{"id":6736,"date":"2024-07-29T19:01:01","date_gmt":"2024-07-29T11:01:01","guid":{"rendered":""},"modified":"2024-07-29T19:01:01","modified_gmt":"2024-07-29T11:01:01","slug":"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316","status":"publish","type":"post","link":"https:\/\/mushiming.com\/6736.html","title":{"rendered":"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316"},"content":{"rendered":"<p>\u53c2\u8003\uff1a\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u8303\u6570\u89c4\u5219\u5316\u4e4b\uff08\u4e00\uff09L0\u3001L1\u4e0eL2\u8303\u6570<\/p>\n<h2>1. \u5e38\u89c1\u7684\u8303\u6570<\/h2>\n<h3>1.1 L0 \u8303\u6570<\/h3>\n<p><strong>\u5411\u91cf\u4e2d\u975e\u96f6\u5143\u7d20\u7684\u4e2a\u6570<\/strong>\uff0c\u5373\u7a00\u758f\u5ea6\uff0c\u9002\u5408\u7a00\u758f\u7f16\u7801\uff0c\u7279\u5f81\u9009\u62e9\u3002<\/p>\n<h3>1.2 L1 \u8303\u6570<\/h3>\n<p>\u53c8\u53eb\u66fc\u54c8\u987f\u8ddd\u79bb\u6216\u6700\u5c0f\u7edd\u5bf9\u8bef\u5dee\uff0c<strong>\u5411\u91cf\u4e2d\u5404\u4e2a\u5143\u7d20\u7edd\u5bf9\u503c\u4e4b\u548c<\/strong>\uff0c\u4e5f\u53eb\u201c\u7a00\u758f\u89c4\u5219\u7b97\u5b50\u201d\u3002<\/p>\n<h3>1.3 L2 \u8303\u6570<\/h3>\n<p>\u53c8\u53eb\u6b27\u5f0f\u8ddd\u79bb\uff0c<strong>\u5411\u91cf\u4e2d\u5404\u5143\u7d20\u5e73\u65b9\u548c\u518d\u5f00\u65b9<\/strong>\u3002<\/p>\n<blockquote>\n<p>L1 \u8303\u6570\u76f8\u5f53\u4e8e\u7ed9\u6a21\u578b\u53c2\u6570<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"\\theta\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c1\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u8bbe\u7f6e\u4e00\u4e2a\u62c9\u666e\u62c9\u65af\u5148\u9a8c\u5206\u5e03\uff1bL2\u8303\u6570\u76f8\u5f53\u4e8e\u7ed9\u6a21\u578b\u53c2\u6570<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"\\theta\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c1\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u8bbe\u7f6e\u4e00\u4e2a\u5747\u503c\u4e3a0\u7684\u9ad8\u65af\u5148\u9a8c\u5206\u5e03\u3002<\/p>\n<\/blockquote>\n<h3>1.4 \u9488\u5bf9\u7ebf\u6027\u56de\u5f52\u95ee\u9898\u600e\u4e48\u9009\u62e9\u60e9\u7f5a\u9879\uff1f<\/h3>\n<p>\u901a\u8fc7\u7f29\u51cf\u56de\u5f52\u7cfb\u6570\u907f\u514d\u8fc7\u62df\u5408\u95ee\u9898\u3002<\/p>\n<p><strong>L1 \u8303\u6570(Lasso\u56de\u5f52)<\/strong><\/p>\n<blockquote>\n<p>1. \u7279\u5f81\u9009\u62e9\uff08\u5c06\u67d0\u4e9b\u7cfb\u6570\u7f29\u51cf\u4e3a0\uff09<\/p>\n<p>2. \u9632\u6b62\u8fc7\u62df\u5408\u3002<\/p>\n<\/blockquote>\n<p><strong>L2 \u8303\u6570(Ridge\u56de\u5f52)<\/strong><\/p>\n<blockquote>\n<p>1. \u89c4\u5219\u5316\uff0c\u8ba9\u4f18\u5316\u6c42\u89e3\u53d8\u5f97\u66f4\u7a33\u5b9a\u5feb\u901f\uff1b<\/p>\n<p>2. \u9632\u6b62\u8fc7\u62df\u5408\u3002<\/p>\n<\/blockquote>\n<h2>2. \u6b63\u5219\u5316<\/h2>\n<h3>2.1 \u6b63\u5219\u5316\u4f5c\u7528<\/h3>\n<p><strong>\u5728\u7ecf\u9a8c\u98ce\u9669\u4e0e\u6a21\u578b\u590d\u6742\u5ea6\u4e4b\u95f4\u505a\u5e73\u8861\uff08\u9009\u62e9\u4e8c\u8005\u540c\u65f6\u8f83\u5c0f\u7684\u6a21\u578b\uff09\uff0c\u9632\u6b62\u8fc7\u62df\u5408\uff0c\u63d0\u9ad8\u6a21\u578b\u6cdb\u5316\u80fd\u529b\u3002<\/strong><\/p>\n<blockquote>\n<p>\u7ed3\u6784\u98ce\u9669 = \u7ecf\u9a8c\u98ce\u9669 (\u6a21\u578b\u5173\u4e8e\u8bad\u7ec3\u6837\u672c\u96c6\u7684\u5e73\u5747\u635f\u5931)+ \u6b63\u5219\u5316\u9879<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"R(f)=\\frac{1}{n}\\sum_{i=1}^{n}L(y_{i},f(x_{i}))+\\lambda \\Omega (f)\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c3\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c3\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u5176\u4e2dlambda\u4e3a\u6b63\u5219\u5316\u53c2\u6570<\/p>\n<\/blockquote>\n<p>\u6b63\u5219\u5316\u662f\u7ed3\u6784\u98ce\u9669\u6700\u5c0f\u5316\u7b56\u7565\u7684\u5b9e\u73b0\uff0c\u901a\u8fc7\u5728\u7ecf\u9a8c\u98ce\u9669\u4e0a\u52a0\u4e0a(\u8868\u793a\u6a21\u578b\u590d\u6742\u5ea6\u7684)\u6b63\u5219\u5316\u9879\u6216\u60e9\u7f5a\u9879\uff0c\u8fbe\u5230\u9009\u62e9\u7ecf\u9a8c\u98ce\u9669\u4e0e\u6a21\u578b\u590d\u6742\u5ea6\u540c\u65f6\u8f83\u5c0f\u6a21\u578b\u7684\u76ee\u7684\u3002\uff08\u5bf9\u53c2\u6570\u505a\u60e9\u7f5a\uff0c\u8ba9\u62df\u5408\u66f2\u7ebf\u53d8\u5f97\u66f4\u5706\u6ed1\uff0c\u6709\u66f4\u5f3a\u7684\u6cdb\u5316\u80fd\u529b\uff09\u3002<\/p>\n<blockquote>\n<p>\u5e7f\u4e49\u4e0a\u7684\u6b63\u5219\u5316\u6280\u672f\uff1a\u80fd\u591f\u663e\u8457\u51cf\u5c11\u65b9\u5dee\uff0c\u800c\u4e0d\u8fc7\u5ea6\u589e\u52a0\u504f\u5dee\u7684\u7b56\u7565\u3002<\/p>\n<p>\u504f\u5dee\u5c0f\u8bf4\u660e\u6a21\u578b\u5bf9\u73b0\u6709\u6570\u636e\u96c6\u62df\u5408\u5f97\u597d\uff0c\u8bef\u5dee\u5c0f\uff0c\u6b64\u65f6\u6a21\u578b\u4e00\u822c\u8f83\u4e3a\u590d\u6742\uff0c\u5b58\u5728\u8fc7\u62df\u5408\u7684\u53ef\u80fd\uff1b<\/p>\n<p>\u65b9\u5dee\u5c0f\u8bf4\u660e\u6a21\u578b\uff08\u4e0d\u592a\u590d\u6742\uff09\u6bd4\u8f83\u7b80\u5355\uff0c\u5177\u6709\u8f83\u597d\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n<\/blockquote>\n<p>\u6a21\u578bError = Bias(\u7cbe\u51c6\u5ea6) + Variance(\u7a33\u5b9a\u6027)\uff0c\u53cd\u6620\u6574\u4e2a\u6a21\u578b\u7684\u51c6\u786e\u5ea6\u3002<\/p>\n<blockquote>\n<p>Bias\uff1a \u6a21\u578b\u5728\u6837\u672c\u4e0a\u7684\u8f93\u51fa\u4e0e\u771f\u5b9e\u503c\u95f4\u7684\u8bef\u5dee\u3002<\/p>\n<p>Variance\uff1a \u6a21\u578b\u6bcf\u4e00\u6b21\u8f93\u51fa\u7ed3\u679c\u4e0e\u8f93\u51fa\u671f\u671b\u4e4b\u95f4\u7684\u8bef\u5dee\u3002<\/p>\n<\/blockquote>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/20210806181836568.png\" =\"\" =\"\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c4\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c4\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u6b63\u5219\u5316\u7684\u4f5c\u7528\u5c31\u662f\u9002\u5f53\u7684\u63a7\u5236\u6a21\u578b\u590d\u6742\u5ea6\uff0c\u4ece\u800c\u4f7f\u6cdb\u5316\u8bef\u5dee\u66f2\u7ebf\u53d6\u6700\u5c0f\u503c\u3002<\/p>\n<h3>2.2 \u6b63\u5219\u5316\u5e38\u7528\u65b9\u6cd5<\/h3>\n<p>L1\uff0cL2\uff0c\u6269\u589e\u6570\u636e\u96c6\uff0c\u65e9\u505c\uff0cDropout\uff0c\u96c6\u6210\u5b66\u4e60\uff0c\u591a\u4efb\u52a1\u5b66\u4e60\uff0c\u5bf9\u6297\u8bad\u7ec3\uff0c\u53c2\u6570\u5171\u4eab\u7b49\u3002<\/p>\n<p>\u5176\u4e2dL1\uff0cL2\u5c5e\u4e8e\u5bf9\u8303\u6570\u505a\u60e9\u7f5a\uff1bDropout\u662f\u6b63\u5219\u5316\u7684\u4e00\u79cd\u65b9\u6cd5\uff0c\u539f\u7406\u7c7b\u4f3cbagging\u3002<\/p>\n<h3>2.3 \u76f8\u5173\u539f\u7406<\/h3>\n<blockquote>\n<p><strong>\u5965\u5361\u59c6\u5243\u5200\u539f\u7406\uff1a<\/strong>\u5728\u6240\u6709\u53ef\u80fd\u9009\u62e9\u7684\u6a21\u578b\u4e2d\uff0c\u6211\u4eec\u5e94\u8be5\u9009\u62e9\u80fd\u591f\u5f88\u597d\u89e3\u91ca\u5df2\u77e5\u6570\u636e\u5e76\u4e14\u5341\u5206\u7b80\u5355\u7684\u6a21\u578b\u3002<\/p>\n<p><strong>NFL(\u6ca1\u6709\u514d\u8d39\u5348\u9910\u539f\u7406):<\/strong> \u5728\u6240\u6709\u95ee\u9898\u540c\u7b49\u91cd\u8981\u7684\u524d\u63d0\u4e0b\uff0c\u65e0\u8bba\u54ea\u79cd\u5b66\u4e60\u7b97\u6cd5\uff0c\u5b83\u4eec\u7684\u671f\u671b\u6027\u80fd\u90fd\u662f\u76f8\u540c\u7684\u3002<\/p>\n<\/blockquote>\n<h2>3. L0 \u4e0eL1 \u6b63\u5219\u5316\u7684\u533a\u522b<\/h2>\n<p>L0 \u8303\u6570\u672c\u8eab\u662f\u7279\u5f81\u9009\u62e9\u7684\u6700\u7406\u60f3\u65b9\u6848\uff0c\u4f46\u56e0\u5176\u5f88\u96be\u4f18\u5316\u6c42\u89e3\uff08\u901a\u5e38\u662fNP\u96be\u95ee\u9898\uff09\u3002\u56e0\u6b64\u5b9e\u9645\u4e2d\u6211\u4eec\u4f7f\u7528L1\u6765\u5f97\u5230L0\u7684\u6700\u4f18\u51f8\u8fd1\u4f3c\uff0c\u6c42\u53d6\u7a00\u758f\u89e3\u3002\u5bf9\u4e8eL1\u8303\u6570\uff0c\u7531\u4e8e|w|\u57280\u5904\u4e0d\u53ef\u5bfc\uff0c\u4f46\u4e3a\u53ef\u53bb\u95f4\u65ad\u70b9\uff0c\u53ef\u4ee5\u901a\u8fc7\u8865\u5145\u8be5\u70b9\u7684\u5b9a\u4e49\u89e3\u51b3\u3002<\/p>\n<p>L0\u548cL1\u6b63\u5219\u53ef\u4ee5\u5f97\u5230\u7a00\u758f\u89e3\uff0c\u800cL2\u4e0d\u80fd\uff0c\u4e14\u53c2\u6570\u4f18\u5316\u901f\u5ea6L1\u5feb\u4e8eL2\uff0c\u4f46L2\u66f4\u5bb9\u6613\u7406\u89e3\uff0c\u8ba1\u7b97\u65b9\u4fbf\uff08\u4e00\u822c\u4e0d\u5bf9\u53c2\u6570b \u8fdb\u884c\u6b63\u5219\uff0c\u56e0\u4e3a\u5b83\u6ca1\u6709\u548c\u6570\u636e\u6709\u76f4\u63a5\u4e58\u6cd5\u4ea4\u4e92\uff09\u3002<\/p>\n<blockquote>\n<p>\u7a00\u758f\u6027(sparsity)\u95ee\u9898\u672c\u8d28\u4e0a\u5bf9\u5e94\u4e86L0\u8303\u6570\u7684\u4f18\u5316\uff0c\u8fd9\u5728\u901a\u5e38\u6761\u4ef6\u4e0b\u662fNP\u96be\u95ee\u9898\u3002<\/p>\n<p>LASSO\u901a\u8fc7L1\u8303\u6570\u6765\u8fd1\u4f3cL0\u8303\u6570\uff0c\u662f\u6c42\u53d6\u7a00\u758f\u89e3\u7684\u91cd\u8981\u6280\u672f\u3002<\/p>\n<\/blockquote>\n<p><strong>L1 \u4f1a\u8d8b\u5411\u4e8e\u4ea7\u751f\u5c11\u91cf\u7684feature\uff0c\u800c\u5176\u4ed6feature\u90fd\u4e3a0\uff1bL2\u5219\u4f1a\u9009\u62e9\u66f4\u591a\u7684\u7279\u5f81\uff0c\u8fd9\u4e9b\u7279\u5f81\u90fd\u4f1a\u63a5\u8fd1\u4e8e0\u3002<\/strong>\u5f53\u9047\u5230\u4e24\u4e2a\u5bf9\u9884\u6d4b\u6709\u5e2e\u52a9\u7684feature\u65f6\uff0cL1\u503e\u5411\u4e8e\u9009\u62e9\u4e00\u4e2a\u66f4\u5927\u7684feature\uff0c\u800cL2\u66f4\u503e\u5411\u4e8e\u628a\u4e24\u8005\u7ed3\u5408\u8d77\u6765\u3002<\/p>\n<blockquote>\n<p>\u8ba9L2\u8303\u6570\u7684\u6b63\u5219\u9879<