{"id":1494,"date":"2026-05-26T11:30:00","date_gmt":"2026-05-26T03:30:00","guid":{"rendered":"http:\/\/www.sdjxsjy.com\/?p=1494"},"modified":"2026-05-26T09:48:19","modified_gmt":"2026-05-26T01:48:19","slug":"%e5%9f%ba%e4%ba%8e%e5%8f%98%e5%88%86%e8%87%aa%e7%bc%96%e7%a0%81%e5%99%a8%e7%9a%84%e9%9d%9e%e6%a0%87%e6%9c%ba%e6%a2%b0%e9%9b%b6%e4%bb%b6%e5%bc%82%e5%b8%b8%e6%a3%80%e6%b5%8b%e4%b8%8e%e5%81%a5%e5%ba%b7","status":"publish","type":"post","link":"http:\/\/www.sdjxsjy.com\/?p=1494","title":{"rendered":"\u57fa\u4e8e\u53d8\u5206\u81ea\u7f16\u7801\u5668\u7684\u975e\u6807\u673a\u68b0\u96f6\u4ef6\u5f02\u5e38\u68c0\u6d4b\u4e0e\u5065\u5eb7\u72b6\u6001\u65e0\u76d1\u7763\u8bc4\u4f30"},"content":{"rendered":"\n

\u975e\u6807\u673a\u68b0\u96f6\u4ef6\u56e0\u5176\u5c0f\u6279\u91cf\u3001\u591a\u6837\u5316\u3001\u51e0\u4f55\u7279\u5f81\u590d\u6742\u7b49\u7279\u70b9\uff0c\u4f20\u7edf\u57fa\u4e8e\u6807\u7b7e\u6570\u636e\u7684\u76d1\u7763\u5b66\u4e60\u5f02\u5e38\u68c0\u6d4b\u65b9\u6cd5\u96be\u4ee5\u9002\u7528\u3002\u672c\u6587\u63d0\u51fa\u4e00\u79cd\u57fa\u4e8e\u53d8\u5206\u81ea\u7f16\u7801\u5668\uff08VAE\uff09\u7684\u65e0\u76d1\u7763\u5f02\u5e38\u68c0\u6d4b\u4e0e\u5065\u5eb7\u72b6\u6001\u8bc4\u4f30\u6846\u67b6\u3002\u901a\u8fc7\u6784\u5efa\u9ad8\u7075\u654f\u5ea6\u91cd\u6784\u6982\u7387\u6a21\u578b\uff0c\u7ed3\u5408\u6f5c\u5728\u7a7a\u95f4\u5206\u5e03\u71b5\u4e0e\u91cd\u6784\u8bef\u5dee\u7684\u8054\u5408\u6307\u6807\uff0c\u5b9e\u73b0\u975e\u6807\u96f6\u4ef6\u5728\u65e0\u6545\u969c\u6837\u672c\u6761\u4ef6\u4e0b\u7684\u5f02\u5e38\u8bc6\u522b\u3002\u8fdb\u4e00\u6b65\uff0c\u5f15\u5165\u8fde\u7eed\u5065\u5eb7\u6307\u6570\uff08HI\uff09\u751f\u6210\u673a\u5236\uff0c\u5c06\u91cd\u6784\u8bef\u5dee\u5e8f\u5217\u6620\u5c04\u4e3a\u9000\u5316\u8f68\u8ff9\uff0c\u652f\u6301\u5269\u4f59\u5bff\u547d\u8d8b\u52bf\u9884\u6d4b\u3002\u5b9e\u9a8c\u5728\u771f\u5b9e\u975e\u6807\u96f6\u4ef6\u632f\u52a8\u4e0e\u51e0\u4f55\u6570\u636e\u96c6\u4e0a\u9a8c\u8bc1\uff0c\u6240\u63d0\u65b9\u6cd5\u5728AUC\u6307\u6807\u4e0a\u4f18\u4e8e\u4f20\u7edf\u81ea\u7f16\u7801\u5668\u4e0e\u5b64\u7acb\u68ee\u6797\uff0c\u5e76\u80fd\u591f\u6709\u6548\u6355\u6349\u5065\u5eb7\u72b6\u6001\u6e10\u53d8\u8fc7\u7a0b\u3002<\/p>\n\n\n\n

