{"id":111922,"date":"2026-10-02T07:49:11","date_gmt":"2026-10-01T23:49:11","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/111922.html"},"modified":"2026-10-02T07:49:11","modified_gmt":"2026-10-01T23:49:11","slug":"%e3%80%8a%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0%e3%80%8b%e6%9c%9f%e6%9c%ab%e7%bb%83%e4%b9%a0%e9%a2%98-%e7%a8%8b%e5%ba%8f%e9%a2%98%e7%ac%ac1%e7%af%87%ef%bc%9a%e7%ba%bf%e6%80%a7%e5%9b%9e%e5%bd%92","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/111922.html","title":{"rendered":"\u300a\u6df1\u5ea6\u5b66\u4e60\u300b\u671f\u672b\u7ec3\u4e60\u9898 | \u7a0b\u5e8f\u9898\u7b2c1\u7bc7\uff1a\u7ebf\u6027\u56de\u5f52\u4e0e\u903b\u8f91\u56de\u5f52\u5b9e\u6218"},"content":{"rendered":"

\u300a\u6df1\u5ea6\u5b66\u4e60\u300b\u671f\u672b\u7ec3\u4e60\u9898 | \u7a0b\u5e8f\u9898\u7b2c1\u7bc7：\u7ebf\u6027\u56de\u5f52\u4e0e\u903b\u8f91\u56de\u5f52\u5b9e\u6218<\/h2>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u4e0b\u4e00\u7bc7：\u300a\u6df1\u5ea6\u5b66\u4e60\u300b\u671f\u672b\u7ec3\u4e60\u9898 | \u7a0b\u5e8f\u9898\u7b2c2\u7bc7 \u2014\u2014 PyTorch Tensor \u57fa\u672c\u521b\u5efa\u3001\u8fd0\u7b97\u4e0e\u81ea\u52a8\u5fae\u5206<\/p>\n

\u6458\u8981：\u672c\u6587\u662f\u300a\u6df1\u5ea6\u5b66\u4e60\u300b\u671f\u672b\u590d\u4e60\u7cfb\u5217\u7684\u7b2c\u4e00\u7bc7，\u805a\u7126\u4e8e\u673a\u5668\u5b66\u4e60\u4e2d\u6700\u57fa\u7840\u4e5f\u6700\u91cd\u8981\u7684\u4e24\u4e2a\u7b97\u6cd5\u2014\u2014\u7ebf\u6027\u56de\u5f52\u548c\u903b\u8f91\u56de\u5f52\u3002\u901a\u8fc7\u623f\u5c4b\u5355\u4ef7\u9884\u6d4b\u548c\u9e22\u5c3e\u82b1\u5206\u7c7b\u4e24\u4e2a\u7ecf\u5178\u6848\u4f8b，\u624b\u628a\u624b\u5e26\u4f60\u638c\u63e1 sklearn \u5efa\u6a21\u5168\u6d41\u7a0b\u3002\u4ee3\u7801\u53ef\u76f4\u63a5\u8fd0\u884c，\u9002\u5408\u671f\u672b\u8003\u8bd5\u590d\u4e60\u4e0e\u5165\u95e8\u5b9e\u8df5\u3002<\/p>\n

\n

📌 \u76ee\u5f55<\/h3>\n
  • \u7ebf\u6027\u56de\u5f52：\u623f\u5c4b\u5355\u4ef7\u9884\u6d4b<\/li>\n
  • \u903b\u8f91\u56de\u5f52：\u9e22\u5c3e\u82b1\u5206\u7c7b<\/li>\n
  • \u6838\u5fc3\u77e5\u8bc6\u70b9\u603b\u7ed3<\/li>\n
  • \u5e38\u89c1\u8003\u8bd5\u9677\u9631\u4e0e\u6ce8\u610f\u4e8b\u9879<\/li>\n
    \n

    1. \u7ebf\u6027\u56de\u5f52：\u623f\u5c4b\u5355\u4ef7\u9884\u6d4b<\/h3>\n

    1.1 \u95ee\u9898\u63cf\u8ff0<\/h4>\n

    \u5df2\u77e5\u4e00\u7ec4\u623f\u5c4b\u9762\u79ef\u4e0e\u5bf9\u5e94\u5355\u4ef7\u7684\u6570\u636e，\u8981\u6c42\u5efa\u7acb\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b，\u5e76\u9884\u6d4b\u9762\u79ef\u4e3a 700 \u5e73\u65b9\u7c73\u7684\u623f\u5c4b\u5355\u4ef7\u3002<\/p>\n

    1.2 \u5b8c\u6574\u4ee3\u7801<\/h4>\n

    import<\/span> numpy as<\/span> np
    \nfrom<\/span> sklearn.<\/span>linear_model import<\/span> LinearRegression<\/p>\n

    # ========== 1. \u51c6\u5907\u6570\u636e ==========<\/span>
    \nX =<\/span> np.<\/span>array(<\/span>[<\/span>150<\/span>,<\/span> 200<\/span>,<\/span> 250<\/span>,<\/span> 300<\/span>,<\/span> 350<\/span>,<\/span> 400<\/span>,<\/span> 600<\/span>]<\/span>)<\/span>.<\/span>reshape(<\/span>–<\/span>1<\/span>,<\/span> 1<\/span>)<\/span> # \u623f\u5c4b\u9762\u79ef（\u7279\u5f81）<\/span>
    \ny =<\/span> np.<\/span>array(<\/span>[<\/span>6450<\/span>,<\/span> 7450<\/span>,<\/span> 8450<\/span>,<\/span> 9450<\/span>,<\/span> 11450<\/span>,<\/span> 15450<\/span>,<\/span> 18450<\/span>]<\/span>)<\/span> # \u623f\u5c4b\u5355\u4ef7（\u6807\u7b7e）<\/span><\/p>\n

    # ========== 2. \u521b\u5efa\u5e76\u8bad\u7ec3\u6a21\u578b ==========<\/span>
    \nmodel =<\/span> LinearRegression(<\/span>)<\/span> # \u521b\u5efa\u7ebf\u6027\u56de\u5f52\u6a21\u578b<\/span>
    \nmodel.<\/span>fit(<\/span>X,<\/span> y)<\/span> # \u8bad\u7ec3\u6a21\u578b<\/span><\/p>\n

    # ========== 3. \u83b7\u53d6\u6a21\u578b\u53c2\u6570 ==========<\/span>
    \nw =<\/span> model.<\/span>coef_ # \u56de\u5f52\u7cfb\u6570（\u659c\u7387）<\/span>
    \nb =<\/span> model.<\/span>intercept_ # \u622a\u8ddd<\/span>
    \nprint<\/span>(<\/span>f"\u56de\u5f52\u65b9\u7a0b: y = <\/span>{<\/span>w[<\/span>0<\/span>]<\/span>:<\/span>.2f<\/span>}<\/span><\/span> * x + <\/span>{<\/span>b:<\/span>.2f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span><\/p>\n

    # ========== 4. \u9884\u6d4b ==========<\/span>
    \npred =<\/span> model.<\/span>predict(<\/span>[<\/span>[<\/span>700<\/span>]<\/span>]<\/span>)<\/span> # \u6ce8\u610f：\u8f93\u5165\u5fc5\u987b\u662f\u4e8c\u7ef4\u6570\u7ec4<\/span>
    \nprint<\/span>(<\/span>"\u9884\u6d4b\u5355\u4ef7:"<\/span>,<\/span> pred[<\/span>0<\/span>]<\/span>)<\/span><\/p>\n

    1.3 \u5173\u952e\u89e3\u6790<\/h4>\n\n\u8981\u70b9\u8bf4\u660e<\/tr>\n\n\n\n\n\n
    reshape(-1, 1)<\/td>\nsklearn \u8981\u6c42\u7279\u5f81\u77e9\u9635\u4e3a 2D \u6570\u7ec4，\u4e00\u7ef4\u6570\u7ec4\u5fc5\u987b\u8f6c\u6362<\/td>\n<\/tr>\n
    model.coef_<\/td>\n\u8fd4\u56de\u6570\u7ec4，\u5373\u4f7f\u662f\u4e00\u5143\u56de\u5f52\u4e5f\u662f [w] \u5f62\u5f0f<\/td>\n<\/tr>\n
    model.predict([[700]])<\/td>\n\u9884\u6d4b\u8f93\u5165\u540c\u6837\u9700\u8981 \u4e8c\u7ef4\u6570\u7ec4，[[700]] \u8868\u793a1\u4e2a\u6837\u672c\u30011\u4e2a\u7279\u5f81<\/td>\n<\/tr>\n
    \u635f\u5931\u51fd\u6570<\/td>\n\u6700\u5c0f\u4e8c\u4e58\u6cd5（OLS），\u6700\u5c0f\u5316\u6b8b\u5dee\u5e73\u65b9\u548c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    1.4 \u8fd0\u884c\u7ed3\u679c\u793a\u4f8b<\/h4>\n

    \u56de\u5f52\u65b9\u7a0b: y = 26.43 * x + 2521.43
    \n\u9884\u6d4b\u5355\u4ef7: 21022.43<\/p>\n

    💡 \u8003\u8bd5\u63d0\u793a：\u5982\u679c\u9898\u76ee\u8981\u6c42\u624b\u5199\u68af\u5ea6\u4e0b\u964d\u800c\u975e\u8c03\u7528 sklearn，\u9700\u8bb0\u4f4f\u53c2\u6570\u66f4\u65b0\u516c\u5f0f： <\/p>\n

    w<\/p>\n

    :<\/p>\n

    =<\/p>\n

    w<\/p>\n

    \u2212<\/p>\n

    \u03b1<\/p>\n

    \u22c5<\/p>\n

    1<\/p>\n

    m<\/p>\n

    \u2211<\/p>\n

    i<\/p>\n

    =<\/p>\n

    1<\/p>\n

    m<\/p>\n

    (<\/p>\n

    h<\/p>\n

    w<\/p>\n

    (<\/p>\n

    x<\/p>\n

    (<\/p>\n

    i<\/p>\n

    )<\/p>\n

    )<\/p>\n

    \u2212<\/p>\n

    y<\/p>\n

    (<\/p>\n

    i<\/p>\n

    )<\/p>\n

    )<\/p>\n

    \u22c5<\/p>\n

    x<\/p>\n

    (<\/p>\n

    i<\/p>\n

    )<\/p>\n

    w := w – \\\\alpha \\\\cdot \\\\frac{1}{m}\\\\sum_{i=1}^{m}(h_w(x^{(i)}) – y^{(i)}) \\\\cdot x^{(i)}<\/p>\n

    <\/span><\/span>w<\/span><\/span>:=<\/span><\/span><\/span><\/span>w<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03b1<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>h<\/span><\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>(<\/span>i<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>y<\/span><\/span>(<\/span>i<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>x<\/span><\/span>(<\/span>i<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \n

    2. \u903b\u8f91\u56de\u5f52：\u9e22\u5c3e\u82b1\u5206\u7c7b<\/h3>\n

    2.1 \u95ee\u9898\u63cf\u8ff0<\/h4>\n

    \u4f7f\u7528 sklearn \u5185\u7f6e\u7684 Iris \u9e22\u5c3e\u82b1\u6570\u636e\u96c6，\u8bad\u7ec3\u903b\u8f91\u56de\u5f52\u5206\u7c7b\u5668，\u5728\u6d4b\u8bd5\u96c6\u4e0a\u8bc4\u4f30\u51c6\u786e\u7387\u3002<\/p>\n

    2.2 \u5b8c\u6574\u4ee3\u7801<\/h4>\n

    import<\/span> numpy as<\/span> np
    \nfrom<\/span> sklearn import<\/span> datasets,<\/span> linear_model
    \nfrom<\/span> sklearn.<\/span>model_selection import<\/span> train_test_split
    \nfrom<\/span> sklearn.<\/span>metrics import<\/span> accuracy_score<\/p>\n

    # ========== 1. \u52a0\u8f7d\u6570\u636e ==========<\/span>
    \niris =<\/span> datasets.<\/span>load_iris(<\/span>)<\/span>
    \nX =<\/span> iris.<\/span>data # (150, 4) \u56db\u4e2a\u7279\u5f81<\/span>
    \ny =<\/span> iris.<\/span>target # (150,) \u4e09\u5206\u7c7b\u6807\u7b7e: 0, 1, 2<\/span><\/p>\n

    # ========== 2. \u5212\u5206\u8bad\u7ec3\u96c6\/\u6d4b\u8bd5\u96c6 ==========<\/span>
    \nX_train,<\/span> X_test,<\/span> y_train,<\/span> y_test =<\/span> train_test_split(<\/span>
    \n X,<\/span> y,<\/span> test_size=<\/span>0.2<\/span>,<\/span> random_state=<\/span>42<\/span> # \u5efa\u8bae\u56fa\u5b9a\u968f\u673a\u79cd\u5b50\u4fdd\u8bc1\u53ef\u590d\u73b0<\/span>
    \n)<\/span><\/p>\n

    # ========== 3. \u8bad\u7ec3\u903b\u8f91\u56de\u5f52\u6a21\u578b ==========<\/span>
    \nmodel =<\/span> linear_model.<\/span>LogisticRegression(<\/span>C=<\/span>1e5<\/span>)<\/span> # C\u8d8a\u5927\u6b63\u5219\u5316\u8d8a\u5f31<\/span>
    \nmodel.<\/span>fit(<\/span>X_train,<\/span> y_train)<\/span><\/p>\n

    # ========== 4. \u9884\u6d4b\u4e0e\u8bc4\u4f30 ==========<\/span>
    \ny_pred =<\/span> model.<\/span>predict(<\/span>X_test)<\/span>
    \naccuracy =<\/span> accuracy_score(<\/span>y_test,<\/span> y_pred)<\/span><\/p>\n

    print<\/span>(<\/span>"\u6a21\u578b\u5728\u6d4b\u8bd5\u96c6\u4e0a\u7684\u51c6\u786e\u7387:"<\/span>,<\/span> accuracy)<\/span><\/p>\n