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"||w||^{2}\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c5\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c5\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u6700\u5c0f\uff0c\u53ef\u4ee5\u4f7fw\u7684\u6bcf\u4e2a\u5143\u7d20\u90fd\u5f88\u5c0f\uff0c\u63a5\u8fd1\u4e8e0\uff0c\u4f46\u4e0d\u4f1a\u50cfL1\u90a3\u6837\u8ba9\u5b83=0\uff0cL2\u76f8\u5bf9\u4e8eL1\u5177\u6709\u66f4\u4e3a\u5e73\u6ed1\u7684\u7279\u6027\uff0c\u56e0\u6b64\u5728\u6a21\u578b\u9884\u6d4b\u4e2d\u5f80\u5f80\u6bd4L1\u5177\u6709\u66f4\u597d\u5730\u9884\u6d4b\u7279\u6027\u3002<\/p>\n<\/blockquote>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/2021080617331858.png\" =\"\" =\"\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c6\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c6\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<\/p>\n<p>&nbsp;L1 \u7ed9\u51fa\u7684\u6700\u4f18\u89e3w*\u66f4\u52a0\u9760\u8fd1\u67d0\u4e9b\u8f74\uff0c\u800c\u5176\u5b83\u8f74\u4e3a0\u3002\u6240\u4ee5L1\u80fd\u4f7f\u5f97\u5230\u7684\u53c2\u6570\u7a00\u758f\u5316\uff0c\u201c\u53ef\u89e3\u91ca\u6027\u201d\u4e5f\u597d\uff1bL2\u7684w*\u66f4\u52a0\u9760\u8fd1\u539f\u70b9\u3002<\/p>\n<h2>4. L1 \u6b63\u5219\u5316\u4e3a\u4ec0\u4e48\u66f4\u5bb9\u6613\u83b7\u5f97\u7a00\u758f\u89e3\uff1f<\/h2>\n<p>L1\u3001L2\u5e38\u88ab\u7528\u6765\u89e3\u51b3\u8fc7\u62df\u5408\u95ee\u9898\uff0c\u800cL1\u8fd8\u53ef\u4ee5\u7528\u4e8e\u7279\u5f81\u9009\u62e9\uff0c\u56e0\u4e3aL1\u4f1a\u4f7f\u5f97\u8f83\u591a\u7684\u53c2\u6570\u4e3a0\uff0c\u4ece\u800c\u4ea7\u751f\u7a00\u758f\u89e3\uff0c\u5c060\u5bf9\u5e94\u7684feature\u9057\u5f03\uff0c\u8fdb\u800c\u7528\u6765\u7279\u5f81\u9009\u62e9\u3002<\/p>\n<p>\u5047\u8bbe\u53ea\u6709\u4e00\u4e2a\u53c2\u6570w\uff0c\u635f\u5931\u51fd\u6570\u4e3aL(w)\uff0c\u5206\u522b\u52a0\u4e0aL1\u3001L2\u6b63\u5219\u5316\u9879\u540e\u6709\uff1a<\/p>\n<blockquote>\n<p><img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"J_{L1}(w)=L(w)+\\lambda |w|\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c7\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c7\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"J_{L2}(w)=L(w)+\\lambda w^{2}\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<\/blockquote>\n<p>\u5047\u8bbeL(w)\u57280\u5904\u7684\u5bfc\u6570\u4e3a<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"d_{0}\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c9\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5373<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"\\frac{\\partial L(w)}{\\partial w}|_{w=0}=d_{0}\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c10\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<blockquote>\n<p><img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"\\frac{\\partial J_{L_{2}}(w)}{\\partial w}|_{w=0}=d_{0}+2\\lambda w|_{w=0}=d_{0}\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c11\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c11\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"\\frac{\\partial