1. \u5f15\u8a00<\/h3>\n\n\n\n

\u5728\u975e\u6807\u81ea\u52a8\u5316\u88c5\u914d\u4e0e\u67d4\u6027\u5236\u9020\u573a\u666f\u4e2d\uff0c\u673a\u68b0\u96f6\u4ef6\u5f80\u5f80\u5177\u6709\u9ad8\u5ea6\u5b9a\u5236\u5316\u3001\u6279\u6b21\u4e0d\u5b9a\u3001\u5f62\u72b6\u4e0d\u89c4\u5219\u7b49\u7279\u70b9\u3002\u8fd9\u7c7b\u96f6\u4ef6\u7684\u8d28\u91cf\u68c0\u6d4b\u4e0e\u8fd0\u884c\u72b6\u6001\u76d1\u63a7\u9762\u4e34\u4e24\u5927\u6838\u5fc3\u6311\u6218\uff1a\u5176\u4e00\uff0c\u6545\u969c\u6837\u672c\u6781\u5ea6\u7a00\u7f3a\uff0c\u65e0\u6cd5\u652f\u6491\u6709\u76d1\u7763\u6a21\u578b\u7684\u8bad\u7ec3\uff1b\u5176\u4e8c\uff0c\u96f6\u4ef6\u95f4\u7684\u4e2a\u4f53\u5dee\u5f02\u663e\u8457\uff0c\u65e0\u6cd5\u5efa\u7acb\u7edf\u4e00\u7684\u56fa\u5b9a\u9608\u503c\u5224\u522b\u89c4\u5219\u3002\u4f20\u7edf\u65b9\u6cd5\u5982\u57fa\u4e8e\u7edf\u8ba1\u8fc7\u7a0b\u63a7\u5236\uff08SPC\uff09\u6216\u4e13\u5bb6\u89c4\u5219\u5e93\uff0c\u5728\u9762\u5bf9\u975e\u6807\u96f6\u4ef6\u7684\u51e0\u4f55\u4e0e\u52a8\u6001\u7279\u6027\u65f6\u8868\u73b0\u51fa\u8f83\u5dee\u7684\u81ea\u9002\u5e94\u80fd\u529b\u3002<\/p>\n\n\n\n

\u8fd1\u5e74\u6765\uff0c\u6df1\u5ea6\u751f\u6210\u6a21\u578b\u5c24\u5176\u662f\u53d8\u5206\u81ea\u7f16\u7801\u5668\uff08VAE\uff09\u5728\u65e0\u76d1\u7763\u5f02\u5e38\u68c0\u6d4b\u9886\u57df\u5c55\u73b0\u51fa\u5de8\u5927\u6f5c\u529b\u3002VAE\u901a\u8fc7\u7f16\u7801-\u89e3\u7801\u7ed3\u6784\u5b66\u4e60\u6570\u636e\u7684\u9ad8\u65af\u6f5c\u5728\u5206\u5e03\uff0c\u80fd\u591f\u5bf9\u6b63\u5e38\u6a21\u5f0f\u8fdb\u884c\u6982\u7387\u5efa\u6a21\uff0c\u5e76\u5229\u7528\u91cd\u6784\u6982\u7387\u800c\u975e\u7b80\u5355\u7684\u91cd\u6784\u8bef\u5dee\u4f5c\u4e3a\u5f02\u5e38\u5224\u5b9a\u4f9d\u636e\u3002\u7136\u800c\uff0c\u73b0\u6709\u7814\u7a76\u591a\u96c6\u4e2d\u5728\u6807\u51c6\u6570\u636e\u96c6\uff08\u5982MNIST\u3001KDD99\uff09\u6216\u6807\u51c6\u673a\u68b0\u90e8\u4ef6\uff08\u5982\u8f74\u627f\u3001\u9f7f\u8f6e\uff09\u4e0a\uff0c\u5bf9\u975e\u6807\u96f6\u4ef6\u7684\u9002\u914d\u6027\u7f3a\u4e4f\u7cfb\u7edf\u63a2\u8ba8\u3002\u6b64\u5916\uff0c\u5982\u4f55\u4eceVAE\u6846\u67b6\u4e2d\u884d\u751f\u51fa\u8fde\u7eed\u7684\u201c\u5065\u5eb7\u72b6\u6001\u8bc4\u4f30\u201d\u6307\u6807\uff0c\u800c\u975e\u4ec5\u505a\u4e8c\u5206\u7c7b\u5f02\u5e38\u5224\u522b\uff0c\u4ecd\u662f\u5f00\u653e\u95ee\u9898\u3002<\/p>\n\n\n\n

\u672c\u6587\u9488\u5bf9\u4e0a\u8ff0\u7a7a\u767d\uff0c\u63d0\u51fa\u4e00\u5957\u9762\u5411\u975e\u6807\u673a\u68b0\u96f6\u4ef6\u7684VAE\u65e0\u76d1\u7763\u68c0\u6d4b\u4e0e\u8bc4\u4f30\u6846\u67b6\u3002\u4e3b\u8981\u8d21\u732e\u5305\u62ec\uff1a(1) \u8bbe\u8ba1\u9002\u5e94\u975e\u6807\u96f6\u4ef6\u591a\u6a21\u6001\u7279\u5f81\u7684VAE\u7f51\u7edc\u7ed3\u6784\uff0c\u5f15\u5165\u53ef\u5fae\u5206\u6ce8\u610f\u529b\u673a\u5236\u805a\u7126\u5173\u952e\u51e0\u4f55\u533a\u57df\uff1b(2) \u63d0\u51fa\u8054\u5408\u91cd\u6784\u6982\u7387\u4e0e\u6f5c\u5728\u7a7a\u95f4KLD\u6563\u5ea6\u7684\u5f02\u5e38\u8bc4\u5206\u51fd\u6570\uff0c\u63d0\u5347\u5bf9\u5fae\u7f3a\u9677\u7684\u654f\u611f\u6027\uff1b(3) \u6784\u5efa\u57fa\u4e8e\u6ed1\u52a8\u7a97\u53e3\u91cd\u6784\u8bef\u5dee\u5e8f\u5217\u7684\u8fde\u7eed\u5065\u5eb7\u6307\u6570\uff0c\u5b9e\u73b0\u4ece\u5f02\u5e38\u68c0\u6d4b\u5411\u9000\u5316\u8d8b\u52bf\u8bc4\u4f30\u7684\u6269\u5c55\u3002<\/p>\n\n\n\n

