{"id":478675,"date":"2023-08-09T09:36:47","date_gmt":"2023-08-09T09:36:47","guid":{"rendered":""},"modified":"2023-09-05T11:17:20","modified_gmt":"2023-09-05T11:17:20","slug":"regularization-l1-l2","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/cn\/wiki\/regularization-l1-l2\/","title":{"rendered":"\u6b63\u5219\u5316\uff08L1\uff0cL2\uff09"},"content":{"rendered":"<h2>\u4ecb\u7ecd<\/h2>\n<p>\u5728\u673a\u5668\u5b66\u4e60\u548c\u6570\u636e\u5206\u6790\u9886\u57df\uff0c\u6b63\u5219\u5316 (L1, L2) \u662f\u65e8\u5728\u7f13\u89e3\u8fc7\u5ea6\u62df\u5408\u548c\u6a21\u578b\u590d\u6742\u6027\u5e26\u6765\u7684\u6311\u6218\u7684\u57fa\u77f3\u6280\u672f\u3002\u6b63\u5219\u5316\u65b9\u6cd5\uff0c\u7279\u522b\u662f L1 (Lasso) \u548c L2 (Ridge) \u6b63\u5219\u5316\uff0c\u4e0d\u4ec5\u5728\u6570\u636e\u79d1\u5b66\u9886\u57df\uff0c\u800c\u4e14\u5728\u4f18\u5316\u5305\u62ec\u4ee3\u7406\u670d\u52a1\u5668\u5728\u5185\u7684\u5404\u79cd\u6280\u672f\u7684\u6027\u80fd\u65b9\u9762\u90fd\u5360\u6709\u4e00\u5e2d\u4e4b\u5730\u3002\u5728\u8fd9\u7bc7\u7efc\u5408\u6027\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u6df1\u5165\u63a2\u8ba8\u4e86\u6b63\u5219\u5316 (L1, L2)\uff0c\u63a2\u7d22\u4e86\u5b83\u7684\u5386\u53f2\u3001\u673a\u5236\u3001\u7c7b\u578b\u3001\u5e94\u7528\u548c\u672a\u6765\u6f5c\u529b\uff0c\u7279\u522b\u5173\u6ce8\u4e86\u5b83\u4e0e\u4ee3\u7406\u670d\u52a1\u5668\u63d0\u4f9b\u7684\u5173\u8054\u3002<\/p>\n<h2>\u8d77\u6e90\u548c\u65e9\u671f\u63d0\u53ca<\/h2>\n<p>\u6b63\u5219\u5316\u6982\u5ff5\u7684\u51fa\u73b0\u662f\u4e3a\u4e86\u5e94\u5bf9\u673a\u5668\u5b66\u4e60\u6a21\u578b\u4e2d\u7684\u8fc7\u5ea6\u62df\u5408\u73b0\u8c61\uff0c\u8fc7\u5ea6\u62df\u5408\u662f\u6307\u6a21\u578b\u8fc7\u5ea6\u9002\u5e94\u8bad\u7ec3\u6570\u636e\uff0c\u800c\u65e0\u6cd5\u5f88\u597d\u5730\u6cdb\u5316\u5230\u65b0\u7684\u3001\u672a\u89c1\u8fc7\u7684\u6570\u636e\u4e0a\u3002\u201c\u6b63\u5219\u5316\u201d\u4e00\u8bcd\u7684\u8bde\u751f\u662f\u4e3a\u4e86\u63cf\u8ff0\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5bf9\u6a21\u578b\u53c2\u6570\u5f15\u5165\u7ea6\u675f\u6216\u60e9\u7f5a\uff0c\u4ece\u800c\u6709\u6548\u5730\u63a7\u5236\u5176\u5e45\u5ea6\u5e76\u9632\u6b62\u51fa\u73b0\u6781\u7aef\u503c\u3002<\/p>\n<p>\u6b63\u5219\u5316\u7684\u57fa\u672c\u601d\u60f3\u6700\u521d\u7531 Norbert Wiener \u5728 20 \u4e16\u7eaa 30 \u5e74\u4ee3\u63d0\u51fa\uff0c\u4f46\u76f4\u5230 20 \u4e16\u7eaa\u672b\uff0c\u8fd9\u4e9b\u6982\u5ff5\u624d\u5728\u673a\u5668\u5b66\u4e60\u548c\u7edf\u8ba1\u5b66\u9886\u57df\u5f97\u5230\u5e7f\u6cdb\u5e94\u7528\u3002\u9ad8\u7ef4\u6570\u636e\u548c\u65e5\u76ca\u590d\u6742\u7684\u6a21\u578b\u7684\u51fa\u73b0\u51f8\u663e\u4e86\u5bf9\u7a33\u5065\u6280\u672f\u7684\u9700\u6c42\uff0c\u4ee5\u4fdd\u6301\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002L1 \u548c L2 \u6b63\u5219\u5316\u662f\u4e24\u79cd\u8457\u540d\u7684\u6b63\u5219\u5316\u5f62\u5f0f\uff0c\u5b83\u4eec\u88ab\u5f15\u5165\u5e76\u6b63\u5f0f\u5316\u4e3a\u5e94\u5bf9\u8fd9\u4e9b\u6311\u6218\u7684\u6280\u672f\u3002<\/p>\n<h2>\u63ed\u793a\u6b63\u5219\u5316\uff08L1\uff0cL2\uff09<\/h2>\n<h3>\u673a\u68b0\u548c\u64cd\u4f5c<\/h3>\n<p>\u6b63\u5219\u5316\u65b9\u6cd5\u901a\u8fc7\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5411\u635f\u5931\u51fd\u6570\u6dfb\u52a0\u60e9\u7f5a\u9879\u6765\u53d1\u6325\u4f5c\u7528\u3002\u8fd9\u4e9b\u60e9\u7f5a\u4f1a\u963b\u6b62\u6a21\u578b\u4e3a\u67d0\u4e9b\u7279\u5f81\u5206\u914d\u8fc7\u5927\u7684\u6743\u91cd\uff0c\u4ece\u800c\u9632\u6b62\u6a21\u578b\u8fc7\u5206\u5f3a\u8c03\u53ef\u80fd\u5bfc\u81f4\u8fc7\u5ea6\u62df\u5408\u7684\u5608\u6742\u6216\u4e0d\u76f8\u5173\u7684\u7279\u5f81\u3002L1 \u548c L2 \u6b63\u5219\u5316\u4e4b\u95f4\u7684\u4e3b\u8981\u533a\u522b\u5728\u4e8e\u5b83\u4eec\u5e94\u7528\u7684\u60e9\u7f5a\u7c7b\u578b\u3002<\/p>\n<p><strong>L1 \u6b63\u5219\u5316\uff08Lasso\uff09\uff1a<\/strong> L1 \u6b63\u5219\u5316\u5f15\u5165\u4e86\u4e0e\u6a21\u578b\u53c2\u6570\u6743\u91cd\u7684\u7edd\u5bf9\u503c\u6210\u6bd4\u4f8b\u7684\u60e9\u7f5a\u9879\u3002\u8fd9\u53ef\u4ee5\u5c06\u4e00\u4e9b\u53c2\u6570\u6743\u91cd\u7cbe\u786e\u5730\u8bbe\u4e3a\u96f6\uff0c\u4ece\u800c\u6709\u6548\u5730\u6267\u884c\u7279\u5f81\u9009\u62e9\u5e76\u4ea7\u751f\u66f4\u7a00\u758f\u7684\u6a21\u578b\u3002<\/p>\n<p><strong>L2 \u6b63\u5219\u5316\uff08\u5cad\uff09\uff1a<\/strong> \u53e6\u4e00\u65b9\u9762\uff0cL2 \u6b63\u5219\u5316\u6dfb\u52a0\u4e86\u4e0e\u53c2\u6570\u6743\u91cd\u5e73\u65b9\u6210\u6bd4\u4f8b\u7684\u60e9\u7f5a\u9879\u3002\u8fd9\u9f13\u52b1\u6a21\u578b\u5c06\u5176\u6743\u91cd\u66f4\u5747\u5300\u5730\u5206\u5e03\u5728\u6240\u6709\u7279\u5f81\u4e0a\uff0c\u800c\u4e0d\u662f\u96c6\u4e2d\u5728\u5c11\u6570\u51e0\u4e2a\u7279\u5f81\u4e0a\u3002\u5b83\u53ef\u4ee5\u9632\u6b62\u6781\u7aef\u503c\u5e76\u63d0\u9ad8\u7a33\u5b9a\u6027\u3002<\/p>\n<h2>\u6b63\u5219\u5316\uff08L1\u3001L2\uff09\u7684\u4e3b\u8981\u7279\u5f81<\/h2>\n<ol>\n<li>\n<p><strong>\u9632\u6b62\u8fc7\u5ea6\u62df\u5408\uff1a<\/strong> \u6b63\u5219\u5316\u6280\u672f\u901a\u8fc7\u6291\u5236\u6a21\u578b\u7684\u590d\u6742\u6027\u663e\u8457\u51cf\u5c11\u8fc7\u5ea6\u62df\u5408\uff0c\u4f7f\u5176\u66f4\u597d\u5730\u63a8\u5e7f\u5230\u65b0\u6570\u636e\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7279\u5f81\u9009\u62e9\uff1a<\/strong> L1 \u6b63\u5219\u5316\u672c\u8d28\u4e0a\u901a\u8fc7\u5c06\u67d0\u4e9b\u7279\u5f81\u6743\u91cd\u8bbe\u4e3a\u96f6\u6765\u6267\u884c\u7279\u5f81\u9009\u62e9\u3002\u8fd9\u5728\u5904\u7406\u9ad8\u7ef4\u6570\u636e\u96c6\u65f6\u975e\u5e38\u6709\u7528\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u53c2\u6570\u7a33\u5b9a\u6027\uff1a<\/strong> L2 \u6b63\u5219\u5316\u589e\u5f3a\u4e86\u53c2\u6570\u4f30\u8ba1\u7684\u7a33\u5b9a\u6027\uff0c\u4f7f\u5f97\u6a21\u578b\u7684\u9884\u6d4b\u5bf9\u8f93\u5165\u6570\u636e\u7684\u7ec6\u5fae\u53d8\u5316\u4e0d\u592a\u654f\u611f\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u6b63\u5219\u5316\u7684\u7c7b\u578b\uff08L1\u3001L2\uff09<\/h2>\n<table>\n<thead>\n<tr>\n<th>\u7c7b\u578b<\/th>\n<th>\u673a\u5236<\/th>\n<th>\u4f7f\u7528\u6848\u4f8b<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>L1 \u6b63\u5219\u5316\uff08Lasso\uff09<\/td>\n<td>\u60e9\u7f5a\u7edd\u5bf9\u53c2\u6570\u503c<\/td>\n<td>\u7279\u5f81\u9009\u62e9\u3001\u7a00\u758f\u6a21\u578b<\/td>\n<\/tr>\n<tr>\n<td>L2 \u6b63\u5219\u5316\uff08\u5cad\uff09<\/td>\n<td>\u60e9\u7f5a\u5e73\u65b9\u53c2\u6570\u503c<\/td>\n<td>\u63d0\u9ad8\u53c2\u6570\u7a33\u5b9a\u6027\u3001\u6574\u4f53\u5e73\u8861\u6027<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u5e94\u7528\u3001\u6311\u6218\u548c\u89e3\u51b3\u65b9\u6848<\/h2>\n<p>\u6b63\u5219\u5316\u6280\u672f\u5177\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u4ece\u7ebf\u6027\u56de\u5f52\u548c\u903b\u8f91\u56de\u5f52\u5230\u795e\u7ecf\u7f51\u7edc\u548c\u6df1\u5ea6\u5b66\u4e60\u3002\u5b83\u4eec\u5728\u5904\u7406\u5c0f\u578b\u6570\u636e\u96c6\u6216\u5177\u6709\u9ad8\u7279\u5f81\u7ef4\u5ea6\u7684\u6570\u636e\u96c6\u65f6\u7279\u522b\u6709\u7528\u3002\u7136\u800c\uff0c\u5e94\u7528\u6b63\u5219\u5316\u5e76\u975e\u6ca1\u6709\u6311\u6218\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u9009\u62e9\u6b63\u5219\u5316\u5f3a\u5ea6\uff1a<\/strong> \u5fc5\u987b\u5728\u9632\u6b62\u8fc7\u5ea6\u62df\u5408\u548c\u4e0d\u8fc7\u5ea6\u9650\u5236\u6a21\u578b\u6355\u6349\u590d\u6742\u6a21\u5f0f\u7684\u80fd\u529b\u4e4b\u95f4\u53d6\u5f97\u5e73\u8861\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u53ef\u89e3\u91ca\u6027\uff1a<\/strong> \u867d\u7136 L1 \u6b63\u5219\u5316\u53ef\u4ee5\u901a\u8fc7\u7279\u5f81\u9009\u62e9\u4ea7\u751f\u66f4\u53ef\u89e3\u91ca\u7684\u6a21\u578b\uff0c\u4f46\u5b83\u53ef\u80fd\u4f1a\u4e22\u5f03\u6f5c\u5728\u7684\u6709\u7528\u4fe1\u606f\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u6bd4\u8f83\u548c\u89c2\u70b9<\/h2>\n<table>\n<thead>\n<tr>\n<th>\u6bd4\u8f83<\/th>\n<th>\u6b63\u5219\u5316\uff08L1\uff0cL2\uff09<\/th>\n<th>Dropout\uff08\u6b63\u5219\u5316\uff09<\/th>\n<th>\u6279\u91cf\u6807\u51c6\u5316<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u673a\u5236<\/td>\n<td>\u4f53\u91cd\u60e9\u7f5a<\/td>\n<td>\u795e\u7ecf\u5143\u5931\u6d3b<\/td>\n<td>\u89c4\u8303\u5316\u5c42\u6fc0\u6d3b<\/td>\n<\/tr>\n<tr>\n<td>\u9884\u9632\u8fc7\u5ea6\u62df\u5408<\/td>\n<td>\u662f\u7684<\/td>\n<td>\u662f\u7684<\/td>\n<td>\u4e0d<\/td>\n<\/tr>\n<tr>\n<td>\u53ef\u89e3\u91ca\u6027<\/td>\n<td>\u9ad8 (L1) \/ \u4e2d\u7b49 (L2)<\/td>\n<td>\u4f4e\u7684<\/td>\n<td>\u4e0d\u9002\u7528<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u672a\u6765\u6f5c\u529b\u548c\u4ee3\u7406\u670d\u52a1\u5668\u96c6\u6210<\/h2>\n<p>\u968f\u7740\u6280\u672f\u7684\u8fdb\u6b65\uff0c\u6b63\u5219\u5316\u7684\u672a\u6765\u524d\u666f\u5149\u660e\u3002\u968f\u7740\u6570\u636e\u7684\u590d\u6742\u6027\u548c\u7ef4\u5ea6\u4e0d\u65ad\u589e\u957f\uff0c\u5bf9\u589e\u5f3a\u6a21\u578b\u6cdb\u5316\u80fd\u529b\u7684\u6280\u672f\u7684\u9700\u6c42\u53d8\u5f97\u66f4\u52a0\u5173\u952e\u3002\u5728\u4ee3\u7406\u670d\u52a1\u5668\u63d0\u4f9b\u9886\u57df\uff0c\u6b63\u5219\u5316\u6280\u672f\u53ef\u4ee5\u5728\u4f18\u5316\u8d44\u6e90\u5206\u914d\u3001\u8d1f\u8f7d\u5e73\u8861\u548c\u63d0\u9ad8\u7f51\u7edc\u6d41\u91cf\u5206\u6790\u7684\u5b89\u5168\u6027\u65b9\u9762\u53d1\u6325\u4f5c\u7528\u3002<\/p>\n<h2>\u7ed3\u8bba<\/h2>\n<p>\u6b63\u5219\u5316\uff08L1\u3001L2\uff09\u662f\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u57fa\u77f3\uff0c\u4e3a\u8fc7\u5ea6\u62df\u5408\u548c\u6a21\u578b\u590d\u6742\u6027\u63d0\u4f9b\u4e86\u6709\u6548\u7684\u89e3\u51b3\u65b9\u6848\u3002L1 \u548c L2 \u6b63\u5219\u5316\u6280\u672f\u5df2\u8fdb\u5165\u5404\u79cd\u5e94\u7528\u9886\u57df\uff0c\u6709\u53ef\u80fd\u5f7b\u5e95\u6539\u53d8\u4ee3\u7406\u670d\u52a1\u5668\u63d0\u4f9b\u7b49\u9886\u57df\u3002\u968f\u7740\u6280\u672f\u7684\u8fdb\u6b65\uff0c\u6b63\u5219\u5316\u6280\u672f\u4e0e\u5c16\u7aef\u6280\u672f\u7684\u7ed3\u5408\u65e0\u7591\u5c06\u63d0\u9ad8\u5404\u4e2a\u9886\u57df\u7684\u6548\u7387\u548c\u6027\u80fd\u3002<\/p>\n<h2>\u76f8\u5173\u94fe\u63a5<\/h2>\n<p>\u6709\u5173\u6b63\u5219\u5316\uff08L1\uff0cL2\uff09\u53ca\u5176\u5e94\u7528\u7684\u66f4\u591a\u6df1\u5165\u4fe1\u606f\uff0c\u8bf7\u8003\u8651\u63a2\u7d22\u4ee5\u4e0b\u8d44\u6e90\uff1a<\/p>\n<ul>\n<li><a href=\"https:\/\/web.stanford.edu\/~hastie\/StatLearnSparsity_files\/SLS.pdf\" target=\"_new\" rel=\"noopener nofollow\">\u65af\u5766\u798f\u5927\u5b66\uff1a\u6b63\u5219\u5316<\/a><\/li>\n<li><a href=\"https:\/\/scikit-learn.org\/stable\/modules\/linear_model.html#regularization\" target=\"_new\" rel=\"noopener nofollow\">Scikit-learn \u6587\u6863\uff1a\u6b63\u5219\u5316<\/a><\/li>\n<li><a href=\"https:\/\/towardsdatascience.com\/introduction-to-regularization-in-machine-learning-91e094a367d5\" target=\"_new\" rel=\"noopener nofollow\">\u8d70\u5411\u6570\u636e\u79d1\u5b66\uff1a\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u6b63\u5219\u5316\u7b80\u4ecb<\/a><\/li>\n<\/ul>\n<p>\u8bbf\u95ee\u4ee5\u4e0b\u7f51\u7ad9\uff0c\u4e86\u89e3\u673a\u5668\u5b66\u4e60\u3001\u6570\u636e\u5206\u6790\u548c\u4ee3\u7406\u670d\u52a1\u5668\u6280\u672f\u7684\u6700\u65b0\u8fdb\u5c55 <a href=\"https:\/\/oneproxy.pro\/cn\/blog\/\" target=\"_new\" rel=\"noopener\">OneProxy<\/a> \u7ecf\u5e38\u3002<\/p>","protected":false},"featured_media":0,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-478675","wiki","type-wiki","status-publish","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Regularization (L1, L2): Enhancing Proxy Server Performance<\/mark>","faq_items":[{"question":"What is Regularization, and why is it important in machine learning?","answer":"<p>Regularization is a technique used in machine learning to prevent overfitting, which occurs when a model becomes too tailored to the training data and struggles to generalize well on new data. It involves adding penalty terms to the model's loss function, curbing the complexity of the model and enhancing its ability to generalize to unseen data.