    2.3 \u5173\u952e\u89e3\u6790<\/h4>\n\n\u8981\u70b9\u8bf4\u660e<\/tr>\n\n\n\n\n\n\n
    LogisticRegression(C=1e5)<\/td>\nC \u662f\u6b63\u5219\u5316\u5f3a\u5ea6\u7684\u5012\u6570，C=1e5 \u2248 \u65e0\u6b63\u5219\u5316，\u7b49\u4ef7\u4e8e\u6807\u51c6\u903b\u8f91\u56de\u5f52<\/td>\n<\/tr>\n
    test_size=0.2<\/td>\n80% \u8bad\u7ec3 \/ 20% \u6d4b\u8bd5，\u8fd9\u662f\u6700\u5e38\u7528\u7684\u5212\u5206\u6bd4\u4f8b<\/td>\n<\/tr>\n
    random_state=42<\/td>\n\u5f3a\u70c8\u5efa\u8bae\u52a0\u4e0a，\u5426\u5219\u6bcf\u6b21\u8fd0\u884c\u7ed3\u679c\u4e0d\u540c，\u8c03\u8bd5\u56f0\u96be<\/td>\n<\/tr>\n
    \u591a\u5206\u7c7b\u7b56\u7565<\/td>\nsklearn \u9ed8\u8ba4\u4f7f\u7528 OvR（One-vs-Rest），\u4e5f\u53ef\u8bbe\u7f6e multi_class='multinomial'<\/td>\n<\/tr>\n
    \u8f93\u51fa\u8303\u56f4<\/td>\n\u903b\u8f91\u56de\u5f52\u8f93\u51fa\u7ecf\u8fc7 Sigmoid\/Softmax，\u503c\u57df\u4e3a (0, 1)，\u5929\u7136\u9002\u5408\u6982\u7387\u89e3\u91ca<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    2.4 \u8fd0\u884c\u7ed3\u679c\u793a\u4f8b<\/h4>\n

    \u6a21\u578b\u5728\u6d4b\u8bd5\u96c6\u4e0a\u7684\u51c6\u786e\u7387: 1.0<\/p>\n

    \u26a0\ufe0f \u6ce8\u610f：\u9e22\u5c3e\u82b1\u6570\u636e\u96c6\u8f83\u5c0f\u4e14 separable，\u51c6\u786e\u7387\u53ef\u80fd\u8fbe\u5230 100%\u3002\u5728\u5b9e\u9645\u8003\u8bd5\u4e2d\u82e5\u6570\u636e\u66f4\u590d\u6742，\u51c6\u786e\u7387\u901a\u5e38\u5728 85%-95% \u4e4b\u95f4\u3002<\/p>\n

    \n

    3. \u6838\u5fc3\u77e5\u8bc6\u70b9\u603b\u7ed3<\/h3>\n

    \u7ebf\u6027\u56de\u5f52 vs \u903b\u8f91\u56de\u5f52\u5bf9\u6bd4<\/h4>\n\n\u7ef4\u5ea6\u7ebf\u6027\u56de\u5f52\u903b\u8f91\u56de\u5f52<\/tr>\n\n\n\n\n\n\n\n
    \u4efb\u52a1\u7c7b\u578b<\/td>\n\u56de\u5f52（\u8fde\u7eed\u503c\u9884\u6d4b）<\/td>\n\u5206\u7c7b（\u79bb\u6563\u7c7b\u522b\u9884\u6d4b）<\/td>\n<\/tr>\n
    \u6fc0\u6d3b\u51fd\u6570<\/td>\n\u65e0<\/td>\nSigmoid（\u4e8c\u5206\u7c7b）\/ Softmax（\u591a\u5206\u7c7b）<\/td>\n<\/tr>\n
    \u635f\u5931\u51fd\u6570<\/td>\nMSE（\u5747\u65b9\u8bef\u5dee）<\/td>\nCross-Entropy（\u4ea4\u53c9\u71b5）<\/td>\n<\/tr>\n
    \u8f93\u51fa\u8303\u56f4<\/td>\n<\/p>\n

    (<\/p>\n

    \u2212<\/p>\n

    \u221e<\/p>\n

    ,<\/p>\n

    +<\/p>\n

    \u221e<\/p>\n

    )<\/p>\n

    (-\\\\infty, +\\\\infty)<\/p>\n

    <\/span><\/span>(<\/span>\u2212<\/span>\u221e<\/span>,<\/span><\/span>+<\/span>\u221e<\/span>)<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    (<\/p>\n

    0<\/p>\n

    ,<\/p>\n

    1<\/p>\n

    )<\/p>\n

    (0, 1)<\/p>\n

    <\/span><\/span>(<\/span>0<\/span>,<\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

    sklearn \u7c7b<\/td>\nLinearRegression<\/td>\nLogisticRegression<\/td>\n<\/tr>\n
    \u6b63\u5219\u5316<\/td>\n\u9700\u7528 Ridge\/Lasso<\/td>\n\u5185\u7f6e L2 \u6b63\u5219（\u7531 C \u63a7\u5236）<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    sklearn \u5efa\u6a21\u56db\u6b65\u6cd5（\u4e07\u80fd\u6a21\u677f）<\/h4>\n

    \u2460 \u51c6\u5907\u6570\u636e \u2192 \u2461 \u521b\u5efa\u6a21\u578b \u2192 \u2462 fit \u8bad\u7ec3 \u2192 \u2463 predict \u9884\u6d4b \/ score \u8bc4\u4f30<\/p>\n

    🎯 \u8fd9\u4e2a\u6a21\u677f\u9002\u7528\u4e8e sklearn \u4e2d\u51e0\u4e4e\u6240\u6709\u76d1\u7763\u5b66\u4e60\u7b97\u6cd5，\u52a1\u5fc5\u7262\u8bb0！<\/p>\n

    \n

    4. \u5e38\u89c1\u8003\u8bd5\u9677\u9631\u4e0e\u6ce8\u610f\u4e8b\u9879<\/h3>\n

    \u274c \u9677\u96311：\u5fd8\u8bb0 reshape<\/h4>\n

    # \u9519\u8bef\u5199\u6cd5<\/span>
    \nX =<\/span> np.<\/span>array(<\/span>[<\/span>150<\/span>,<\/span> 200<\/span>,<\/span> 250<\/span>]<\/span>)<\/span>
    \nmodel.<\/span>fit(<\/span>X,<\/span> y)<\/span> # ValueError!<\/span><\/p>\n

    # \u6b63\u786e\u5199\u6cd5<\/span>
    \nX =<\/span> np.<\/span>array(<\/span>[<\/span>150<\/span>,<\/span> 200<\/span>,<\/span> 250<\/span>]<\/span>)<\/span>.<\/span>reshape(<\/span>–<\/span>1<\/span>,<\/span> 1<\/span>)<\/span><\/p>\n

    \u274c \u9677\u96312：predict \u4f20\u5165\u4e00\u7ef4\u6570\u7ec4<\/h4>\n

    # \u9519\u8bef<\/span>
    \nmodel.<\/span>predict(<\/span>[<\/span>700<\/span>]<\/span>)<\/span><\/p>\n

    # \u6b63\u786e<\/span>
    \nmodel.<\/span>predict(<\/span>[<\/span>[<\/span>700<\/span>]<\/span>]<\/span>)<\/span><\/p>\n

    \u274c \u9677\u96313：\u6df7\u6dc6 coef_ \u548c intercept_<\/h4>\n
      \n
    • coef_ \u2192 \u6743\u91cd\/\u659c\u7387（\u53ef\u80fd\u6709\u591a\u4e2a）<\/li>\n
    • intercept_ \u2192 \u504f\u7f6e\/\u622a\u8ddd（\u6807\u91cf\u6216\u6570\u7ec4）<\/li>\n<\/ul>\n

      \u274c \u9677\u96314：\u672a\u5212\u5206\u6d4b\u8bd5\u96c6\u76f4\u63a5\u8bc4\u4f30<\/h4>\n

      \u5728\u8bad\u7ec3\u96c6\u4e0a\u8bc4\u4f30\u6ca1\u6709\u610f\u4e49，\u5fc5\u987b\u4f7f\u7528\u672a\u89c1\u8fc7\u7684\u6d4b\u8bd5\u96c6\u6765\u8861\u91cf\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n

      \u2705 \u52a0\u5206\u9879：\u53ef\u89c6\u5316<\/h4>\n

      \u5982\u679c\u8003\u8bd5\u65f6\u95f4\u5141\u8bb8，\u6dfb\u52a0\u6563\u70b9\u56fe+\u56de\u5f52\u7ebf\u53ef\u4ee5\u8ba9\u7b54\u6848\u66f4\u51fa\u5f69：<\/p>\n

      import<\/span> matplotlib.<\/span>pyplot as<\/span> plt<\/p>\n

      plt.<\/span>scatter(<\/span>X,<\/span> y,<\/span> color=<\/span>'blue'<\/span>,<\/span> label=<\/span>'\u771f\u5b9e\u6570\u636e'<\/span>)<\/span>
      \nplt.<\/span>plot(<\/span>X,<\/span> model.<\/span>predict(<\/span>X)<\/span>,<\/span> color=<\/span>'red'<\/span>,<\/span> label=<\/span>'\u56de\u5f52\u7ebf'<\/span>)<\/span>
      \nplt.<\/span>xlabel(<\/span>'\u623f\u5c4b\u9762\u79ef'<\/span>)<\/span>
      \nplt.<\/span>ylabel(<\/span>'\u5355\u4ef7'<\/span>)<\/span>
      \nplt.<\/span>legend(<\/span>)<\/span>
      \nplt.<\/span>show(<\/span>)<\/span><\/p>\n

      \n

      📝 \u5199\u5728\u6700\u540e<\/h3>\n

      \u672c\u7bc7\u8986\u76d6\u4e86\u6df1\u5ea6\u5b66\u4e60\/\u673a\u5668\u5b66\u4e60\u8bfe\u7a0b\u4e2d\u6700\u57fa\u7840\u7684\u4e24\u4e2a\u7a0b\u5e8f\u9898\u3002\u7ebf\u6027\u56de\u5f52\u548c\u903b\u8f91\u56de\u5f52\u4e0d\u4ec5\u662f\u671f\u672b\u8003\u8bd5\u7684\u9ad8\u9891\u8003\u70b9，\u66f4\u662f\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u3001\u6df1\u5ea6\u5b66\u4e60\u7684\u57fa\u77f3\u3002<\/p>\n

      \u4e0b\u4e00\u7bc7\u9884\u544a：\u300a\u6df1\u5ea6\u5b66\u4e60\u300b\u671f\u672b\u7ec3\u4e60\u9898 | \u7a0b\u5e8f\u9898\u7b2c2\u7bc7 \u2014\u2014 PyTorch Tensor \u57fa\u672c\u521b\u5efa\u3001\u8fd0\u7b97\u4e0e\u81ea\u52a8\u5fae\u5206<\/p>\n

      \u5982\u679c\u89c9\u5f97\u6709\u5e2e\u52a9，\u6b22\u8fce \u70b9\u8d5e 👍 + \u6536\u85cf \u2b50 + \u5173\u6ce8 \u4e09\u8fde\u652f\u6301！\u4f60\u7684\u9f13\u52b1\u662f\u6211\u6301\u7eed\u66f4\u65b0\u7684\u6700\u5927\u52a8\u529b～<\/p>\n

      \n

      \u5173\u952e\u8bcd：#\u6df1\u5ea6\u5b66\u4e60 #\u673a\u5668\u5b66\u4e60 #\u7ebf\u6027\u56de\u5f52 #\u903b\u8f91\u56de\u5f52 #sklearn #\u671f\u672b\u8003\u8bd5 #Python<\/p>\n

      \n

      \u540e\u671f\u5b8c\u5584\u7248 | \u3010\u6df1\u5ea6\u5b66\u4e60\u671f\u672b\u901a\u5173\u3011\u7ebf\u6027\u56de\u5f52\u4e0e\u903b\u8f91\u56de\u5f52\u5b9e\u6218：\u4ece\u6570\u5b66\u539f\u7406\u5230sklearn\u6ee1\u5206\u4ee3\u7801\u8be6\u89e3<\/h2>\n

      \u6458\u8981：\u672c\u6587\u662f\u300a\u6df1\u5ea6\u5b66\u4e60\u300b\u671f\u672b\u590d\u4e60\u7cfb\u5217\u7684\u5f00\u7bc7\u4e4b\u4f5c，\u65e8\u5728\u4e3a\u5907\u8003\u540c\u5b66\u53ca\u673a\u5668\u5b66\u4e60\u521d\u5b66\u8005\u6784\u5efa\u4e00\u5957\u201c\u7406\u8bba+\u4ee3\u7801+\u907f\u5751\u201d\u4e09\u4f4d\u4e00\u4f53\u7684\u77e5\u8bc6\u4f53\u7cfb\u3002\u6587\u7ae0\u4e0d\u4ec5\u63d0\u4f9b\u4e86\u53ef\u76f4\u63a5\u8fd0\u884c\u7684sklearn\u6807\u51c6\u4ee3\u7801\u6a21\u677f，\u66f4\u6df1\u5165\u5256\u6790\u4e86\u7ebf\u6027\u56de\u5f52\u4e0e\u903b\u8f91\u56de\u5f52\u80cc\u540e\u7684\u6570\u5b66\u672c\u8d28\u3001\u635f\u5931\u51fd\u6570\u63a8\u5bfc\u53ca\u4f18\u5316\u7b56\u7565\u3002\u901a\u8fc7\u623f\u5c4b\u5355\u4ef7\u9884\u6d4b\u4e0e\u9e22\u5c3e\u82b1\u5206\u7c7b\u4e24\u4e2a\u7ecf\u5178\u6848\u4f8b，\u914d\u5408Mermaid\u53ef\u89c6\u5316\u56fe\u8868\u3001\u5e38\u89c1\u8003\u8bd5\u9677\u9631\u89e3\u6790\u53caFAQ\u9ad8\u9891\u95ee\u7b54，\u5e2e\u52a9\u8bfb\u8005\u5728\u7406\u89e3\u7b97\u6cd5\u5185\u6838\u7684\u540c\u65f6，\u638c\u63e1\u5e94\u5bf9\u671f\u672b\u8003\u8bd5\u4e0e\u5de5\u7a0b\u5b9e\u8df5\u7684\u6838\u5fc3\u80fd\u529b\u3002\u5168\u6587\u6db5\u76d6\u6570\u636e\u9884\u5904\u7406\u3001\u6a21\u578b\u8bad\u7ec3\u3001\u8bc4\u4f30\u6307\u6807\u3001\u6b63\u5219\u5316\u539f\u7406\u7b49\u5173\u952e\u8003\u70b9，\u5e76\u9644\u5e26\u6269\u5c55\u9605\u8bfb\u4e0e\u884c\u52a8\u5efa\u8bae，\u529b\u6c42\u6210\u4e3a\u4f60\u6848\u5934\u5fc5\u5907\u7684\u590d\u4e60\u624b\u518c\u3002<\/p>\n