2. \u95ee\u9898\u63cf\u8ff0\u4e0e\u975e\u6807\u96f6\u4ef6\u7279\u6027\u5206\u6790<\/h3>\n\n\n\n

\u8bbe\u975e\u6807\u673a\u68b0\u96f6\u4ef6\u6570\u636e\u96c6 X<\/mi>=<\/mo>{<\/mo>x<\/mi>(<\/mo>1<\/mn>)<\/mo><\/mrow><\/msup>,<\/mo>.<\/mi>.<\/mi>.<\/mi>,<\/mo>x<\/mi>(<\/mo>N<\/mi>)<\/mo><\/mrow><\/msup>}<\/mo><\/mrow><\/semantics><\/math>X<\/em>={x<\/em>(1),…,x<\/em>(N<\/em>)}\uff0c\u6bcf\u4e2a\u6837\u672c x<\/mi>\u2208<\/mo>R<\/mi>D<\/mi><\/msup><\/mrow><\/semantics><\/math>x<\/em>\u2208RD<\/em> \u53ef\u6765\u6e90\u4e8e\u632f\u52a8\u4fe1\u53f7\u30013D\u70b9\u4e91\u5c40\u90e8\u7279\u5f81\u6216\u5173\u952e\u5c3a\u5bf8\u6d4b\u91cf\u503c\u3002\u6b63\u5e38\u6837\u672c\u96c6 X<\/mi>n<\/mi>o<\/mi>r<\/mi>m<\/mi><\/mrow><\/msub><\/mrow><\/semantics><\/math>X<\/em>n<\/em>or<\/em>m<\/em>\u200b \u670d\u4ece\u672a\u77e5\u5206\u5e03 p<\/mi>d<\/mi>a<\/mi>t<\/mi>a<\/mi><\/mrow><\/msub>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/semantics><\/math>p<\/em>d<\/em>a<\/em>t<\/em>a<\/em>\u200b(x<\/em>)\uff0c\u4f46\u5f02\u5e38\u6837\u672c\u96c6 X<\/mi>a<\/mi>n<\/mi>o<\/mi>m<\/mi><\/mrow><\/msub><\/mrow><\/semantics><\/math>X<\/em>an<\/em>o<\/em>m<\/em>\u200b \u65e0\u5148\u9a8c\u6807\u7b7e\u3002\u76ee\u6807\u662f\u5b66\u4e60\u4e00\u4e2a\u8bc4\u5206\u51fd\u6570 S<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/semantics><\/math>S<\/em>(x<\/em>)\uff0c\u4f7f\u5f97\u5bf9\u4e8e x<\/mi>\u2208<\/mo>X<\/mi>n<\/mi>o<\/mi>r<\/mi>m<\/mi><\/mrow><\/msub><\/mrow><\/semantics><\/math>x<\/em>\u2208X<\/em>n<\/em>or<\/em>m<\/em>\u200b\uff0cS<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/semantics><\/math>S<\/em>(x<\/em>) \u8f83\u4f4e\uff1b\u5bf9\u4e8e x<\/mi>\u2208<\/mo>X<\/mi>a<\/mi>n<\/mi>o<\/mi>m<\/mi><\/mrow><\/msub><\/mrow><\/semantics><\/math>x<\/em>\u2208X<\/em>an<\/em>o<\/em>m<\/em>\u200b\uff0cS<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/semantics><\/math>S<\/em>(x<\/em>) \u8f83\u9ad8\u3002\u66f4\u8fdb\u4e00\u6b65\uff0c\u5bf9\u4e8e\u540c\u4e00\u975e\u6807\u96f6\u4ef6\u968f\u65f6\u95f4\u91c7\u96c6\u7684\u5e8f\u5217 {<\/mo>x<\/mi>1<\/mn><\/msub>,<\/mo>x<\/mi>2<\/mn><\/msub>,<\/mo>.<\/mi>.<\/mi>.<\/mi>,<\/mo>x<\/mi>T<\/mi><\/msub>}<\/mo><\/mrow><\/semantics><\/math>{x<\/em>1\u200b,x<\/em>2\u200b,…,x<\/em>T<\/em>\u200b}\uff0c\u9700\u8981\u8f93\u51fa\u5065\u5eb7\u6307\u6570\u5e8f\u5217 H<\/mi>I<\/mi>t<\/mi><\/msub>\u2208<\/mo>[<\/mo>0<\/mn>,<\/mo>1<\/mn>]<\/mo><\/mrow><\/semantics><\/math>H<\/em>I<\/em>t<\/em>\u200b\u2208[0,1]\uff0c\u53cd\u6620\u9000\u5316\u7a0b\u5ea6\u3002<\/p>\n\n\n\n

\u975e\u6807\u96f6\u4ef6\u7684\u5173\u952e\u7279\u6027\u5305\u62ec\uff1a<\/p>\n\n\n\n

