2}\Vert w\Vert^2\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-76ff2212a121b77d2e4badd1a4f811ad_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L}{\partial w_j}=\left\{ \begin{array}{lr}\lambda w_j \quad if\ y^{(l)}(w^Tx^{(l)}+w_0)\geq 1\\\lambda w_j - y^{(l)}x_j^{(l)} \quad if\ otherwise \\\end{array} \\\frac{\partial L}{\partial w_0}=\left\{ \begin{array}{lr}0 \quad if\ y^{(l)}(w^Tx^{(l)}+w_0)\geq 1\\- y^{(l)} \quad if\ o.w. \\\end{array}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-14ba26e3b1152b8276478b9f3272723b_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-34-1024x549.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-35-1024x596.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-36-1024x288.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-37-1024x477.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-38.png\")
<\/div><\/figure>\n\n\n\n![\"l=\frac{1}{2}\sum_i (r_i-y_i)^2\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-74a855afc908e4dbb39cbce5f3b7fbe6_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/af6e468744ff73f7c5d231c1e6a0efc-1024x410.jpg\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/009f56e6bd3072dfa404b33efac36d5-1024x413.jpg\")
<\/div><\/figure>\n\n\n\n![\"\frac{\partial L}{\partial w_{i,j}^k} \quad i \in {1,2,\cdots,n}; j\in {1,2,\cdots,n}; k\in {1,2,\cdots\,L+1}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-66e2ff5b17b4b4c4b0355a0de8b4c783_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L}{\partial w_{i,1}^{L+1}} \quad i \in {1,2,\cdots,n}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-942cfbee08cb726b9cb566dd1fbfce2c_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L}{\partial w_{i,1}^{L+1}}=\frac{\partial L}{\partial a_{1}^{L+2}}\frac{\partial a_{1}^{L+2}}{\partial w_{i,1}^{L+1}}=\frac{\partial L}{\partial a_{1}^{L+2}}x_{1}^{L+1}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-cf527985cf6b2dddb70ba742cb9af792_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial x_{j}^{L}}{\partial w_{i,j}^{L-1}} \quad i\in {1,2,\cdots,n}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-ac6a40bb379baf579b6dd0f457cc6b46_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial x_{j}^{L}}{\partial w_{i,j}^{L-1}}=\frac{\partial x_{j}^{L}}{\partial a_{j}^{L}}\frac{\partial a_{j}^{L}}{\partial w_{i,j}^{L-1}}=\frac{\partial x_{j}^{L}}{\partial a_{j}^{L}}x_{i}^{L-1}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-7f124da5943e7c6354c5d2035e46ab15_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L}{\partial x_{i}^{L+1}} \quad i \in {1,2,\cdots,n}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-b790d58b87be72141614d4ef1ed13864_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L}{\partial x_{i}^{L+1}}=\frac{\partial L}{\partial a_{1}^{L+2}}\frac{\partial a_{1}^{L+2}}{\partial x_{i}^{L+1}}=\frac{\partial L}{\partial a_{1}^{L+2}}w_{i,1}^{L+1}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-03afdd1a0856f894a59813f3aa1d0128_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\frac{\partial L}{\partial w_{i,j}^{L}}=\frac{\partial a_{j}^{L}}{\partial w_{i,j}^{L}} \frac{\partial L}{\partial a_{j}^{L}}\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-4bfb36e2664a318da2bcbf96766f9952_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\delta^{L}=\sigma'(x^L)\cdot (r-y)\\\delta^{L-1}=\sigma'(x^{L-1})\cdot (W^L)^T \delta^L \\\cdots\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-aab8c781f0134ae12b7e0277397c26e5_l3.png\" "\\"Rendered")
<\/div><\/p>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-39-1024x413.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-41-1024x381.png\")
<\/div><\/figure>\n\n\n\n![\"\"](\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-42.png\")
<\/div><\/figure>\n\n\n\n