      \n

      \u4e00\u3001 \u5f15\u8a00：\u4e3a\u4ec0\u4e48\u671f\u672b\u590d\u4e60\u5fc5\u987b\u6b7b\u78d5\u8fd9\u4e24\u4e2a\u6a21\u578b<\/h3>\n

      \u5728\u6df1\u5ea6\u5b66\u4e60\u767e\u82b1\u9f50\u653e\u7684\u4eca\u5929，\u8bb8\u591a\u540c\u5b66\u5728\u590d\u4e60\u65f6\u5f80\u5f80\u6025\u4e8e\u6c42\u6210，\u76f4\u63a5\u8df3\u5165CNN\u3001RNN\u6216Transformer\u7684\u590d\u6742\u7ed3\u6784\u4e2d，\u5374\u5ffd\u89c6\u4e86\u673a\u5668\u5b66\u4e60\u5927\u53a6\u7684\u57fa\u77f3\u2014\u2014\u7ebf\u6027\u56de\u5f52（Linear Regression） \u4e0e\u903b\u8f91\u56de\u5f52（Logistic Regression）\u3002\u8fd9\u79cd\u201c\u5934\u91cd\u811a\u8f7b\u201d\u7684\u590d\u4e60\u7b56\u7565\u5728\u671f\u672b\u8003\u8bd5\u548c\u5b9e\u9645\u9762\u8bd5\u4e2d\u6781\u6613\u66b4\u9732\u77ed\u677f\u3002<\/p>\n

      \u4e8b\u5b9e\u4e0a，\u8fd9\u4e24\u4e2a\u6a21\u578b\u4e0d\u4ec5\u662f\u5386\u5e74\u300a\u6df1\u5ea6\u5b66\u4e60\u300b\u4e0e\u300a\u673a\u5668\u5b66\u4e60\u300b\u8bfe\u7a0b\u8003\u8bd5\u4e2d\u7a0b\u5e8f\u9898\u7684\u5fc5\u8003\u9879，\u66f4\u662f\u7406\u89e3\u540e\u7eed\u6240\u6709\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u201c\u5143\u77e5\u8bc6\u201d\u30021<\/sup> \u7ebf\u6027\u56de\u5f52\u6559\u4f1a\u6211\u4eec\u4ec0\u4e48\u662f\u635f\u5931\u51fd\u6570（Loss Function）\u3001\u4ec0\u4e48\u662f\u68af\u5ea6\u4e0b\u964d（Gradient Descent）\u3001\u4ec0\u4e48\u662f\u8fc7\u62df\u5408\u4e0e\u6b63\u5219\u5316；\u800c\u903b\u8f91\u56de\u5f52\u5219\u5f15\u5165\u4e86\u6fc0\u6d3b\u51fd\u6570（Activation Function）\u3001\u4ea4\u53c9\u71b5\u635f\u5931（Cross-Entropy Loss） \u4ee5\u53ca \u6982\u7387\u5efa\u6a21 \u7684\u601d\u60f3，\u8fd9\u4e9b\u6982\u5ff5\u4e0e\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u5168\u8fde\u63a5\u5c42\u3001Softmax\u8f93\u51fa\u5c42\u5b8c\u5168\u540c\u6e90\u3002<\/p>\n

      \u672c\u6587\u5c06\u6452\u5f03\u67af\u71e5\u7684\u7eaf\u7406\u8bba\u5806\u780c，\u91c7\u7528\u201c\u573a\u666f\u9a71\u52a8+\u4ee3\u7801\u843d\u5730+\u539f\u7406\u900f\u89c6\u201d\u7684\u6a21\u5f0f，\u5e26\u4f60\u5f7b\u5e95\u5403\u900f\u8fd9\u4e24\u4e2a\u6a21\u578b\u3002\u65e0\u8bba\u4f60\u662f\u4e3a\u4e86\u5e94\u4ed8\u5373\u5c06\u5230\u6765\u7684\u671f\u672b\u8003\u8bd5，\u8fd8\u662f\u4e3a\u4e86\u592f\u5b9e\u5de5\u7a0b\u57fa\u7840，\u8fd9\u7bc7\u6587\u7ae0\u90fd\u5c06\u4e3a\u4f60\u63d0\u4f9b\u4e00\u4efd\u8be6\u5c3d\u7684\u5b9e\u6218\u6307\u5357\u3002<\/p>\n

      \n

      \u4e8c\u3001 \u7ebf\u6027\u56de\u5f52：\u623f\u5c4b\u5355\u4ef7\u9884\u6d4b\u7684\u5168\u6d41\u7a0b\u89e3\u6790<\/h3>\n

      2.1 \u95ee\u9898\u5b9a\u4e49\u4e0e\u6570\u5b66\u672c\u8d28<\/h4>\n

      \u7ebf\u6027\u56de\u5f52\u662f\u6700\u57fa\u7840\u7684\u76d1\u7763\u5b66\u4e60\u7b97\u6cd5，\u5176\u6838\u5fc3\u76ee\u6807\u662f\u627e\u5230\u4e00\u4e2a\u7ebf\u6027\u6620\u5c04\u5173\u7cfb，\u4f7f\u5f97\u9884\u6d4b\u503c<\/p>\n

      y<\/p>\n

      ^<\/p>\n

      \\\\hat{y}<\/p>\n

      <\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0e\u771f\u5b9e\u6807\u7b7e<\/p>\n

      y<\/p>\n

      y<\/p>\n

      <\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\u7684\u8bef\u5dee\u6700\u5c0f\u5316\u3002\u5728\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u4e2d，\u6a21\u578b\u5047\u8bbe\u6570\u636e\u670d\u4ece\u5982\u4e0b\u5206\u5e03：<\/p>\n

      <\/p>\n

      y<\/p>\n

      ^<\/p>\n

      =<\/p>\n

      w<\/p>\n

      x<\/p>\n

      +<\/p>\n

      b<\/p>\n

      \\\\hat{y} = wx + b <\/p>\n

      <\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>w<\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>b<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u5176\u4e2d<\/p>\n

      w<\/p>\n

      w<\/p>\n

      <\/span><\/span>w<\/span><\/span><\/span><\/span><\/span>\u4e3a\u6743\u91cd（Weight），<\/p>\n

      b<\/p>\n

      b<\/p>\n

      <\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u4e3a\u504f\u7f6e（Bias）\u3002\u5728\u7edf\u8ba1\u5b66\u89c6\u89d2\u4e0b，\u8fd9\u7b49\u4ef7\u4e8e\u5bfb\u627e\u4e00\u6761\u76f4\u7ebf，\u4f7f\u5f97\u6240\u6709\u6837\u672c\u70b9\u5230\u8be5\u76f4\u7ebf\u7684\u5782\u76f4\u8ddd\u79bb\u5e73\u65b9\u548c\u6700\u5c0f，\u5373\u666e\u901a\u6700\u5c0f\u4e8c\u4e58\u6cd5（Ordinary Least Squares, OLS）\u30022<\/sup><\/p>\n

      💡 \u6838\u5fc3\u8981\u70b9：\u7ebf\u6027\u56de\u5f52\u7684\u201c\u7ebf\u6027\u201d\u6307\u7684\u662f\u53c2\u6570<\/p>\n

      w<\/p>\n

      w<\/p>\n

      <\/span><\/span>w<\/span><\/span><\/span><\/span><\/span>\u548c<\/p>\n

      b<\/p>\n

      b<\/p>\n

      <\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u662f\u7ebf\u6027\u7684，\u800c\u975e\u7279\u5f81<\/p>\n

      x<\/p>\n

      x<\/p>\n

      <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u5fc5\u987b\u662f\u7ebf\u6027\u7684\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u591a\u9879\u5f0f\u6269\u5c55\u5c06\u7ebf\u6027\u56de\u5f52\u5e94\u7528\u4e8e\u975e\u7ebf\u6027\u5173\u7cfb\u62df\u5408，\u8fd9\u5728\u8003\u8bd5\u4e2d\u5e38\u4f5c\u4e3a\u8fdb\u9636\u8003\u70b9\u51fa\u73b0\u3002<\/p>\n

      2.2 sklearn\u5efa\u6a21\u56db\u6b65\u6cd5\u6807\u51c6\u6a21\u677f<\/h4>\n

      \u5728scikit-learn\u5e93\u4e2d，\u51e0\u4e4e\u6240\u6709\u76d1\u7763\u5b66\u4e60\u7b97\u6cd5\u90fd\u9075\u5faa\u7edf\u4e00\u7684API\u8bbe\u8ba1\u54f2\u5b66\u3002\u638c\u63e1\u8fd9\u4e2a\u201c\u4e07\u80fd\u6a21\u677f\u201d，\u76f8\u5f53\u4e8e\u638c\u63e1\u4e86sklearn\u7684\u534a\u58c1\u6c5f\u5c71\u3002<\/p>\n

      import<\/span> numpy as<\/span> np
      \nfrom<\/span> sklearn.<\/span>linear_model import<\/span> LinearRegression<\/p>\n

      # ========== \u6b65\u9aa41: \u6570\u636e\u51c6\u5907 (Data Preparation) ==========<\/span>
      \n# \u7279\u5f81\u77e9\u9635X\u5fc5\u987b\u662f\u4e8c\u7ef4\u6570\u7ec4 (n_samples, n_features)<\/span>
      \n# \u6807\u7b7e\u5411\u91cfy\u901a\u5e38\u662f\u4e00\u7ef4\u6570\u7ec4 (n_samples,)<\/span>
      \nX =<\/span> np.<\/span>array(<\/span>[<\/span>150<\/span>,<\/span> 200<\/span>,<\/span> 250<\/span>,<\/span> 300<\/span>,<\/span> 350<\/span>,<\/span> 400<\/span>,<\/span> 600<\/span>]<\/span>)<\/span>.<\/span>reshape(<\/span>–<\/span>1<\/span>,<\/span> 1<\/span>)<\/span>
      \ny =<\/span> np.<\/span>array(<\/span>[<\/span>6450<\/span>,<\/span> 7450<\/span>,<\/span> 8450<\/span>,<\/span> 9450<\/span>,<\/span> 11450<\/span>,<\/span> 15450<\/span>,<\/span> 18450<\/span>]<\/span>)<\/span><\/p>\n

      # ========== \u6b65\u9aa42: \u6a21\u578b\u5b9e\u4f8b\u5316 (Model Instantiation) ==========<\/span>
      \n# LinearRegression\u9ed8\u8ba4\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3，\u65e0\u9700\u6307\u5b9a\u5b66\u4e60\u7387<\/span>
      \nmodel =<\/span> LinearRegression(<\/span>)<\/span><\/p>\n

      # ========== \u6b65\u9aa43: \u6a21\u578b\u8bad\u7ec3 (Model Fitting) ==========<\/span>
      \n# fit\u65b9\u6cd5\u5185\u90e8\u5b8c\u6210\u53c2\u6570w\u548cb\u7684\u8ba1\u7b97<\/span>
      \nmodel.<\/span>fit(<\/span>X,<\/span> y)<\/span><\/p>\n

      # ========== \u6b65\u9aa44: \u9884\u6d4b\u4e0e\u53c2\u6570\u83b7\u53d6 (Prediction & Inspection) ==========<\/span>
      \nw =<\/span> model.<\/span>coef_ # \u8fd4\u56de\u6570\u7ec4\u5f62\u5f0f，\u5373\u4f7f\u662f\u4e00\u5143\u56de\u5f52\u4e5f\u662f[w]<\/span>
      \nb =<\/span> model.<\/span>intercept_ # \u8fd4\u56de\u6807\u91cf<\/span>
      \npred =<\/span> model.<\/span>predict(<\/span>[<\/span>[<\/span>700<\/span>]<\/span>]<\/span>)<\/span> # \u9884\u6d4b\u8f93\u5165\u4e5f\u5fc5\u987b\u662f\u4e8c\u7ef4\u6570\u7ec4<\/span><\/p>\n

      print<\/span>(<\/span>f"\u2705 \u56de\u5f52\u65b9\u7a0b: y = <\/span>{<\/span>w[<\/span>0<\/span>]<\/span>:<\/span>.4f<\/span>}<\/span><\/span> * x + <\/span>{<\/span>b:<\/span>.4f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span>
      \nprint<\/span>(<\/span>f"\u2705 700\u5e73\u7c73\u623f\u5c4b\u9884\u6d4b\u5355\u4ef7: <\/span>{<\/span>pred[<\/span>0<\/span>]<\/span>:<\/span>.2f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span><\/p>\n

      2.3 \u5173\u952eAPI\u6df1\u5ea6\u89e3\u6790\u4e0e\u907f\u5751\u6307\u5357<\/h4>\n