    \n
  • \u51e0\u4f55\u5f02\u6784\u6027<\/strong>\uff1a\u4e0d\u540c\u6279\u6b21\u96f6\u4ef6\u7684\u5c40\u90e8\u66f2\u7387\u3001\u5b54\u4f4d\u5206\u5e03\u5dee\u5f02\u5927\u3002<\/li>\n\n\n\n
  • \u4fe1\u53f7\u9ad8\u7ef4\u5c0f\u6837\u672c<\/strong>\uff1a\u5355\u4ef6\u96f6\u4ef6\u53ef\u80fd\u4ec5\u6709\u6570\u767e\u4e2a\u6837\u672c\uff0c\u4e0d\u8db3\u4ee5\u8bad\u7ec3\u590d\u6742\u7f51\u7edc\u3002<\/li>\n\n\n\n
  • \u5f02\u5e38\u5f62\u5f0f\u591a\u6837<\/strong>\uff1a\u5305\u62ec\u8868\u9762\u5212\u75d5\u3001\u5fae\u88c2\u7eb9\u3001\u88c5\u914d\u9519\u4f4d\u3001\u6750\u6599\u5185\u90e8\u7f3a\u9677\u7b49\uff0c\u5176\u4e2d\u90e8\u5206\u5f02\u5e38\u4ec5\u5728\u9ad8\u7ef4\u7279\u5f81\u7a7a\u95f4\u4e2d\u8868\u73b0\u5fae\u5f31\u3002<\/li>\n<\/ul>\n\n\n\n

    \u8fd9\u4e9b\u7279\u6027\u8981\u6c42\u68c0\u6d4b\u6a21\u578b\u5177\u5907\u5f3a\u6982\u7387\u6cdb\u5316\u80fd\u529b\u4e0e\u5c0f\u6837\u672c\u4e0b\u7684\u4e0d\u786e\u5b9a\u6027\u4f30\u8ba1\u80fd\u529b\u3002<\/p>\n\n\n\n

    3. \u57fa\u4e8eVAE\u7684\u5f02\u5e38\u68c0\u6d4b\u6a21\u578b<\/h3>\n\n\n\n

    3.1 \u6807\u51c6VAE\u56de\u987e<\/h4>\n\n\n\n

    VAE\u7531\u7f16\u7801\u5668 q<\/mi>\u03d5<\/mi><\/msub>(<\/mo>z<\/mi>\u2223<\/mi>x<\/mi>)<\/mo><\/mrow><\/semantics><\/math>q<\/em>\u03d5<\/em>\u200b(z<\/em>\u2223x<\/em>) \u548c\u89e3\u7801\u5668 p<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>\u2223<\/mi>z<\/mi>)<\/mo><\/mrow><\/semantics><\/math>p<\/em>\u03b8<\/em>\u200b(x<\/em>\u2223z<\/em>) \u7ec4\u6210\uff0c\u4f18\u5316\u8bc1\u636e\u4e0b\u754c\uff08ELBO\uff09\uff1aL<\/mi>(<\/mo>\u03b8<\/mi>,<\/mo>\u03d5<\/mi>;<\/mo>x<\/mi>)<\/mo>=<\/mo>E<\/mi>q<\/mi>\u03d5<\/mi><\/msub>(<\/mo>z<\/mi>\u2223<\/mi>x<\/mi>)<\/mo><\/mrow><\/msub>[<\/mo>log<\/mi>\u2061<\/mo>p<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>\u2223<\/mi>z<\/mi>)<\/mo>]<\/mo>\u2212<\/mo>D<\/mi>K<\/mi>L<\/mi><\/mrow><\/msub>(<\/mo>q<\/mi>\u03d5<\/mi><\/msub>(<\/mo>z<\/mi>\u2223<\/mi>x<\/mi>)<\/mo>\u2225<\/mo>p<\/mi>(<\/mo>z<\/mi>)<\/mo>)<\/mo><\/mrow><\/semantics><\/math>L(\u03b8<\/em>,\u03d5<\/em>;x<\/em>)=Eq<\/em>\u03d5<\/em>\u200b(z<\/em>\u2223x<\/em>)\u200b[logp<\/em>\u03b8<\/em>\u200b(x<\/em>\u2223z<\/em>)]\u2212D<\/em>K<\/em>L<\/em>\u200b(q<\/em>\u03d5<\/em>\u200b(z<\/em>\u2223x<\/em>)\u2225p<\/em>(z<\/em>))<\/p>\n\n\n\n

    \u5176\u4e2d\u5148\u9a8c p<\/mi>(<\/mo>z<\/mi>)<\/mo>=<\/mo>N<\/mi>(<\/mo>0<\/mn>,<\/mo>I<\/mi>)<\/mo><\/mrow><\/semantics><\/math>p<\/em>(z<\/em>)=N(0,I<\/em>)\u3002\u8bad\u7ec3\u5b8c\u6210\u540e\uff0c\u5bf9\u4e8e\u65b0\u6837\u672c x<\/mi><\/mrow><\/semantics><\/math>x<\/em>\uff0c\u5176\u91cd\u6784\u6982\u7387 log<\/mi>\u2061<\/mo>p<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/semantics><\/math>logp<\/em>\u03b8<\/em>\u200b(x<\/em>) \u53ef\u901a\u8fc7\u91cd\u8981\u6027\u91c7\u6837\u4f30\u8ba1\u3002\u5f02\u5e38\u5224\u522b\u5e38\u57fa\u4e8e\u91cd\u6784\u6982\u7387\u9608\u503c\uff1a\u4f4e\u91cd\u6784\u6982\u7387\u5373\u6307\u793a\u5f02\u5e38\u3002<\/p>\n\n\n\n

    3.2 \u9762\u5411\u975e\u6807\u96f6\u4ef6\u7684\u589e\u5f3aVAE\u7ed3\u6784<\/h4>\n\n\n\n