J_{L_{1}}(w)}{\\partial w}|_{w=0^{-}}=d_{0}-\\lambda\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c12\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c12\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"\\frac{\\partial J_{L_{1}}(w)}{\\partial w}|_{w=0^{+}}=d_{0}+\\lambda\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c13\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c13\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<\/blockquote>\n<p><strong>\u6613\u77e5\uff1a<\/strong><\/p>\n<p>\u5f53\u5f15\u5165L2\u6b63\u5219\u65f6\uff0c\u4ee3\u4ef7\u51fd\u6570\u57280\u5904\u7684\u5bfc\u6570\u4ecd\u662f<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"d_{0}\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c9\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff1b<\/p>\n<p>\u800c\u5f15\u5165L1\u6b63\u5219\u540e\uff0c\u4ee3\u4ef7\u51fd\u6570\u57280\u5904\u7684\u5bfc\u6570\u6709\u4e00\u4e2a\u7a81\u53d8\uff0c\u4ece<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"d_{0}-\\lambda\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c15\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c15\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5230<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"d_{0}+\\lambda\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c16\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c16\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u82e5<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"d_{0}-\\lambda\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c15\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c15\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e0e<img decoding=\"async\" src=\"https:\/\/latex.csdn.net\/eq\" =\"\" =\"d_{0}+\\lambda\" alt=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316 (https:\/\/mushiming.com\/)  \u7b2c16\u5f20\" title=\"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u5316  \u7b2c16\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5f02\u53f7\uff0c\u5219\u57280\u5904\u4f1a\u662f\u4e00\u4e2a\u6781\u5c0f\u503c\u70b9\u3002<\/p>\n<p>\u56e0\u6b64\u4f18\u5316\u65f6\uff0c\u5f88\u53ef\u80fd\u4f18\u5316\u5230\u8be5\u6781\u5c0f\u503c\u70b9\u4e0a\uff0c\u5373w=0\u5904\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u6b63\u5219\u5316 \u8303\u6570_\u4ec0\u4e48\u662f\u6b63\u5219\u53161.\u7a00\u758f\u6027(sparsity)\u95ee\u9898\u672c\u8d28\u4e0a\u5bf9\u5e94\u4e86L0\u8303\u6570\u7684\u4f18\u5316\uff0c\u8fd9\u5728\u901a\u5e38\u6761\u4ef6\u4e0b\u662fNP\u96be\u95ee\u9898","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/6736"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=6736"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/6736\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=6736"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=6736"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=6736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}