      \u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d，\u6709\u51e0\u4e2a\u7ec6\u8282\u662f\u8003\u8bd5\u6263\u5206\u70b9\u548c\u5de5\u7a0bBug\u7684\u91cd\u707e\u533a，\u5fc5\u987b\u5f15\u8d77\u9ad8\u5ea6\u91cd\u89c6：<\/p>\n\nAPI\/\u64cd\u4f5c\u6b63\u786e\u7528\u6cd5\u9519\u8bef\u793a\u8303\u539f\u7406\u8bf4\u660e<\/tr>\n\n\n\n\n\n
      \u7279\u5f81\u5f62\u72b6<\/td>\nX.reshape(-1, 1)<\/td>\nX = np.array([…])<\/td>\nsklearn\u8981\u6c42\u7279\u5f81\u77e9\u9635\u4e25\u683c\u4e3a2D，\u4ee5\u517c\u5bb9\u591a\u7279\u5f81\u573a\u666f\u3002\u4e00\u7ef4\u6570\u7ec4\u4f1a\u5bfc\u81f4ValueError\u3002<\/td>\n<\/tr>\n
      \u9884\u6d4b\u8f93\u5165<\/td>\nmodel.predict([[700]])<\/td>\nmodel.predict([700])<\/td>\npredict\u671f\u671b\u63a5\u6536\u6837\u672c\u77e9\u9635，[[700]]\u8868\u793a1\u4e2a\u6837\u672c\u00d71\u4e2a\u7279\u5f81\u3002<\/td>\n<\/tr>\n
      \u7cfb\u6570\u83b7\u53d6<\/td>\nmodel.coef_[0]<\/td>\nmodel.coef_<\/td>\ncoef_\u59cb\u7ec8\u8fd4\u56de\u6570\u7ec4，\u6253\u5370\u65b9\u7a0b\u65f6\u9700\u7d22\u5f15\u53d6\u503c，\u5426\u5219\u8f93\u51fa\u5e26\u65b9\u62ec\u53f7\u3002<\/td>\n<\/tr>\n
      \u622a\u8ddd\u83b7\u53d6<\/td>\nmodel.intercept_<\/td>\nmodel.b_<\/td>\nsklearn\u7edf\u4e00\u547d\u540d\u4e3aintercept_，\u4e0d\u5b58\u5728b_\u5c5e\u6027\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \u26a0\ufe0f \u8b66\u544a：\u5728\u8003\u8bd5\u4e2d，\u5982\u679c\u9898\u76ee\u8981\u6c42\u201c\u624b\u5199\u68af\u5ea6\u4e0b\u964d\u201d\u800c\u975e\u8c03\u7528sklearn，\u8bf7\u52a1\u5fc5\u533a\u5206\u6279\u91cf\u68af\u5ea6\u4e0b\u964d（BGD）\u3001\u968f\u673a\u68af\u5ea6\u4e0b\u964d（SGD）\u4e0e\u5c0f\u6279\u91cf\u68af\u5ea6\u4e0b\u964d（Mini-batch GD） \u7684\u533a\u522b\u3002sklearn\u7684LinearRegression\u9ed8\u8ba4\u4f7f\u7528\u7684\u662f\u57fa\u4e8e\u77e9\u9635\u8fd0\u7b97\u7684\u89e3\u6790\u89e3（Normal Equation），\u5373<\/p>\n

      (<\/p>\n

      X<\/p>\n

      T<\/p>\n

      X<\/p>\n

      )<\/p>\n

      \u2212<\/p>\n

      1<\/p>\n

      X<\/p>\n

      T<\/p>\n

      y<\/p>\n

      (X^TX)^{-1}X^Ty<\/p>\n

      <\/span><\/span>(<\/span>X<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span>)<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>，\u800c\u975e\u8fed\u4ee3\u4f18\u5316\u3002\u53ea\u6709\u5f53\u4f7f\u7528SGDRegressor\u65f6\u624d\u662f\u68af\u5ea6\u4e0b\u964d\u6cd5\u30023<\/sup><\/p>\n

      2.4 \u7ed3\u679c\u53ef\u89c6\u5316\u4e0e\u6b8b\u5dee\u5206\u6790<\/h4>\n

      \u4ec5\u4ec5\u8f93\u51fa\u4e00\u4e2a\u9884\u6d4b\u503c\u662f\u4e0d\u591f\u7684，\u4f18\u79c0\u7684\u7b54\u5377\u6216\u5de5\u7a0b\u62a5\u544a\u5e94\u5f53\u5305\u542b\u53ef\u89c6\u5316\u9a8c\u8bc1\u3002\u4ee5\u4e0b\u4ee3\u7801\u5c55\u793a\u4e86\u5982\u4f55\u7ed8\u5236\u56de\u5f52\u7ebf\u4e0e\u6563\u70b9\u56fe，\u8fd9\u662f\u52a0\u5206\u9879：<\/p>\n

      import<\/span> matplotlib.<\/span>pyplot as<\/span> plt<\/p>\n

      # \u8bbe\u7f6e\u4e2d\u6587\u5b57\u4f53\u652f\u6301<\/span>
      \nplt.<\/span>rcParams[<\/span>'font.sans-serif'<\/span>]<\/span> =<\/span> [<\/span>'SimHei'<\/span>,<\/span> 'Arial Unicode MS'<\/span>]<\/span>
      \nplt.<\/span>rcParams[<\/span>'axes.unicode_minus'<\/span>]<\/span> =<\/span> False<\/span><\/p>\n

      plt.<\/span>figure(<\/span>figsize=<\/span>(<\/span>10<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
      \n# \u7ed8\u5236\u771f\u5b9e\u6570\u636e\u6563\u70b9<\/span>
      \nplt.<\/span>scatter(<\/span>X,<\/span> y,<\/span> color=<\/span>'royalblue'<\/span>,<\/span> s=<\/span>80<\/span>,<\/span> label=<\/span>'\u771f\u5b9e\u6837\u672c'<\/span>,<\/span> zorder=<\/span>5<\/span>)<\/span>
      \n# \u7ed8\u5236\u56de\u5f52\u7ebf<\/span>
      \nX_line =<\/span> np.<\/span>linspace(<\/span>X.<\/span>min<\/span>(<\/span>)<\/span>,<\/span> X.<\/span>max<\/span>(<\/span>)<\/span>,<\/span> 100<\/span>)<\/span>.<\/span>reshape(<\/span>–<\/span>1<\/span>,<\/span> 1<\/span>)<\/span>
      \ny_line =<\/span> model.<\/span>predict(<\/span>X_line)<\/span>
      \nplt.<\/span>plot(<\/span>X_line,<\/span> y_line,<\/span> color=<\/span>'crimson'<\/span>,<\/span> linewidth=<\/span>2<\/span>,<\/span> label=<\/span>f'\u62df\u5408\u76f4\u7ebf: y=<\/span>{<\/span>w[<\/span>0<\/span>]<\/span>:<\/span>.1f<\/span>}<\/span><\/span>x+<\/span>{<\/span>b:<\/span>.0f<\/span>}<\/span><\/span>'<\/span><\/span>)<\/span><\/p>\n

      plt.<\/span>xlabel(<\/span>'\u623f\u5c4b\u9762\u79ef (\u33a1)'<\/span>,<\/span> fontsize=<\/span>14<\/span>)<\/span>
      \nplt.<\/span>ylabel(<\/span>'\u5355\u4ef7 (\u5143\/\u33a1)'<\/span>,<\/span> fontsize=<\/span>14<\/span>)<\/span>
      \nplt.<\/span>title(<\/span>'\u4e00\u5143\u7ebf\u6027\u56de\u5f52：\u623f\u5c4b\u5355\u4ef7\u9884\u6d4b'<\/span>,<\/span> fontsize=<\/span>16<\/span>)<\/span>
      \nplt.<\/span>legend(<\/span>fontsize=<\/span>12<\/span>)<\/span>
      \nplt.<\/span>grid(<\/span>True<\/span>,<\/span> linestyle=<\/span>'–'<\/span>,<\/span> alpha=<\/span>0.7<\/span>)<\/span>
      \nplt.<\/span>tight_layout(<\/span>)<\/span>
      \nplt.<\/span>show(<\/span>)<\/span><\/p>\n

      \n

      \u4e09\u3001 \u903b\u8f91\u56de\u5f52：\u9e22\u5c3e\u82b1\u5206\u7c7b\u7684\u6df1\u5c42\u673a\u5236<\/h3>\n

      3.1 \u4ece\u56de\u5f52\u5230\u5206\u7c7b\u7684\u601d\u7ef4\u8dc3\u8fc1<\/h4>\n

      \u5c3d\u7ba1\u540d\u5b57\u91cc\u5e26\u6709\u201c\u56de\u5f52\u201d，\u4f46\u903b\u8f91\u56de\u5f52\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u5206\u7c7b\u7b97\u6cd5\u3002\u5b83\u4e4b\u6240\u4ee5\u88ab\u79f0\u4e3a\u201c\u56de\u5f52\u201d，\u662f\u56e0\u4e3a\u5b83\u6cbf\u7528\u4e86\u7ebf\u6027\u56de\u5f52\u7684\u7ebf\u6027\u7ec4\u5408\u90e8\u5206<\/p>\n

      z<\/p>\n

      =<\/p>\n

      w<\/p>\n

      T<\/p>\n

      x<\/p>\n

      +<\/p>\n

      b<\/p>\n

      z = w^Tx + b<\/p>\n

      <\/span><\/span>z<\/span><\/span>=<\/span><\/span><\/span><\/span>w<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>，\u4f46\u5728\u6b64\u57fa\u7840\u4e0a\u589e\u52a0\u4e86\u4e00\u4e2a\u975e\u7ebf\u6027\u7684Sigmoid\u6fc0\u6d3b\u51fd\u6570，\u5c06\u8fde\u7eed\u503c\u6620\u5c04\u5230<\/p>\n

      (<\/p>\n

      0<\/p>\n

      ,<\/p>\n

      1<\/p>\n

      )<\/p>\n

      (0, 1)<\/p>\n

      <\/span><\/span>(<\/span>0<\/span>,<\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span>\u533a\u95f4，\u4ece\u800c\u8d4b\u4e88\u8f93\u51fa\u201c\u6982\u7387\u201d\u7684\u8bed\u4e49\u3002<\/p>\n

      <\/p>\n

      P<\/p>\n

      (<\/p>\n

      y<\/p>\n

      =<\/p>\n

      1<\/p>\n

      \u2223<\/p>\n

      x<\/p>\n

      )<\/p>\n

      =<\/p>\n

      \u03c3<\/p>\n

      (<\/p>\n

      z<\/p>\n

      )<\/p>\n

      =<\/p>\n

      1<\/p>\n

      1<\/p>\n

      +<\/p>\n

      e<\/p>\n

      \u2212<\/p>\n

      z<\/p>\n

      P(y=1|x) = \\\\sigma(z) = \\\\frac{1}{1 + e^{-z}} <\/p>\n

      <\/span><\/span>P<\/span>(<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>1\u2223<\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03c3<\/span>(<\/span>z<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span>e<\/span><\/span>\u2212<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u8fd9\u4e00\u53d8\u6362\u89e3\u51b3\u4e86\u7ebf\u6027\u56de\u5f52\u7528\u4e8e\u5206\u7c7b\u65f6\u7684\u4e24\u5927\u81f4\u547d\u7f3a\u9677：\u4e00\u662f\u8f93\u51fa\u8303\u56f4\u4e0d\u53d7\u9650，\u65e0\u6cd5\u89e3\u91ca\u4e3a\u6982\u7387；\u4e8c\u662f\u5f02\u5e38\u70b9\u5bf9\u7ebf\u6027\u8fb9\u754c\u5f71\u54cd\u8fc7\u5927\u3002Sigmoid\u51fd\u6570\u7684\u9971\u548c\u7279\u6027\u5929\u7136\u5730\u6291\u5236\u4e86\u6781\u7aef\u503c\u7684\u5f71\u54cd\u30024<\/sup><\/p>\n

      3.2 \u5b8c\u6574\u5b9e\u6218\u4ee3\u7801\u4e0e\u53c2\u6570\u8c03\u4f18<\/h4>\n

      \u4e0b\u9762\u4ee5\u7ecf\u5178\u7684Iris\u6570\u636e\u96c6\u4e3a\u4f8b，\u5c55\u793a\u903b\u8f91\u56de\u5f52\u5728\u591a\u5206\u7c7b\u4efb\u52a1\u4e2d\u7684\u6807\u51c6\u6d41\u7a0b\u3002<\/p>\n

      import<\/span> numpy as<\/span> np
      \nfrom<\/span> sklearn import<\/span> datasets,<\/span> linear_model
      \nfrom<\/span> sklearn.<\/span>model_selection import<\/span> train_test_split
      \nfrom<\/span> sklearn.<\/span>metrics import<\/span> accuracy_score,<\/span> classification_report<\/p>\n

      # ========== 1. \u52a0\u8f7d\u4e0e\u63a2\u7d22\u6570\u636e ==========<\/span>
      \niris =<\/span> datasets.<\/span>load_iris(<\/span>)<\/span>
      \nX =<\/span> iris.<\/span>data # shape: (150, 4)<\/span>
      \ny =<\/span> iris.<\/span>target # shape: (150,), \u7c7b\u522b: 0, 1, 2<\/span><\/p>\n

      # ========== 2. \u5212\u5206\u6570\u636e\u96c6 (\u5173\u952e\u6b65\u9aa4) ==========<\/span>
      \n# random_state\u4fdd\u8bc1\u7ed3\u679c\u53ef\u590d\u73b0，test_size=0.2\u662f\u7ecf\u9a8c\u503c<\/span>
      \nX_train,<\/span> X_test,<\/span> y_train,<\/span> y_test =<\/span> train_test_split(<\/span>
      \n X,<\/span> y,<\/span> test_size=<\/span>0.2<\/span>,<\/span> random_state=<\/span>42<\/span>,<\/span> stratify=<\/span>y
      \n)<\/span><\/p>\n

      # ========== 3. \u6784\u5efa\u4e0e\u8bad\u7ec3\u6a21\u578b ==========<\/span>
      \n# C=1e5\u8868\u793a\u6781\u5f31\u7684\u6b63\u5219\u5316，\u8fd1\u4f3c\u4e8e\u65e0\u6b63\u5219\u5316\u7684\u6700\u5927\u4f3c\u7136\u4f30\u8ba1<\/span>
      \n# solver='lbfgs'\u9002\u5408\u4e2d\u5c0f\u89c4\u6a21\u6570\u636e\u96c6，multinomial\u652f\u6301\u591a\u5206\u7c7b<\/span>
      \nmodel =<\/span> linear_model.<\/span>LogisticRegression(<\/span>
      \n C=<\/span>1e5<\/span>,<\/span>
      \n solver=<\/span>'lbfgs'<\/span>,<\/span>
      \n multi_class=<\/span>'multinomial'<\/span>,<\/span>
      \n max_iter=<\/span>1000<\/span>
      \n)<\/span>
      \nmodel.<\/span>fit(<\/span>X_train,<\/span> y_train)<\/span><\/p>\n