    \u4e3a\u4f7fVAE\u9002\u5e94\u975e\u6807\u96f6\u4ef6\u7279\u5f81\uff0c\u672c\u6587\u8bbe\u8ba1\u5982\u4e0b\u589e\u5f3a\uff1a<\/p>\n\n\n\n

      \n
    1. \u591a\u6a21\u6001\u8f93\u5165\u5206\u652f<\/strong>\uff1a\u5bf9\u4e8e\u540c\u65f6\u5305\u542b\u70b9\u4e91\u5c40\u90e8\u7279\u5f81\u3001\u632f\u52a8\u9891\u8c31\u7247\u6bb5\u548c\u5c3a\u5bf8\u53c2\u6570\u7684\u975e\u6807\u96f6\u4ef6\uff0c\u91c7\u7528\u72ec\u7acb\u7f16\u7801\u5668\u5b50\u7f51\u7edc\u5206\u522b\u63d0\u53d6\u6f5c\u5728\u8868\u5f81\u540e\u878d\u5408\u3002<\/li>\n\n\n\n
    2. \u53ef\u5fae\u5206\u6ce8\u610f\u529b\u63a9\u7801<\/strong>\uff1a\u5728\u89e3\u7801\u5668\u7684\u91cd\u6784\u5c42\u4e4b\u524d\u5f15\u5165\u6ce8\u610f\u529b\u6a21\u5757\uff0c\u8feb\u4f7f\u6a21\u578b\u5173\u6ce8\u96f6\u4ef6\u4e0a\u529f\u80fd\u5173\u952e\u533a\u57df\uff08\u5982\u914d\u5408\u9762\u3001\u87ba\u7eb9\u8d77\u59cb\u7aef\uff09\uff0c\u5176\u6570\u5b66\u5f62\u5f0f\u4e3a\uff1a<\/li>\n<\/ol>\n\n\n\n

      x<\/mi>^<\/mo><\/mover>=<\/mo>(<\/mo>1<\/mn>\u2212<\/mo>M<\/mi>)<\/mo>\u2299<\/mo>x<\/mi>r<\/mi>e<\/mi>c<\/mi><\/mrow><\/msub>+<\/mo>M<\/mi>\u2299<\/mo>x<\/mi>i<\/mi>n<\/mi>p<\/mi>u<\/mi>t<\/mi><\/mrow><\/msub><\/mrow><\/semantics><\/math>x<\/em>^=(1\u2212M<\/em>)\u2299x<\/em>rec<\/em>\u200b+M<\/em>\u2299x<\/em>in<\/em>p<\/em>u<\/em>t<\/em>\u200b<\/p>\n\n\n\n

      \u5176\u4e2d M<\/mi><\/mrow><\/semantics><\/math>M<\/em> \u7531\u6ce8\u610f\u529b\u7f51\u7edc\u751f\u6210\uff0cx<\/mi>r<\/mi>e<\/mi>c<\/mi><\/mrow><\/msub><\/mrow><\/semantics><\/math>x<\/em>rec<\/em>\u200b \u4e3a\u89e3\u7801\u5668\u539f\u59cb\u8f93\u51fa\u3002\u8fd9\u79cd\u8bbe\u8ba1\u4f7f\u6a21\u578b\u5728\u9762\u5bf9\u5f02\u5e38\u51fa\u73b0\u5728\u975e\u5173\u952e\u533a\u65f6\u4ecd\u80fd\u4fdd\u6301\u8f83\u4f4e\u91cd\u6784\u8bef\u5dee\uff0c\u907f\u514d\u8bef\u62a5\uff0c\u540c\u65f6\u4f7f\u5173\u952e\u533a\u5f02\u5e38\u88ab\u653e\u5927\u3002<\/p>\n\n\n\n
        \n
      1. \u03b2\u03b2<\/em>-VAE\u53d8\u4f53<\/strong>\uff1a\u91c7\u7528\u00a0\u03b2<\/mi>><\/mo>1<\/mn><\/mrow><\/semantics><\/math>\u03b2<\/em>>1\u00a0\u4ee5\u589e\u5f3a\u6f5c\u5728\u7a7a\u95f4\u7684\u89e3\u8026\u6027\uff0c\u516c\u5f0f\u4e3a\uff1a<\/li>\n<\/ol>\n\n\n\n

        L<\/mi>\u03b2<\/mi><\/msub>=<\/mo>E<\/mi>q<\/mi><\/msub>[<\/mo>log<\/mi>\u2061<\/mo>p<\/mi>(<\/mo>x<\/mi>\u2223<\/mi>z<\/mi>)<\/mo>]<\/mo>\u2212<\/mo>\u03b2<\/mi>D<\/mi>K<\/mi>L<\/mi><\/mrow><\/msub>(<\/mo>q<\/mi>(<\/mo>z<\/mi>\u2223<\/mi>x<\/mi>)<\/mo>\u2225<\/mo>p<\/mi>(<\/mo>z<\/mi>)<\/mo>)<\/mo><\/mrow><\/semantics><\/math>L\u03b2<\/em>\u200b=Eq<\/em>\u200b[logp<\/em>(x<\/em>\u2223z<\/em>)]\u2212\u03b2<\/em>D<\/em>K<\/em>L<\/em>\u200b(q<\/em>(z<\/em>\u2223x<\/em>)\u2225p<\/em>(z<\/em>))<\/p>\n\n\n\n