<\/p>"},{"question":"What are L1 and L2 regularization, and how do they work?","answer":"<p>L1 regularization (Lasso) and L2 regularization (Ridge) are two prominent types of regularization. L1 introduces a penalty based on the absolute values of parameter weights, driving some weights to zero and performing feature selection. L2 adds a penalty based on the squared values of parameter weights, distributing weights more evenly across features and improving stability.<\/p>"},{"question":"What are the key benefits of using regularization?","answer":"<p>Regularization techniques offer several advantages, including preventing overfitting, enhancing model stability, and promoting generalization to new data. L1 regularization aids in feature selection, while L2 regularization balances parameter values.<\/p>"},{"question":"How do L1 and L2 regularization differ in their effects on model interpretability?","answer":"<p>L1 regularization tends to lead to higher model interpretability due to its feature selection capability. It can help identify the most relevant features by driving some feature weights to zero. L2 regularization, while promoting stability, may not directly provide the same level of interpretability.<\/p>"},{"question":"What are the challenges in applying regularization?","answer":"<p>Choosing the right strength of regularization is crucial; too much can lead to underfitting, while too little may not prevent overfitting effectively. Additionally, L1 regularization might discard useful information along with noisy features.<\/p>"},{"question":"How can regularization techniques impact proxy server provision?","answer":"<p>In the realm of proxy server provision, regularization techniques could optimize resource allocation, load balancing, and enhance security in network traffic analysis. Regularization could contribute to efficient and secure proxy server operation.<\/p>"},{"question":"How can I learn more about regularization and its applications?","answer":"<p>For a deeper understanding of regularization (L1, L2) and its applications, you can explore resources such as the Stanford University documentation on regularization, the Scikit-learn documentation on linear models, and informative articles on platforms like Towards Data Science. Stay informed about the latest advancements by visiting OneProxy's blog regularly.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/478675","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/478675\/revisions"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media?parent=478675"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}