      # ========== 4. \u5168\u9762\u8bc4\u4f30 ==========<\/span>
      \ny_pred =<\/span> model.<\/span>predict(<\/span>X_test)<\/span>
      \nacc =<\/span> accuracy_score(<\/span>y_test,<\/span> y_pred)<\/span><\/p>\n

      print<\/span>(<\/span>f"🎯 \u6d4b\u8bd5\u96c6\u51c6\u786e\u7387: <\/span>{<\/span>acc:<\/span>.4f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span>
      \nprint<\/span>(<\/span>"\\\\n📊 \u8be6\u7ec6\u5206\u7c7b\u62a5\u544a:"<\/span>)<\/span>
      \nprint<\/span>(<\/span>classification_report(<\/span>y_test,<\/span> y_pred,<\/span> target_names=<\/span>iris.<\/span>target_names)<\/span>)<\/span><\/p>\n

      3.3 \u8d85\u53c2\u6570C\u7684\u6b63\u5219\u5316\u672c\u8d28<\/h4>\n

      \u5728\u903b\u8f91\u56de\u5f52\u4e2d，\u8d85\u53c2\u6570<\/p>\n

      C<\/p>\n

      C<\/p>\n

      <\/span><\/span>C<\/span><\/span><\/span><\/span><\/span>\u662f\u6700\u5e38\u8003\u7684\u77e5\u8bc6\u70b9\u4e4b\u4e00\u3002\u8bb8\u591a\u540c\u5b66\u8bef\u4ee5\u4e3a<\/p>\n

      C<\/p>\n

      C<\/p>\n

      <\/span><\/span>C<\/span><\/span><\/span><\/span><\/span>\u8d8a\u5927\u6b63\u5219\u5316\u8d8a\u5f3a，\u4e8b\u5b9e\u6070\u6070\u76f8\u53cd\u3002<\/p>\n

      <\/p>\n

      C<\/p>\n

      C<\/p>\n

      <\/span><\/span>C<\/span><\/span><\/span><\/span><\/span>\u662f\u6b63\u5219\u5316\u5f3a\u5ea6\u7684\u5012\u6570\u3002sklearn\u7684\u903b\u8f91\u56de\u5f52\u76ee\u6807\u51fd\u6570\u5b9e\u9645\u4e0a\u662f：<\/p>\n

      <\/p>\n

      min<\/p>\n

      \u2061<\/p>\n

      w<\/p>\n

      (<\/p>\n

      1<\/p>\n

      2<\/p>\n

      \u2223<\/p>\n

      \u2223<\/p>\n

      w<\/p>\n

      \u2223<\/p>\n

      \u2223<\/p>\n

      2<\/p>\n

      +<\/p>\n

      C<\/p>\n

      \u2211<\/p>\n

      i<\/p>\n

      =<\/p>\n

      1<\/p>\n

      n<\/p>\n

      Loss<\/p>\n

      (<\/p>\n

      y<\/p>\n

      i<\/p>\n

      ,<\/p>\n

      f<\/p>\n

      (<\/p>\n

      x<\/p>\n

      i<\/p>\n

      )<\/p>\n

      )<\/p>\n

      )<\/p>\n

      \\\\min_w \\\\left( \\\\frac{1}{2}||w||^2 + C \\\\sum_{i=1}^{n} \\\\text{Loss}(y_i, f(x_i)) \\\\right) <\/p>\n

      <\/span><\/span><\/span>w<\/span><\/span><\/span><\/span>min<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223\u2223<\/span>w<\/span>\u2223<\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>C<\/span><\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>Loss<\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>f<\/span>(<\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>))<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u6216\u8005\u7b49\u4ef7\u5730\u5199\u4f5c\u66f4\u5e38\u89c1\u7684\u5f62\u5f0f：<\/p>\n

      <\/p>\n

      min<\/p>\n

      \u2061<\/p>\n

      w<\/p>\n

      (<\/p>\n

      \u2223<\/p>\n

      \u2223<\/p>\n

      w<\/p>\n

      \u2223<\/p>\n

      \u2223<\/p>\n

      2<\/p>\n

      +<\/p>\n

      1<\/p>\n

      C<\/p>\n

      \u2211<\/p>\n

      i<\/p>\n

      =<\/p>\n

      1<\/p>\n

      n<\/p>\n

      Loss<\/p>\n

      (<\/p>\n

      y<\/p>\n

      i<\/p>\n

      ,<\/p>\n

      f<\/p>\n

      (<\/p>\n

      x<\/p>\n

      i<\/p>\n

      )<\/p>\n

      )<\/p>\n

      )<\/p>\n

      \\\\min_w \\\\left( ||w||^2 + \\\\frac{1}{C} \\\\sum_{i=1}^{n} \\\\text{Loss}(y_i, f(x_i)) \\\\right) <\/p>\n

      <\/span><\/span><\/span>w<\/span><\/span><\/span><\/span>min<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>\u2223\u2223<\/span>w<\/span>\u2223<\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>Loss<\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>f<\/span>(<\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>))<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u7531\u6b64\u53ef\u89c1：<\/p>\n

        \n
      • \n

        C<\/p>\n

        C<\/p>\n

        <\/span><\/span>C<\/span><\/span><\/span><\/span><\/span>\u503c\u5f88\u5927（\u5982<\/p>\n

        10<\/p>\n

        5<\/p>\n

        10^5<\/p>\n

        <\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）：\u6b63\u5219\u5316\u9879\u6743\u91cd\u8d8b\u8fd1\u4e8e0，\u6a21\u578b\u503e\u5411\u4e8e\u5b8c\u7f8e\u62df\u5408\u8bad\u7ec3\u6570\u636e，\u5bb9\u6613\u8fc7\u62df\u5408\u3002<\/li>\n

      • \n

        C<\/p>\n

        C<\/p>\n

        <\/span><\/span>C<\/span><\/span><\/span><\/span><\/span>\u503c\u5f88\u5c0f（\u5982<\/p>\n

        0.01<\/p>\n

        0.01<\/p>\n

        <\/span><\/span>0.01<\/span><\/span><\/span><\/span><\/span>）：\u6b63\u5219\u5316\u9879\u4e3b\u5bfc\u4f18\u5316\u76ee\u6807，\u5f3a\u5236\u6743\u91cd<\/p>\n

        w<\/p>\n

        w<\/p>\n

        <\/span><\/span>w<\/span><\/span><\/span><\/span><\/span>\u8d8b\u8fd1\u4e8e0，\u6a21\u578b\u66f4\u7b80\u5355，\u5bb9\u6613\u6b20\u62df\u5408\u3002<\/li>\n<\/ul>\n

        💡 \u5c0f\u8d34\u58eb：\u5728\u8003\u8bd5\u4e2d\u82e5\u672a\u6307\u5b9a<\/p>\n

        C<\/p>\n

        C<\/p>\n

        <\/span><\/span>C<\/span><\/span><\/span><\/span><\/span>\u503c，\u5efa\u8bae\u8bbe\u7f6e\u4e3a1.0（\u9ed8\u8ba4\u503c）\u62161e5（\u6a21\u62df\u6807\u51c6\u903b\u8f91\u56de\u5f52）\u3002\u82e5\u9898\u76ee\u660e\u786e\u8981\u6c42\u201c\u9632\u6b62\u8fc7\u62df\u5408\u201d，\u5219\u5e94\u5c1d\u8bd5\u8f83\u5c0f\u7684<\/p>\n

        C<\/p>\n

        C<\/p>\n

        <\/span><\/span>C<\/span><\/span><\/span><\/span><\/span>\u503c\u6216\u4f7f\u7528\u4ea4\u53c9\u9a8c\u8bc1\u9009\u62e9\u6700\u4f18<\/p>\n

        C<\/p>\n

        C<\/p>\n

        <\/span><\/span>C<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

        3.4 \u591a\u5206\u7c7b\u7b56\u7565：OvR vs Multinomial<\/h4>\n

        \u903b\u8f91\u56de\u5f52\u539f\u751f\u662f\u4e8c\u5206\u7c7b\u5668，\u5904\u7406\u591a\u5206\u7c7b\u95ee\u9898\u65f6\u4e3b\u8981\u6709\u4e24\u79cd\u7b56\u7565，\u8fd9\u4e5f\u662f\u7b80\u7b54\u9898\u7684\u9ad8\u9891\u8003\u70b9：<\/p>\n

      • One-vs-Rest (OvR)：\u8bad\u7ec3\n

        K<\/p>\n

        K<\/p>\n

        <\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>\u4e2a\u4e8c\u5206\u7c7b\u5668，\u6bcf\u4e2a\u5206\u7c7b\u5668\u533a\u5206\u201c\u7b2c<\/p>\n

        k<\/p>\n

        k<\/p>\n

        <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u7c7b\u201d\u4e0e\u201c\u975e\u7b2c<\/p>\n

        k<\/p>\n

        k<\/p>\n

        <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u7c7b\u201d\u3002\u9884\u6d4b\u65f6\u53d6\u7f6e\u4fe1\u5ea6\u6700\u9ad8\u7684\u7c7b\u522b\u3002\u4f18\u70b9\u662f\u7b80\u5355\u5e76\u884c，\u7f3a\u70b9\u662f\u7c7b\u522b\u4e0d\u5e73\u8861\u65f6\u6548\u679c\u5dee\u3002<\/li>\n

      • Multinomial (Softmax)：\u76f4\u63a5\u4f7f\u7528Softmax\u51fd\u6570\u63a8\u5e7f\u5230\u591a\u7c7b，\u8054\u5408\u4f18\u5316\u6240\u6709\u7c7b\u522b\u7684\u53c2\u6570\u3002\u7406\u8bba\u4e0a\u66f4\u4f18，\u4f46\u8ba1\u7b97\u91cf\u7a0d\u5927\u3002sklearn\u4e2d\u901a\u8fc7multi_class='multinomial'\u542f\u7528\u3002<\/li>\n
        \n

        \u56db\u3001 \u6838\u5fc3\u77e5\u8bc6\u56fe\u8c31：\u7ebf\u6027\u56de\u5f52\u4e0e\u903b\u8f91\u56de\u5f52\u7684\u5bf9\u7acb\u7edf\u4e00<\/h3>\n

        \u4e3a\u4e86\u5e2e\u52a9\u5927\u5bb6\u5728\u8111\u6d77\u4e2d\u5efa\u7acb\u6e05\u6670\u7684\u77e5\u8bc6\u7ed3\u6784，\u4e0b\u8868\u4ece\u591a\u4e2a\u7ef4\u5ea6\u5bf9\u4e24\u4e2a\u6a21\u578b\u8fdb\u884c\u4e86\u6df1\u5ea6\u5bf9\u6bd4\u3002\u8fd9\u5f20\u8868\u5efa\u8bae\u80cc\u8bf5，\u8db3\u4ee5\u5e94\u5bf9\u5927\u90e8\u5206\u6bd4\u8f83\u7c7b\u7b80\u7b54\u9898\u3002<\/p>\n\n\u6bd4\u8f83\u7ef4\u5ea6\u7ebf\u6027\u56de\u5f52 (Linear Regression)\u903b\u8f91\u56de\u5f52 (Logistic Regression)<\/tr>\n\n\n\n\n\n\n\n\n\n\n
        \u4efb\u52a1\u7c7b\u578b<\/td>\n\u56de\u5f52（\u8fde\u7eed\u503c\u9884\u6d4b）<\/td>\n\u5206\u7c7b（\u79bb\u6563\u6807\u7b7e\u9884\u6d4b）<\/td>\n<\/tr>\n
        \u8f93\u51fa\u542b\u4e49<\/td>\n\u5177\u4f53\u7684\u6570\u503c\u9884\u6d4b<\/td>\n\u5c5e\u4e8e\u67d0\u7c7b\u7684\u6982\u7387<\/td>\n<\/tr>\n
        \u6fc0\u6d3b\u51fd\u6570<\/td>\n\u6052\u7b49\u6620\u5c04 <\/p>\n

        f<\/p>\n

        (<\/p>\n

        z<\/p>\n

        )<\/p>\n

        =<\/p>\n

        z<\/p>\n

        f(z)=z<\/p>\n

        <\/span><\/span>f<\/span>(<\/span>z<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>z<\/span><\/span><\/span><\/span><\/span><\/td>\n

        		Sigmoid \/ Softmax<\/td>\n<\/tr>\n
        \u635f\u5931\u51fd\u6570<\/td>\n\u5747\u65b9\u8bef\u5dee MSE<\/td>\n\u4ea4\u53c9\u71b5 Cross-Entropy<\/td>\n<\/tr>\n
        \u4f18\u5316\u65b9\u6cd5<\/td>\n\u89e3\u6790\u89e3 \/ BGD \/ SGD<\/td>\nBGD \/ L-BFGS \/ SGD (\u65e0\u89e3\u6790\u89e3)<\/td>\n<\/tr>\n
        \u5bf9\u5f02\u5e38\u503c\u654f\u611f\u5ea6<\/td>\n\u9ad8（\u5e73\u65b9\u653e\u5927\u4e86\u8bef\u5dee）<\/td>\n\u4f4e（Sigmoid\u9971\u548c\u533a\u6291\u5236\u68af\u5ea6）<\/td>\n<\/tr>\n
        \u6b63\u5219\u5316\u53d8\u4f53<\/td>\nRidge(L2), Lasso(L1), ElasticNet<\/td>\n\u5185\u7f6eL1\/L2，\u7531\u53c2\u6570C\u63a7\u5236<\/td>\n<\/tr>\n
        \u51b3\u7b56\u8fb9\u754c<\/td>\n\u8d85\u5e73\u9762（\u9608\u503c\u9700\u81ea\u5b9a\u4e49）<\/td>\n\u8d85\u5e73\u9762（\u9ed8\u8ba4\u9608\u503c0.5）<\/td>\n<\/tr>\n
        sklearn\u7c7b\u540d<\/td>\nLinearRegression<\/td>\nLogisticRegression<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        4.1 \u635f\u5931\u51fd\u6570\u7684\u51e0\u4f55\u610f\u4e49<\/h4>\n

        \u7406\u89e3\u635f\u5931\u51fd\u6570\u662f\u7406\u89e3\u6a21\u578b\u884c\u4e3a\u7684\u5173\u952e\u3002<\/p>\n