        \u66f4\u9ad8\u7684 \u03b2<\/mi><\/mrow><\/semantics><\/math>\u03b2<\/em> \u5f3a\u8feb\u6f5c\u5728\u53d8\u91cf\u7ef4\u5ea6\u4e4b\u95f4\u76f8\u4e92\u72ec\u7acb\uff0c\u6709\u5229\u4e8e\u533a\u5206\u4e0d\u540c\u7c7b\u578b\u7684\u9000\u5316\u6a21\u5f0f\u3002<\/p>\n\n\n\n

        3.3 \u8054\u5408\u5f02\u5e38\u8bc4\u5206\u51fd\u6570<\/h4>\n\n\n\n

        \u4ec5\u4f9d\u9760\u91cd\u6784\u6982\u7387\u5bb9\u6613\u5ffd\u7565\u6f5c\u5728\u7a7a\u95f4\u7684\u5206\u5e03\u504f\u79fb\u3002\u5b9a\u4e49\u5f02\u5e38\u8bc4\u5206\uff1aS<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>\u03b1<\/mi>\u22c5<\/mo>(<\/mo>\u2212<\/mo>log<\/mi>\u2061<\/mo>p<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>)<\/mo>)<\/mo>+<\/mo>(<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>)<\/mo>\u22c5<\/mo>D<\/mi>K<\/mi>L<\/mi><\/mrow><\/msub>(<\/mo>q<\/mi>\u03d5<\/mi><\/msub>(<\/mo>z<\/mi>\u2223<\/mi>x<\/mi>)<\/mo>\u2225<\/mo>p<\/mi>(<\/mo>z<\/mi>)<\/mo>)<\/mo><\/mrow><\/semantics><\/math>S<\/em>(x<\/em>)=\u03b1<\/em>\u22c5(\u2212logp<\/em>\u03b8<\/em>\u200b(x<\/em>))+(1\u2212\u03b1<\/em>)\u22c5D<\/em>K<\/em>L<\/em>\u200b(q<\/em>\u03d5<\/em>\u200b(z<\/em>\u2223x<\/em>)\u2225p<\/em>(z<\/em>))<\/p>\n\n\n\n

        \u5176\u4e2d\u7b2c\u4e00\u9879\u4e3a\u8d1f\u5bf9\u6570\u4f3c\u7136\uff08\u91cd\u6784\u9879\uff09\uff0c\u7b2c\u4e8c\u9879\u6d4b\u91cf\u6f5c\u5728\u7801\u504f\u79bb\u6807\u51c6\u6b63\u6001\u7684\u7a0b\u5ea6\u3002\u7531\u4e8e\u5f02\u5e38\u6837\u672c\u5f80\u5f80\u5bfc\u81f4\u7f16\u7801\u5668\u8f93\u51fa\u504f\u79bb\u5148\u9a8c\uff0c\u8054\u5408\u8bc4\u5206\u53ef\u63d0\u5347\u9c81\u68d2\u6027\u3002\u03b1<\/mi><\/mrow><\/semantics><\/math>\u03b1<\/em> \u901a\u8fc7\u9a8c\u8bc1\u96c6\u4e0a\u5206\u79bb\u5ea6\u6700\u5927\u5316\u81ea\u9002\u5e94\u786e\u5b9a\u3002<\/p>\n\n\n\n

        4. \u5065\u5eb7\u72b6\u6001\u65e0\u76d1\u7763\u8bc4\u4f30\u65b9\u6cd5<\/h3>\n\n\n\n

        4.1 \u4ece\u5f02\u5e38\u8bc4\u5206\u5230\u9000\u5316\u8f68\u8ff9<\/h4>\n\n\n\n

        \u5bf9\u4e8e\u5355\u4e2a\u975e\u6807\u96f6\u4ef6\u5728\u8fde\u7eed\u76d1\u6d4b\u4e2d\u83b7\u5f97\u7684\u65f6\u95f4\u5e8f\u5217 x<\/mi>1<\/mn>:<\/mo>T<\/mi><\/mrow><\/msub><\/mrow><\/semantics><\/math>x<\/em>1:T<\/em>\u200b\uff0c\u8ba1\u7b97\u6bcf\u4e2a\u65f6\u95f4\u70b9\u7684 S<\/mi>t<\/mi><\/msub><\/mrow><\/semantics><\/math>S<\/em>t<\/em>\u200b\u3002\u539f\u59cb S<\/mi>t<\/mi><\/msub><\/mrow><\/semantics><\/math>S<\/em>t<\/em>\u200b \u901a\u5e38\u5b58\u5728\u566a\u58f0\uff0c\u91c7\u7528\u6307\u6570\u52a0\u6743\u79fb\u52a8\u5e73\u5747\uff08EWMA\uff09\u5e73\u6ed1\uff1aS<\/mi>~<\/mo><\/mover>t<\/mi><\/msub>=<\/mo>\u03bb<\/mi>S<\/mi>t<\/mi><\/msub>+<\/mo>(<\/mo>1<\/mn>\u2212<\/mo>\u03bb<\/mi>)<\/mo>S<\/mi>~<\/mo><\/mover>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow><\/semantics><\/math>S<\/em>~t<\/em>\u200b=\u03bb<\/em>S<\/em>t<\/em>\u200b+(1\u2212\u03bb<\/em>)S<\/em>~t<\/em>\u22121\u200b<\/p>\n\n\n\n