          \n
        • MSE\u7684\u635f\u5931\u66f2\u9762：\u5bf9\u4e8e\u7ebf\u6027\u56de\u5f52，MSE\u5173\u4e8e\u53c2\u6570\n

          w<\/p>\n

          w<\/p>\n

          <\/span><\/span>w<\/span><\/span><\/span><\/span><\/span>\u662f\u4e00\u4e2a\u51f8\u4e8c\u6b21\u51fd\u6570，\u5448\u5b8c\u7f8e\u7684\u7897\u72b6，\u53ea\u6709\u4e00\u4e2a\u5168\u5c40\u6700\u5c0f\u503c\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u7ebf\u6027\u56de\u5f52\u53ef\u4ee5\u7528\u89e3\u6790\u89e3\u4e00\u6b65\u5230\u4f4d\u7684\u539f\u56e0\u3002<\/li>\n

        • \u4ea4\u53c9\u71b5\u7684\u635f\u5931\u66f2\u9762：\u5bf9\u4e8e\u903b\u8f91\u56de\u5f52，\u867d\u7136\u5f15\u5165\u4e86\u975e\u7ebf\u6027Sigmoid，\u4f46\u4ea4\u53c9\u71b5\u635f\u5931\u5173\u4e8e\u53c2\u6570\n

          w<\/p>\n

          w<\/p>\n

          <\/span><\/span>w<\/span><\/span><\/span><\/span><\/span>\u4f9d\u7136\u662f\u51f8\u51fd\u6570\u3002\u8fd9\u4fdd\u8bc1\u4e86\u68af\u5ea6\u4e0b\u964d\u4e00\u5b9a\u80fd\u6536\u655b\u5230\u5168\u5c40\u6700\u4f18\u3002\u6ce8\u610f：\u5982\u679c\u4f7f\u7528MSE\u4f5c\u4e3a\u903b\u8f91\u56de\u5f52\u7684\u635f\u5931\u51fd\u6570，\u635f\u5931\u66f2\u9762\u5c06\u53d8\u4e3a\u975e\u51f8，\u5bfc\u81f4\u68af\u5ea6\u4e0b\u964d\u9677\u5165\u5c40\u90e8\u6700\u4f18，\u56e0\u6b64\u903b\u8f91\u56de\u5f52\u7edd\u4e0d\u80fd\u7528MSE\u30025<\/sup><\/li>\n<\/ul>\n

          \n

          \u4e94\u3001 \u8003\u573a\u751f\u5b58\u6307\u5357：\u5e38\u89c1\u9677\u9631\u4e0e\u8c03\u8bd5\u6280\u5de7<\/h3>\n

          \u6839\u636e\u5386\u5e74\u9605\u5377\u7ecf\u9a8c，\u4ee5\u4e0b\u56db\u4e2a\u95ee\u9898\u662f\u5b66\u751f\u5931\u5206\u7684\u91cd\u707e\u533a\u3002\u8bf7\u5728\u8003\u524d\u9010\u4e00\u81ea\u67e5\u3002<\/p>\n

          \u274c \u9677\u96311：\u7ef4\u5ea6\u707e\u96be（Shape Mismatch）<\/h4>\n

          \u8fd9\u662f\u65b0\u624b\u6700\u5e38\u9047\u5230\u7684\u62a5\u9519\u3002sklearn\u7684\u8bbe\u8ba1\u539f\u5219\u662f\u201c\u4e07\u7269\u7686\u77e9\u9635\u201d\u3002<\/p>\n

            \n
          • \u75c7\u72b6：ValueError: Expected 2D array, got 1D array instead<\/li>\n
          • \u75c5\u56e0：\u4f20\u5165\u4e86\u4e00\u7ef4\u6570\u7ec4\u7ed9fit\u6216predict\u3002<\/li>\n
          • \u5904\u65b9：\u6c38\u8fdc\u4f7f\u7528reshape(-1, 1)\u5c06\u5355\u7279\u5f81\u8f6c\u6362\u4e3a\u5217\u5411\u91cf；\u4f7f\u7528reshape(1, -1)\u5c06\u5355\u6837\u672c\u8f6c\u6362\u4e3a\u884c\u5411\u91cf\u3002<\/li>\n<\/ul>\n

            \u274c \u9677\u96312：\u6570\u636e\u6cc4\u9732（Data Leakage）<\/h4>\n
              \n
            • \u75c7\u72b6：\u8bad\u7ec3\u96c6\u51c6\u786e\u738799%，\u6d4b\u8bd5\u96c6\u51c6\u786e\u738760%\u3002<\/li>\n
            • \u75c5\u56e0：\u5728\u5212\u5206\u6570\u636e\u96c6\u4e4b\u524d\u8fdb\u884c\u4e86\u5168\u5c40\u6807\u51c6\u5316\/\u5f52\u4e00\u5316，\u5bfc\u81f4\u6d4b\u8bd5\u96c6\u7684\u7edf\u8ba1\u4fe1\u606f\u6cc4\u9732\u5230\u4e86\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u3002<\/li>\n
            • \u5904\u65b9：\u5148split，\u518dtransform\u3002\u6807\u51c6\u5316\u5668\u53ea\u80fd\u5728\u8bad\u7ec3\u96c6\u4e0afit，\u7136\u540e\u5206\u522btransform\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u3002<\/li>\n<\/ul>\n

              \u274c \u9677\u96313：\u6df7\u6dc6\u8bc4\u4f30\u6307\u6807<\/h4>\n
                \n
              • \u75c7\u72b6：\u5728\u4e0d\u5e73\u8861\u6570\u636e\u96c6\u4e0a\u53ea\u770bAccuracy\u3002<\/li>\n
              • \u75c5\u56e0：\u5f53\u6b63\u8d1f\u6837\u672c\u6bd4\u4f8b\u4e3a1:99\u65f6，\u5168\u731c\u8d1f\u6837\u672c\u4e5f\u670999%\u51c6\u786e\u7387，\u4f46\u8fd9\u6beb\u65e0\u610f\u4e49\u3002<\/li>\n
              • \u5904\u65b9：\u5206\u7c7b\u4efb\u52a1\u5fc5\u770bPrecision\u3001Recall\u3001F1-Score\u53caConfusion Matrix\u3002\u56de\u5f52\u4efb\u52a1\u5173\u6ce8MSE\u3001RMSE\u3001MAE\u53ca\n

                R<\/p>\n

                2<\/p>\n

                R^2<\/p>\n

                <\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5206\u6570\u3002<\/li>\n<\/ul>\n

                \u2705 \u8c03\u8bd5\u795e\u5668：\u68c0\u67e5\u4e2d\u95f4\u72b6\u6001<\/h4>\n

                \u5f53\u6a21\u578b\u8868\u73b0\u4e0d\u7b26\u5408\u9884\u671f\u65f6，\u4e0d\u8981\u76f2\u76ee\u8c03\u53c2，\u8bf7\u6309\u4ee5\u4e0b\u987a\u5e8f\u6392\u67e5：<\/p>\n

              • \u6253\u5370X.shape, y.shape\u786e\u8ba4\u7ef4\u5ea6\u3002<\/li>\n
              • \u6253\u5370y.unique()\u786e\u8ba4\u6807\u7b7e\u662f\u5426\u6b63\u786e\u7f16\u7801（\u59820\/1\u800c\u975e1\/2）\u3002<\/li>\n
              • \u68c0\u67e5\u662f\u5426\u5b58\u5728NaN\u6216Inf\u503c\u3002<\/li>\n
              • \u67e5\u770bmodel.coef_\u7684\u91cf\u7ea7，\u82e5\u6743\u91cd\u8fc7\u5927\u8bf4\u660e\u672a\u6807\u51c6\u5316\u6216\u6b63\u5219\u5316\u592a\u5f31\u3002<\/li>\n
                \n

                \u516d\u3001 \u8fdb\u9636\u601d\u8003：\u4ece\u4f20\u7edfML\u5230\u6df1\u5ea6\u5b66\u4e60\u7684\u6865\u6881<\/h3>\n

                \u4e3a\u4e86\u8ba9\u8fd9\u7bc7\u590d\u4e60\u7b14\u8bb0\u5177\u6709\u66f4\u957f\u8fdc\u7684\u4ef7\u503c，\u6211\u4eec\u9700\u8981\u601d\u8003：\u8fd9\u4e24\u4e2a\u6a21\u578b\u4e0e\u6df1\u5ea6\u5b66\u4e60\u6709\u4f55\u5173\u8054？<\/p>\n

              • \u903b\u8f91\u56de\u5f52 = \u5355\u5c42\u795e\u7ecf\u7f51\u7edc：\u4e00\u4e2a\u6ca1\u6709\u9690\u85cf\u5c42\u3001\u8f93\u51fa\u5c42\u4f7f\u7528Sigmoid\/Softmax\u6fc0\u6d3b\u51fd\u6570\u3001\u635f\u5931\u51fd\u6570\u4e3a\u4ea4\u53c9\u71b5\u7684\u795e\u7ecf\u7f51\u7edc，\u5c31\u662f\u903b\u8f91\u56de\u5f52\u3002\u7406\u89e3\u4e86\u903b\u8f91\u56de\u5f52，\u5c31\u7406\u89e3\u4e86\u6df1\u5ea6\u5b66\u4e60\u5206\u7c7b\u4efb\u52a1\u7684\u201c\u6700\u540e\u4e00\u516c\u91cc\u201d\u3002<\/li>\n
              • \u7279\u5f81\u5de5\u7a0b\u7684\u81ea\u52a8\u5316：\u7ebf\u6027\u6a21\u578b\u4f9d\u8d56\u4eba\u5de5\u6784\u9020\u7279\u5f81（\u5982\u591a\u9879\u5f0f\u3001\u4ea4\u4e92\u9879）\u3002\u6df1\u5ea6\u5b66\u4e60\u901a\u8fc7\u591a\u5c42\u975e\u7ebf\u6027\u53d8\u6362\u81ea\u52a8\u5b66\u4e60\u9ad8\u9636\u7279\u5f81\u8868\u793a，\u672c\u8d28\u4e0a\u662f\u7528\u7b97\u529b\u6362\u53d6\u4e86\u7279\u5f81\u5de5\u7a0b\u7684\u4eba\u529b\u3002<\/li>\n
              • \u6b63\u5219\u5316\u7684\u4f20\u627f：L2\u6b63\u5219\u5316\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d\u88ab\u79f0\u4e3aWeight Decay，L1\u6b63\u5219\u5316\u5bf9\u5e94\u7a00\u758f\u6027\u7ea6\u675f\u3002Dropout\u3001BatchNorm\u7b49\u73b0\u4ee3\u6280\u672f，\u90fd\u53ef\u4ee5\u770b\u4f5c\u662f\u5bf9\u4f20\u7edf\u6b63\u5219\u5316\u601d\u60f3\u7684\u6f14\u8fdb\u3002<\/li>\n

                📌 \u6838\u5fc3\u8981\u70b9：\u4e0d\u8981\u628a\u7ebf\u6027\u56de\u5f52\u548c\u903b\u8f91\u56de\u5f52\u89c6\u4e3a\u201c\u8fc7\u65f6\u201d\u7684\u6280\u672f\u3002\u5728\u8868\u683c\u6570\u636e\u3001\u5c0f\u6837\u672c\u573a\u666f\u3001\u53ef\u89e3\u91ca\u6027\u8981\u6c42\u9ad8\u7684\u4e1a\u52a1\u4e2d，\u5b83\u4eec\u4f9d\u7136\u662f\u9996\u9009\u3002\u6df1\u5ea6\u5b66\u4e60\u5e76\u975e\u4e07\u80fd\u94a5\u5319，\u624e\u5b9e\u7684\u53e4\u5178ML\u529f\u5e95\u624d\u662f\u533a\u5206\u201c\u8c03\u5305\u4fa0\u201d\u4e0e\u201c\u7b97\u6cd5\u5de5\u7a0b\u5e08\u201d\u7684\u5206\u6c34\u5cad\u3002<\/p>\n

                \n

                \u4e03\u3001 FAQ：\u9ad8\u9891\u7591\u96be\u95ee\u9898\u89e3\u7b54<\/h3>\n

                \u4ee5\u4e0b\u95ee\u9898\u6309\u201c\u641c\u7d22\u70ed\u5ea6 \u00d7 \u8bfb\u8005\u7126\u8651\u6743\u91cd\u201d\u7efc\u5408\u6392\u5e8f，\u8986\u76d6\u4e86\u4ece\u5907\u8003\u5230\u5b9e\u6218\u7684\u5178\u578b\u56f0\u60d1\u3002<\/p>\n

                Q1: \u903b\u8f91\u56de\u5f52\u4e3a\u4ec0\u4e48\u4e0d\u53eb\u201c\u903b\u8f91\u5206\u7c7b\u201d？ A: \u5386\u53f2\u539f\u56e0\u3002\u8be5\u6a21\u578b\u6700\u65e9\u7531\u7edf\u8ba1\u5b66\u5bb6David Cox\u57281958\u5e74\u63d0\u51fa，\u7528\u4e8e\u63cf\u8ff0\u751f\u7269\u751f\u957f\u66f2\u7ebf，\u5176\u6838\u5fc3\u662fLogit\u53d8\u6362（\u5bf9\u6570\u51e0\u7387），\u5c5e\u4e8e\u5e7f\u4e49\u7ebf\u6027\u6a21\u578b（GLM）\u5bb6\u65cf\u3002\u5728\u7edf\u8ba1\u5b66\u4f20\u7edf\u4e2d，\u8fd9\u7c7b\u6a21\u578b\u7edf\u79f0\u4e3a\u201c\u56de\u5f52\u201d\u3002\u867d\u7136\u73b0\u4ee3\u673a\u5668\u5b66\u4e60\u5c06\u5176\u7528\u4e8e\u5206\u7c7b，\u4f46\u540d\u79f0\u6cbf\u7528\u81f3\u4eca\u30026<\/sup><\/p>\n