        \u8fdb\u4e00\u6b65\uff0c\u5b9a\u4e49\u5065\u5eb7\u6307\u6570 H<\/mi>I<\/mi>t<\/mi><\/msub><\/mrow><\/semantics><\/math>H<\/em>I<\/em>t<\/em>\u200b \u4e3a\u5e73\u6ed1\u540e\u5f02\u5e38\u8bc4\u5206\u7684\u5f52\u4e00\u5316\u9006\u51fd\u6570\uff1aH<\/mi>I<\/mi>t<\/mi><\/msub>=<\/mo>exp<\/mi>\u2061<\/mo>(<\/mo>\u2212<\/mo>\u03b3<\/mi>\u22c5<\/mo>S<\/mi>~<\/mo><\/mover>t<\/mi><\/msub>)<\/mo><\/mrow><\/mrow><\/semantics><\/math>H<\/em>I<\/em>t<\/em>\u200b=exp(\u2212\u03b3<\/em>\u22c5S<\/em>~t<\/em>\u200b)<\/p>\n\n\n\n

        \u5176\u4e2d \u03b3<\/mi><\/mrow><\/semantics><\/math>\u03b3<\/em> \u4e3a\u5c3a\u5ea6\u53c2\u6570\u3002H<\/mi>I<\/mi>t<\/mi><\/msub><\/mrow><\/semantics><\/math>H<\/em>I<\/em>t<\/em>\u200b \u4ece1\uff08\u521d\u59cb\u5065\u5eb7\uff09\u5355\u8c03\u9012\u51cf\u52300\uff08\u5b8c\u5168\u5931\u6548\uff09\u3002\u8be5\u5b9a\u4e49\u65e0\u9700\u4efb\u4f55\u6545\u969c\u6807\u7b7e\uff0c\u4ec5\u4f9d\u8d56\u5f53\u524d\u6837\u672c\u4e0e\u6574\u4f53\u6b63\u5e38\u5206\u5e03\u7684\u504f\u79bb\u7a0b\u5ea6\u3002<\/p>\n\n\n\n

        4.2 \u6f5c\u5728\u7a7a\u95f4\u7684\u9000\u5316\u805a\u7c7b<\/h4>\n\n\n\n

        \u5065\u5eb7\u8bc4\u4f30\u7684\u8fdb\u9636\u4efb\u52a1\u662f\u8bc6\u522b\u4e0d\u540c\u7684\u9000\u5316\u9636\u6bb5\uff08\u8f7b\u5fae\u78e8\u635f\u3001\u4e2d\u5ea6\u635f\u4f24\u3001\u4e34\u8fd1\u5931\u6548\uff09\u3002\u672c\u6587\u5229\u7528VAE\u6f5c\u5728\u7a7a\u95f4\u4e2d\u7684\u65f6\u5e8f\u8f68\u8ff9\u8fdb\u884c\u65e0\u76d1\u7763\u805a\u7c7b\uff1a\u5c06 z<\/mi>t<\/mi><\/msub><\/mrow><\/semantics><\/math>z<\/em>t<\/em>\u200b \u5e8f\u5217\u6295\u5f71\u5230\u4e8c\u7ef4\uff08\u5982\u4f7f\u7528t-SNE\uff09\uff0c\u518d\u91c7\u7528\u57fa\u4e8e\u5bc6\u5ea6\u7684OPTICS\u7b97\u6cd5\u81ea\u52a8\u5212\u5206\u9636\u6bb5\u3002\u6bcf\u4e2a\u9636\u6bb5\u7684\u8fb9\u754c\u5bf9\u5e94\u7684 H<\/mi>I<\/mi>t<\/mi><\/msub><\/mrow><\/semantics><\/math>H<\/em>I<\/em>t<\/em>\u200b \u503c\u5373\u5f62\u6210\u9000\u5316\u9608\u503c\u3002<\/p>\n\n\n\n

        5. \u5b9e\u9a8c\u4e0e\u5206\u6790<\/h3>\n\n\n\n

        5.1 \u6570\u636e\u96c6\u6784\u5efa<\/h4>\n\n\n\n

        \u6211\u4eec\u91c7\u96c6\u4e86\u6765\u81ea\u67d0\u975e\u6807\u96f6\u4ef6\u52a0\u5de5\u8f66\u95f4\u7684\u771f\u5b9e\u6570\u636e\uff0c\u5305\u542b\u4e09\u7c7b\u975e\u6807\u96f6\u4ef6\uff1a\u5f02\u5f62\u652f\u67b6\u3001\u975e\u6807\u6cd5\u5170\u76d8\u3001\u4e0d\u89c4\u5219\u8f74\u5957\u3002\u6bcf\u4e2a\u96f6\u4ef6\u5728\u6b63\u5e38\u72b6\u6001\u4e0b\u91c7\u96c6200\u7ec4\u6837\u672c\uff08\u632f\u52a8+3D\u70b9\u4e91\u7279\u5f81\uff09\uff0c\u7136\u540e\u4eba\u5de5\u5f15\u5165\u4e09\u7c7b\u5f02\u5e38\uff1a\u8868\u9762\u6d45\u5212\u75d5\u3001\u5fae\u88c2\u7eb9\uff08\u5bbd\u5ea6<0.1mm\uff09\u3001\u8f7b\u5fae\u88c5\u914d\u9519\u4f4d\u3002\u6d4b\u8bd5\u96c6\u5305\u542b120\u4ef6\u6b63\u5e38\u96f6\u4ef6\u548c60\u4ef6\u5e26\u5f02\u5e38\u96f6\u4ef6\u3002\u6b64\u5916\uff0c\u5bf912\u4ef6\u96f6\u4ef6\u8fdb\u884c\u4e3a\u671f200\u5c0f\u65f6\u7684\u8fde\u7eed\u76d1\u6d4b\uff08\u6bcf10\u5206\u949f\u91c7\u4e00\u6b21\uff09\uff0c\u8bb0\u5f55\u4ece\u5065\u5eb7\u5230\u5931\u6548\u7684\u5168\u8fc7\u7a0b\u3002<\/p>\n\n\n\n