                Q2: \u4ec0\u4e48\u65f6\u5019\u8be5\u7528\u7ebf\u6027\u56de\u5f52，\u4ec0\u4e48\u65f6\u5019\u8be5\u7528\u903b\u8f91\u56de\u5f52？ A: \u770b\u6807\u7b7e<\/p>\n

                y<\/p>\n

                y<\/p>\n

                <\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u7684\u7c7b\u578b\u3002\u82e5<\/p>\n

                y<\/p>\n

                y<\/p>\n

                <\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u662f\u8fde\u7eed\u6570\u503c（\u5982\u623f\u4ef7\u3001\u6e29\u5ea6\u3001\u9500\u91cf），\u7528\u7ebf\u6027\u56de\u5f52；\u82e5<\/p>\n

                y<\/p>\n

                y<\/p>\n

                <\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u662f\u79bb\u6563\u7c7b\u522b（\u5982\u662f\u5426\u60a3\u75c5\u3001\u732b\u72d7\u8bc6\u522b\u3001\u60c5\u611f\u503e\u5411），\u7528\u903b\u8f91\u56de\u5f52\u3002\u5207\u52ff\u7528\u7ebf\u6027\u56de\u5f52\u505a\u5206\u7c7b，\u56e0\u4e3a\u5176\u8f93\u51fa\u65e0\u754c\u4e14\u5bf9\u5f02\u5e38\u503c\u654f\u611f\u3002<\/p>\n

                Q3: sklearn\u7684LogisticRegression\u9ed8\u8ba4\u6709\u6b63\u5219\u5316\u5417？ A: \u662f\u7684\u3002\u8fd9\u4e0e\u8bb8\u591a\u6559\u79d1\u4e66\u4e0a\u7684\u201c\u6807\u51c6\u903b\u8f91\u56de\u5f52\u201d\u4e0d\u540c\u3002sklearn\u9ed8\u8ba4\u4f7f\u7528L2\u6b63\u5219\u5316，\u4e14<\/p>\n

                C<\/p>\n

                =<\/p>\n

                1.0<\/p>\n

                C=1.0<\/p>\n

                <\/span><\/span>C<\/span><\/span>=<\/span><\/span><\/span><\/span>1.0<\/span><\/span><\/span><\/span><\/span>\u3002\u82e5\u60f3\u590d\u73b0\u6559\u79d1\u4e66\u4e0a\u7684\u65e0\u6b63\u5219\u5316\u7248\u672c，\u9700\u8bbe\u7f6eC=1e5\u6216\u66f4\u5927\u3002\u8fd9\u4e00\u70b9\u5728\u590d\u73b0\u5b9e\u9a8c\u7ed3\u679c\u65f6\u6781\u6613\u8e29\u5751\u3002<\/p>\n

                Q4: \u4e3a\u4ec0\u4e48\u6211\u7684\u903b\u8f91\u56de\u5f52\u51c6\u786e\u7387\u5f88\u4f4e，\u4f46loss\u5374\u5728\u4e0b\u964d？ A: \u53ef\u80fd\u539f\u56e0\u5305\u62ec：\u2460 \u9608\u503c0.5\u4e0d\u9002\u5408\u5f53\u524d\u6570\u636e\u5206\u5e03（\u9700\u8c03\u6574\u9608\u503c）；\u2461 \u7c7b\u522b\u4e25\u91cd\u4e0d\u5e73\u8861（\u9700\u4f7f\u7528class_weight=\u2018balanced\u2019）；\u2462 \u7279\u5f81\u672a\u6807\u51c6\u5316\u5bfc\u81f4\u6536\u655b\u7f13\u6162；\u2463 \u6a21\u578b\u6b20\u62df\u5408，\u9700\u589e\u52a0\u7279\u5f81\u6216\u51cf\u5c0f\u6b63\u5219\u5316\u5f3a\u5ea6<\/p>\n

                C<\/p>\n

                C<\/p>\n

                <\/span><\/span>C<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

                Q5: \u8003\u8bd5\u4e2d\u8981\u6c42\u624b\u63a8\u68af\u5ea6\u4e0b\u964d，\u516c\u5f0f\u8bb0\u4e0d\u4f4f\u600e\u4e48\u529e？ A: \u8bb0\u4f4f\u6838\u5fc3\u7ed3\u6784：\u65b0\u53c2\u6570 = \u65e7\u53c2\u6570 – \u5b66\u4e60\u7387 \u00d7 \u68af\u5ea6\u3002\u5bf9\u4e8e\u7ebf\u6027\u56de\u5f52MSE，\u68af\u5ea6\u662f\u201c\u8bef\u5dee\u00d7\u7279\u5f81\u201d\u7684\u5747\u503c；\u5bf9\u4e8e\u903b\u8f91\u56de\u5f52\u4ea4\u53c9\u71b5，\u68af\u5ea6\u5f62\u5f0f\u60ca\u4eba\u5730\u76f8\u4f3c，\u53ea\u662f\u201c\u8bef\u5dee\u201d\u53d8\u6210\u4e86\u201c\u9884\u6d4b\u6982\u7387-\u771f\u5b9e\u6807\u7b7e\u201d\u3002\u8fd9\u79cd\u5f62\u5f0f\u4e0a\u7684\u7edf\u4e00\u6027\u4e0d\u662f\u5de7\u5408，\u800c\u662f\u6307\u6570\u65cf\u5206\u5e03\u7684\u4f18\u826f\u6027\u8d28\u51b3\u5b9a\u7684\u3002<\/p>\n

                \n

                \u516b\u3001 \u9644\u5f55：\u53ef\u89c6\u5316\u8f85\u52a9\u7406\u89e3<\/h3>\n

                A.1 Sklearn\u5efa\u6a21\u5168\u6d41\u7a0b\u56fe<\/h4>\n

                #mermaid-svg-ue4jtI5JWiozbGfd{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-ue4jtI5JWiozbGfd .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-ue4jtI5JWiozbGfd .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-ue4jtI5JWiozbGfd .error-icon{fill:#552222;}#mermaid-svg-ue4jtI5JWiozbGfd .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-ue4jtI5JWiozbGfd .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-ue4jtI5JWiozbGfd .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-ue4jtI5JWiozbGfd .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-ue4jtI5JWiozbGfd .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-ue4jtI5JWiozbGfd .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-ue4jtI5JWiozbGfd .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-ue4jtI5JWiozbGfd .marker{fill:#333333;stroke:#333333;}#mermaid-svg-ue4jtI5JWiozbGfd .marker.cross{stroke:#333333;}#mermaid-svg-ue4jtI5JWiozbGfd svg{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-ue4jtI5JWiozbGfd p{margin:0;}#mermaid-svg-ue4jtI5JWiozbGfd .label{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;color:#333;}#mermaid-svg-ue4jtI5JWiozbGfd .cluster-label text{fill:#333;}#mermaid-svg-ue4jtI5JWiozbGfd .cluster-label span{color:#333;}#mermaid-svg-ue4jtI5JWiozbGfd .cluster-label span p{background-color:transparent;}#mermaid-svg-ue4jtI5JWiozbGfd .label text,#mermaid-svg-ue4jtI5JWiozbGfd span{fill:#333;color:#333;}#mermaid-svg-ue4jtI5JWiozbGfd .node rect,#mermaid-svg-ue4jtI5JWiozbGfd .node circle,#mermaid-svg-ue4jtI5JWiozbGfd .node ellipse,#mermaid-svg-ue4jtI5JWiozbGfd .node polygon,#mermaid-svg-ue4jtI5JWiozbGfd .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-ue4jtI5JWiozbGfd .rough-node .label text,#mermaid-svg-ue4jtI5JWiozbGfd .node .label text,#mermaid-svg-ue4jtI5JWiozbGfd .image-shape .label,#mermaid-svg-ue4jtI5JWiozbGfd .icon-shape .label{text-anchor:middle;}#mermaid-svg-ue4jtI5JWiozbGfd .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-ue4jtI5JWiozbGfd .rough-node .label,#mermaid-svg-ue4jtI5JWiozbGfd .node .label,#mermaid-svg-ue4jtI5JWiozbGfd .image-shape .label,#mermaid-svg-ue4jtI5JWiozbGfd .icon-shape .label{text-align:center;}#mermaid-svg-ue4jtI5JWiozbGfd .node.clickable{cursor:pointer;}#mermaid-svg-ue4jtI5JWiozbGfd .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-ue4jtI5JWiozbGfd .arrowheadPath{fill:#333333;}#mermaid-svg-ue4jtI5JWiozbGfd .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-ue4jtI5JWiozbGfd .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-ue4jtI5JWiozbGfd .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-ue4jtI5JWiozbGfd .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-ue4jtI5JWiozbGfd .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-ue4jtI5JWiozbGfd .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-ue4jtI5JWiozbGfd .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-ue4jtI5JWiozbGfd .cluster text{fill:#333;}#mermaid-svg-ue4jtI5JWiozbGfd .cluster span{color:#333;}#mermaid-svg-ue4jtI5JWiozbGfd div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-ue4jtI5JWiozbGfd .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-ue4jtI5JWiozbGfd rect.text{fill:none;stroke-width:0;}#mermaid-svg-ue4jtI5JWiozbGfd .icon-shape,#mermaid-svg-ue4jtI5JWiozbGfd .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-ue4jtI5JWiozbGfd .icon-shape p,#mermaid-svg-ue4jtI5JWiozbGfd .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-ue4jtI5JWiozbGfd .icon-shape .label rect,#mermaid-svg-ue4jtI5JWiozbGfd .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-ue4jtI5JWiozbGfd .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-ue4jtI5JWiozbGfd .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-ue4jtI5JWiozbGfd :root{–mermaid-font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;}<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u7f3a\u5931\/\u5f02\u5e38<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u6b63\u5e38<\/p>\n

                <\/span><\/p>\n

                <\/span><\/p>\n

                <\/span><\/p>\n

                <\/span><\/p>\n

                <\/span><\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u6b20\u62df\u5408<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u8fc7\u62df\u5408<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u6ee1\u610f<\/p>\n

                <\/span><\/p>\n

                <\/span><\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u539f\u59cb\u6570\u636e<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u6570\u636e\u8d28\u91cf\u68c0\u67e5<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u6e05\u6d17\u4e0e\u9884\u5904\u7406<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u7279\u5f81\u5de5\u7a0b<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u5212\u5206\u8bad\u7ec3\u96c6\/\u6d4b\u8bd5\u96c6<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u6a21\u578b\u5b9e\u4f8b\u5316<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                model.fit \u8bad\u7ec3<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u6a21\u578b\u8bc4\u4f30<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u589e\u52a0\u7279\u5f81\/\u51cf\u5c0f\u6b63\u5219\u5316<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                \u589e\u52a0\u6570\u636e\/\u589e\u5927\u6b63\u5219\u5316<\/p>\n

                <\/span><\/p>\n

                <\/p>\n

                model.predict \u90e8\u7f72<\/p>\n

                <\/span><\/p>\n

                A.2 \u7ebf\u6027\u56de\u5f52 vs \u903b\u8f91\u56de\u5f52\u51b3\u7b56\u8fb9\u754c\u5bf9\u6bd4<\/h4>\n

                #mermaid-svg-rjz3RAFlIUkIiak7{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-rjz3RAFlIUkIiak7 .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-rjz3RAFlIUkIiak7 .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-rjz3RAFlIUkIiak7 .error-icon{fill:#552222;}#mermaid-svg-rjz3RAFlIUkIiak7 .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-rjz3RAFlIUkIiak7 .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-rjz3RAFlIUkIiak7 .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-rjz3RAFlIUkIiak7 .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-rjz3RAFlIUkIiak7 .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-rjz3RAFlIUkIiak7 .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-rjz3RAFlIUkIiak7 .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-rjz3RAFlIUkIiak7 .marker{fill:#333333;stroke:#333333;}#mermaid-svg-rjz3RAFlIUkIiak7 .marker.cross{stroke:#333333;}#mermaid-svg-rjz3RAFlIUkIiak7 svg{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-rjz3RAFlIUkIiak7 p{margin:0;}#mermaid-svg-rjz3RAFlIUkIiak7 :root{–mermaid-font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;}<\/p>\n

                \u6838SVM \/ MLP<\/p>\n

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

                \u7ebf\u6027\u56de\u5f52 (Linear Regression)<\/p>\n

                \u903b\u8f91\u56de\u5f52 (Logistic Regression)<\/p>\n

                \u9500\u91cf\u8d8b\u52bf<\/p>\n

                \u56fe\u50cf\u8bc6\u522b<\/p>\n

                \u9e22\u5c3e\u82b1\u5206\u7c7b<\/p>\n

                \u623f\u5c4b\u4ef7\u683c<\/p>\n

                \u8fde\u7eed\u8f93\u51fa<\/p>\n

                \u79bb\u6563\u8f93\u51fa<\/p>\n

                \u7ebf\u6027\u5173\u7cfb<\/p>\n

                \u975e\u7ebf\u6027\u5173\u7cfb<\/p>\n

                \u6a21\u578b\u9009\u62e9\u51b3\u7b56\u77e9\u9635<\/p>\n

                A.3 \u903b\u8f91\u56de\u5f52Sigmoid\u51fd\u6570\u7279\u6027<\/h4>\n

                #mermaid-svg-xJ4TzQqDB0cA5efI{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-xJ4TzQqDB0cA5efI .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-xJ4TzQqDB0cA5efI .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-xJ4TzQqDB0cA5efI .error-icon{fill:#552222;}#mermaid-svg-xJ4TzQqDB0cA5efI .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-xJ4TzQqDB0cA5efI .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-xJ4TzQqDB0cA5efI .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-xJ4TzQqDB0cA5efI .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-xJ4TzQqDB0cA5efI .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-xJ4TzQqDB0cA5efI .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-xJ4TzQqDB0cA5efI .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-xJ4TzQqDB0cA5efI .marker{fill:#333333;stroke:#333333;}#mermaid-svg-xJ4TzQqDB0cA5efI .marker.cross{stroke:#333333;}#mermaid-svg-xJ4TzQqDB0cA5efI svg{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-xJ4TzQqDB0cA5efI p{margin:0;}#mermaid-svg-xJ4TzQqDB0cA5efI :root{–mermaid-font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;}<\/p>\n

                Sigmoid\u6fc0\u6d3b\u51fd\u6570\u66f2\u7ebf<\/p>\n

                -6<\/p>\n

                -4.8<\/p>\n

                -3.6<\/p>\n

                -2.4<\/p>\n

                -1.2<\/p>\n

                0<\/p>\n

                1.2<\/p>\n

                2.4<\/p>\n

                3.6<\/p>\n

                4.8<\/p>\n

                6<\/p>\n

                x<\/p>\n

                1<\/p>\n

                0.9<\/p>\n

                0.8<\/p>\n

                0.7<\/p>\n

                0.6<\/p>\n

                0.5<\/p>\n

                0.4<\/p>\n

                0.3<\/p>\n

                0.2<\/p>\n

                0.1<\/p>\n

                0<\/p>\n

                y<\/p>\n

                \n

                \u4e5d\u3001 \u6269\u5c55\u9605\u8bfb\u63a8\u8350<\/h3>\n

                \u4e3a\u6ee1\u8db3\u4e0d\u540c\u7a0b\u5ea6\u7684\u5b66\u4e60\u9700\u6c42，\u4ee5\u4e0b\u8d44\u6e90\u6309\u4f18\u5148\u7ea7\u6392\u5217：<\/p>\n

              • \u300a\u7edf\u8ba1\u5b66\u4e60\u65b9\u6cd5\u300b\u674e\u822a – \u7b2c6\u7ae0 \u903b\u8f91\u65af\u8c1b\u56de\u5f52\n
                  \n
                • \u6458\u8981：\u56fd\u5185\u6700\u4e25\u8c28\u7684\u63a8\u5bfc，\u5305\u542b\u6700\u5927\u71b5\u6a21\u578b\u4e0e\u903b\u8f91\u56de\u5f52\u7684\u5173\u7cfb\u3002<\/li>\n
                • \u9002\u7528\u4eba\u7fa4：\u8003\u7814\u515a\u3001\u8ffd\u6c42\u6570\u5b66\u4e25\u8c28\u6027\u7684\u540c\u5b66\u3002<\/li>\n<\/ul>\n<\/li>\n
                • Scikit-learn\u5b98\u65b9\u6587\u6863 – Linear Models\n
                    \n
                  • \u6458\u8981：API\u7ec6\u8282\u3001\u53c2\u6570\u542b\u4e49\u3001\u7b97\u6cd5\u5b9e\u73b0\u6e90\u7801\u7684\u6700\u6743\u5a01\u6765\u6e90\u3002<\/li>\n
                  • \u9002\u7528\u4eba\u7fa4：\u5de5\u7a0b\u5f00\u53d1\u8005\u3001\u9700\u8981\u67e5\u9605\u5177\u4f53\u53c2\u6570\u7528\u6cd5\u7684\u540c\u5b66\u3002<\/li>\n<\/ul>\n<\/li>\n
                  • Andrew Ng Machine Learning Course – Week 2-3\n
                      \n
                    • \u6458\u8981：\u76f4\u89c9\u5f0f\u8bb2\u89e3，\u5411\u91cf\u5316\u7f16\u7a0b\u601d\u60f3\u542f\u8499，\u68af\u5ea6\u4e0b\u964d\u53ef\u89c6\u5316\u6781\u4f73\u3002<\/li>\n
                    • \u9002\u7528\u4eba\u7fa4：\u96f6\u57fa\u7840\u5165\u95e8\u3001\u504f\u597d\u89c6\u9891\u5b66\u4e60\u7684\u540c\u5b66\u3002<\/li>\n<\/ul>\n<\/li>\n
                    • \u300aPattern Recognition and Machine Learning\u300bBishop – Chapter 4\n
                        \n
                      • \u6458\u8981：\u4ece\u8d1d\u53f6\u65af\u89c6\u89d2\u91cd\u65b0\u5ba1\u89c6\u7ebf\u6027\u6a21\u578b，\u5f15\u5165\u6982\u7387\u56fe\u6a21\u578b\u89c2\u70b9\u3002<\/li>\n
                      • \u9002\u7528\u4eba\u7fa4：\u7814\u7a76\u751f\u3001\u5e0c\u671b\u6df1\u5165\u7406\u89e3\u6982\u7387\u673a\u5668\u5b66\u4e60\u7684\u7814\u7a76\u8005\u3002<\/li>\n<\/ul>\n<\/li>\n
                        \n

                        \u5341\u3001 \u603b\u7ed3\u4e0e\u884c\u52a8\u5efa\u8bae<\/h3>\n

                        \u7ebf\u6027\u56de\u5f52\u4e0e\u903b\u8f91\u56de\u5f52\u770b\u4f3c\u7b80\u5355，\u5b9e\u5219\u8574\u542b\u7740\u673a\u5668\u5b66\u4e60\u6700\u6838\u5fc3\u7684\u8303\u5f0f：\u6570\u636e\u2192\u6a21\u578b\u2192\u635f\u5931\u2192\u4f18\u5316\u2192\u8bc4\u4f30\u3002\u638c\u63e1\u4e86\u8fd9\u6761\u4e3b\u7ebf，\u540e\u7eed\u5b66\u4e60SVM\u3001\u51b3\u7b56\u6811\u4e43\u81f3\u6df1\u5ea6\u5b66\u4e60，\u90fd\u4e0d\u8fc7\u662f\u8fd9\u6761\u4e3b\u7ebf\u4e0a\u7684\u5206\u652f\u4e0e\u5ef6\u4f38\u3002<\/p>\n

                        \u7ed9\u4f60\u7684\u884c\u52a8\u6e05\u5355：<\/p>\n

                      • \u2705 \u4eca\u65e5：\u4e0d\u770b\u4efb\u4f55\u53c2\u8003，\u72ec\u7acb\u9ed8\u5199\u51fa\u7ebf\u6027\u56de\u5f52\u548c\u903b\u8f91\u56de\u5f52\u7684sklearn\u56db\u6b65\u6cd5\u4ee3\u7801\u3002<\/li>\n
                      • \u2705 \u660e\u65e5：\u627e\u4e00\u4efd\u65b0\u7684\u6570\u636e\u96c6（\u5982Boston Housing\u6216Titanic），\u4ece\u5934\u5230\u5c3e\u8dd1\u901a\u5168\u6d41\u7a0b，\u5e76\u751f\u6210\u53ef\u89c6\u5316\u62a5\u544a\u3002<\/li>\n
                      • \u2705 \u672c\u5468：\u5c1d\u8bd5\u624b\u5199\u4e00\u904d\u68af\u5ea6\u4e0b\u964d\u66f4\u65b0\u516c\u5f0f，\u5e76\u7528NumPy\u5b9e\u73b0，\u5bf9\u6bd4sklearn\u7ed3\u679c\u3002<\/li>\n
                      • \u2705 \u8003\u524d：\u56de\u987e\u672c\u6587\u7684\u201c\u9677\u9631\u201d\u4e0e\u201cFAQ\u201d\u7ae0\u8282，\u786e\u4fdd\u4e0d\u5728\u57fa\u7840\u95ee\u9898\u4e0a\u4e22\u5206\u3002<\/li>\n

                        📝 \u5199\u5728\u6700\u540e：\u6280\u672f\u5b66\u4e60\u7684\u672c\u8d28\u4e0d\u662f\u8bb0\u5fc6API，\u800c\u662f\u5efa\u7acb\u5bf9\u6570\u636e\u4e0e\u6a21\u578b\u4e4b\u95f4\u5173\u7cfb\u7684\u76f4\u89c9\u3002\u613f\u8fd9\u7bc7\u7b14\u8bb0\u80fd\u6210\u4e3a\u4f60\u901a\u5f80\u6df1\u5ea6\u5b66\u4e60\u6bbf\u5802\u7684\u4e00\u5757\u575a\u5b9e\u57ab\u811a\u77f3\u3002\u4e0b\u4e00\u7bc7\u6211\u4eec\u5c06\u8fdb\u5165PyTorch\u7684\u4e16\u754c，\u63a2\u8ba8Tensor\u8fd0\u7b97\u4e0e\u81ea\u52a8\u5fae\u5206\u673a\u5236，\u656c\u8bf7\u671f\u5f85！<\/p>\n

                        \n
                      • \n

                        \u5728Ian Goodfellow\u7b49\u4eba\u7684\u300aDeep Learning\u300b\u4e00\u4e66\u4e2d，\u7b2c5\u7ae0\u4e13\u95e8\u56de\u987e\u4e86\u673a\u5668\u5b66\u4e60\u57fa\u7840，\u660e\u786e\u6307\u51fa\u7ebf\u6027\u6a21\u578b\u662f\u7406\u89e3\u6df1\u5ea6\u7f51\u7edc\u5bb9\u91cf\u3001\u8fc7\u62df\u5408\u53ca\u4f18\u5316\u7684\u5fc5\u8981\u524d\u7f6e\u77e5\u8bc6\u3002 \u21a9\ufe0e<\/p>\n<\/li>\n

                      • \n

                        \u6700\u5c0f\u4e8c\u4e58\u6cd5\u7531\u9ad8\u65af\u548c\u52d2\u8ba9\u5fb7\u572819\u4e16\u7eaa\u521d\u72ec\u7acb\u63d0\u51fa，\u6700\u521d\u7528\u4e8e\u5929\u4f53\u8f68\u9053\u8ba1\u7b97\u3002\u5176\u7edf\u8ba1\u6027\u8d28（\u5982BLUE\u6700\u4f73\u7ebf\u6027\u65e0\u504f\u4f30\u8ba1）\u9700\u6ee1\u8db3Gauss-Markov\u5047\u8bbe，\u8fd9\u5728\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u4e2d\u5c24\u4e3a\u91cd\u8981\u3002 \u21a9\ufe0e<\/p>\n<\/li>\n

                      • \n

                        \u89e3\u6790\u89e3\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a<\/p>\n

                        O<\/p>\n

                        (<\/p>\n

                        n<\/p>\n

                        2<\/p>\n

                        d<\/p>\n

                        +<\/p>\n

                        d<\/p>\n

                        3<\/p>\n

                        )<\/p>\n

                        O(n^2d + d^3)<\/p>\n

                        <\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d<\/p>\n

                        n<\/p>\n

                        n<\/p>\n

                        <\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u4e3a\u6837\u672c\u6570，<\/p>\n

                        d<\/p>\n

                        d<\/p>\n

                        <\/span><\/span>d<\/span><\/span><\/span><\/span><\/span>\u4e3a\u7279\u5f81\u6570\u3002\u5f53<\/p>\n

                        d<\/p>\n

                        ><\/p>\n

                        10000<\/p>\n

                        d > 10000<\/p>\n

                        <\/span><\/span>d<\/span><\/span>><\/span><\/span><\/span><\/span>10000<\/span><\/span><\/span><\/span><\/span>\u65f6，\u77e9\u9635\u6c42\u9006\u53d8\u5f97\u6781\u5176\u6602\u8d35，\u6b64\u65f6SGD\u662f\u66f4\u4f18\u9009\u62e9\u3002 \u21a9\ufe0e<\/p>\n<\/li>\n

                      • \n

                        Sigmoid\u51fd\u6570\u7684\u5bfc\u6570\u4e3a<\/p>\n

                        \u03c3<\/p>\n

                        (<\/p>\n

                        z<\/p>\n

                        )<\/p>\n

                        (<\/p>\n

                        1<\/p>\n

                        \u2212<\/p>\n

                        \u03c3<\/p>\n

                        (<\/p>\n

                        z<\/p>\n

                        )<\/p>\n

                        )<\/p>\n

                        \\\\sigma(z)(1-\\\\sigma(z))<\/p>\n

                        <\/span><\/span>\u03c3<\/span>(<\/span>z<\/span>)<\/span>(<\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03c3<\/span>(<\/span>z<\/span>))<\/span><\/span><\/span><\/span><\/span>，\u8fd9\u610f\u5473\u7740\u5f53\u8f93\u51fa\u63a5\u8fd10\u62161\u65f6，\u68af\u5ea6\u8d8b\u8fd1\u4e8e0，\u5bfc\u81f4\u201c\u68af\u5ea6\u6d88\u5931\u201d\u95ee\u9898\u3002\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u6df1\u5c42\u7f51\u7edc\u4e2dReLU\u9010\u6e10\u53d6\u4ee3Sigmoid\u7684\u539f\u56e0\u4e4b\u4e00，\u4f46\u5728\u6d45\u5c42\u903b\u8f91\u56de\u5f52\u4e2dSigmoid\u4f9d\u7136\u6709\u6548\u3002 \u21a9\ufe0e<\/p>\n<\/li>\n

                      • \n

                        \u4ea4\u53c9\u71b5\u635f\u5931\u6e90\u4e8e\u4fe1\u606f\u8bba\u4e2d\u7684KL\u6563\u5ea6\u3002\u6700\u5c0f\u5316\u4ea4\u53c9\u71b5\u7b49\u4ef7\u4e8e\u6700\u5927\u5316\u4f3c\u7136\u51fd\u6570，\u8fd9\u4e3a\u903b\u8f91\u56de\u5f52\u63d0\u4f9b\u4e86\u575a\u5b9e\u7684\u6982\u7387\u8bba\u57fa\u7840，\u800cMSE\u7f3a\u4e4f\u8fd9\u79cd\u6982\u7387\u89e3\u91ca\u3002 \u21a9\ufe0e<\/p>\n<\/li>\n

                      • \n

                        Logit\u51fd\u6570\u5b9a\u4e49\u4e3a<\/p>\n

                        ln<\/p>\n

                        \u2061<\/p>\n

                        (<\/p>\n

                        p<\/p>\n

                        1<\/p>\n

                        \u2212<\/p>\n

                        p<\/p>\n

                        )<\/p>\n

                        \\\\ln(\\\\frac{p}{1-p})<\/p>\n

                        <\/span><\/span>ln<\/span>(<\/span><\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5373\u5bf9\u6570\u51e0\u7387\u3002\u903b\u8f91\u56de\u5f52\u5b9e\u9645\u4e0a\u662f\u201c\u5bf9\u6570\u51e0\u7387\u56de\u5f52\u201d\u7684\u7b80\u79f0\u3002\u8fd9\u4e00\u547d\u540d\u53cd\u6620\u4e86\u5176\u4f5c\u4e3a\u5e7f\u4e49\u7ebf\u6027\u6a21\u578b\u7684\u8eab\u4efd，\u5373\u901a\u8fc7\u94fe\u63a5\u51fd\u6570\u5c06\u7ebf\u6027\u9884\u6d4b\u5668\u4e0e\u54cd\u5e94\u53d8\u91cf\u7684\u671f\u671b\u8054\u7cfb\u8d77\u6765\u3002 \u21a9\ufe0e<\/p>\n<\/li>\n","protected":false},"excerpt":{"rendered":"

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