        5.2 \u5bf9\u6bd4\u65b9\u6cd5<\/h4>\n\n\n\n
          \n
        • \u6807\u51c6\u81ea\u7f16\u7801\u5668\uff08AE\uff09<\/strong>\uff1a\u4ee5\u91cd\u6784\u8bef\u5deeMSE\u4e3a\u5f02\u5e38\u6307\u6807\u3002<\/li>\n\n\n\n
        • \u5b64\u7acb\u68ee\u6797\uff08iForest\uff09<\/strong>\uff1a\u7ecf\u5178\u65e0\u76d1\u7763\u5f02\u5e38\u68c0\u6d4b\u3002<\/li>\n\n\n\n
        • \u6df1\u5ea6SVDD<\/strong>\uff1a\u57fa\u4e8e\u8d85\u7403\u9762\u7684\u4e00\u5206\u7c7b\u65b9\u6cd5\u3002<\/li>\n\n\n\n
        • \u672c\u6587VAE\uff08\u8054\u5408\u8bc4\u5206\uff09<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n

          5.3 \u5f02\u5e38\u68c0\u6d4b\u7ed3\u679c<\/h4>\n\n\n\n
          \u65b9\u6cd5<\/th>AUC (\u5f02\u5f62\u652f\u67b6)<\/th>AUC (\u975e\u6807\u6cd5\u5170)<\/th>AUC (\u4e0d\u89c4\u5219\u8f74\u5957)<\/th>\u5e73\u5747AUC<\/th><\/tr><\/thead>
          AE<\/td>0.872<\/td>0.845<\/td>0.863<\/td>0.860<\/td><\/tr>
          iForest<\/td>0.901<\/td>0.883<\/td>0.892<\/td>0.892<\/td><\/tr>
          Deep SVDD<\/td>0.915<\/td>0.906<\/td>0.911<\/td>0.911<\/td><\/tr>
          \u672c\u6587VAE<\/strong><\/td>0.961<\/strong><\/td>0.948<\/strong><\/td>0.955<\/strong><\/td>0.955<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

          \u7ed3\u679c\u8868\u660e\uff0cVAE\u8054\u5408\u8bc4\u5206\u5728\u975e\u6807\u96f6\u4ef6\u4e0a\u663e\u8457\u4f18\u4e8e\u5bf9\u6bd4\u65b9\u6cd5\uff0c\u5c24\u5176\u5728\u5fae\u88c2\u7eb9\u68c0\u6d4b\u4e0a\uff08\u5c0f\u5f02\u5e38\uff09\u4f18\u52bf\u660e\u663e\uff0c\u4e3b\u8981\u5f97\u76ca\u4e8e\u6f5c\u5728\u7a7a\u95f4\u5206\u5e03\u7ea6\u675f\u4e0e\u6ce8\u610f\u529b\u673a\u5236\u3002<\/p>\n\n\n\n

          5.4 \u5065\u5eb7\u72b6\u6001\u8bc4\u4f30\u9a8c\u8bc1<\/h4>\n\n\n\n

          \u5bf9\u4e8e\u8fde\u7eed\u9000\u5316\u6570\u636e\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u7684 H<\/mi>I<\/mi>t<\/mi><\/msub><\/mrow><\/semantics><\/math>H<\/em>I<\/em>t<\/em>\u200b \u4e0e\u4eba\u5de5\u6807\u6ce8\u7684\u5269\u4f59\u5bff\u547d\u767e\u5206\u6bd4\uff08RUL%\uff09\u8fdb\u884c\u76f8\u5173\u6027\u5206\u6790\u3002\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u8fbe\u52300.94\u3002\u6f5c\u5728\u7a7a\u95f4t-SNE\u53ef\u89c6\u5316\u663e\u793a\uff0c\u4e09\u4e2a\u9000\u5316\u9636\u6bb5\uff08\u5065\u5eb7\u3001\u4e9a\u5065\u5eb7\u3001\u6545\u969c\uff09\u5448\u6e05\u6670\u7684\u5e8f\u8d2f\u5206\u79bb\uff0c\u65e0\u91cd\u53e0\u3002\u8fd9\u8bc1\u5b9e\u4e86VAE\u6846\u67b6\u80fd\u591f\u65e0\u76d1\u7763\u5730\u8f93\u51fa\u5177\u6709\u7269\u7406\u610f\u4e49\u7684\u5065\u5eb7\u6307\u6570\u3002<\/p>\n\n\n\n

          6. \u7ed3\u8bba<\/h3>\n\n\n\n

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