{"id":54035,"date":"2025-08-12T21:09:57","date_gmt":"2025-08-12T13:09:57","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/54035.html"},"modified":"2025-08-12T21:09:57","modified_gmt":"2025-08-12T13:09:57","slug":"%e6%94%af%e6%8c%81%e5%90%91%e9%87%8f%e5%9b%9e%e5%bd%92%ef%bc%88svr%ef%bc%89%ef%bc%9a%e7%94%a8%e5%b0%91%e6%95%b0%e5%85%b3%e9%94%ae%e6%a0%b7%e6%9c%ac%e6%90%9e%e5%ae%9a%e9%9d%9e","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/54035.html","title":{"rendered":"\u652f\u6301\u5411\u91cf\u56de\u5f52\uff08SVR\uff09\uff1a\u7528\u201c\u5c11\u6570\u5173\u952e\u6837\u672c\u201d\u641e\u5b9a\u975e\u7ebf\u6027\u56de\u5f52\uff0c\u8fdeSVM\u90fd\u8981\u7ed9\u5b83\u70b9\u8d5e\uff01"},"content":{"rendered":"<h2><\/h2>\n<p>\u505a\u56de\u5f52\u9884\u6d4b\u65f6&#xff0c;\u4f60\u662f\u4e0d\u662f\u5e38\u9047\u5230\u8fd9\u6837\u7684\u96be\u9898&#xff1a;\u6570\u636e\u662f\u975e\u7ebf\u6027\u7684&#xff08;\u6bd4\u5982\u623f\u4ef7\u968f\u9762\u79ef\u589e\u957f\u5148\u6162\u540e\u5feb&#xff09;&#xff0c;\u7279\u5f81\u7ef4\u5ea6\u8fd8\u9ad8&#xff08;\u6bd4\u5982\u5305\u542b100\u4e2a\u7528\u6237\u884c\u4e3a\u7279\u5f81&#xff09;&#xff0c;\u7528\u7ebf\u6027\u56de\u5f52\u62df\u5408\u6548\u679c\u5dee&#xff0c;\u7528\u590d\u6742\u6a21\u578b\u53c8\u5bb9\u6613\u8fc7\u62df\u5408&#xff1f;<\/p>\n<p>\u4eca\u5929\u8981\u8bb2\u7684\u652f\u6301\u5411\u91cf\u56de\u5f52&#xff08;SVR&#xff09;&#xff0c;\u582a\u79f0\u89e3\u51b3\u8fd9\u7c7b\u95ee\u9898\u7684\u201c\u5229\u5668\u201d\u3002\u5b83\u7ee7\u627f\u4e86\u652f\u6301\u5411\u91cf\u673a&#xff08;SVM&#xff09;\u7684\u201c\u6838\u6280\u5de7\u201d&#xff0c;\u80fd\u8f7b\u677e\u5904\u7406\u975e\u7ebf\u6027\u5173\u7cfb&#xff1b;\u66f4\u5389\u5bb3\u7684\u662f&#xff0c;\u5b83\u53ea\u9760\u201c\u5c11\u6570\u5173\u952e\u6837\u672c\u201d&#xff08;\u652f\u6301\u5411\u91cf&#xff09;\u6784\u5efa\u6a21\u578b&#xff0c;\u65e2\u9ad8\u6548\u53c8\u4e0d\u6613\u8fc7\u62df\u5408\u3002\u4ece\u539f\u7406\u5230\u4ee3\u7801&#xff0c;\u4e00\u6b21\u8bb2\u900fSVR\u7684\u201c\u72ec\u95e8\u79d8\u7c4d\u201d&#xff01;<\/p>\n<h3>\u4e00\u3001SVR&#xff1a;\u4e0d\u6b62\u80fd\u5206\u7c7b&#xff0c;\u56de\u5f52\u4e5f\u5f88\u5728\u884c<\/h3>\n<p>\u652f\u6301\u5411\u91cf\u673a&#xff08;SVM&#xff09;\u5927\u5bb6\u53ef\u80fd\u66f4\u719f\u6089\u5b83\u7684\u5206\u7c7b\u529f\u80fd&#xff08;\u6bd4\u5982\u533a\u5206\u201c\u5783\u573e\u90ae\u4ef6\u201d\u548c\u201c\u6b63\u5e38\u90ae\u4ef6\u201d&#xff09;&#xff0c;\u4f46\u5b83\u7684\u201c\u4eb2\u621a\u201dSVR&#xff08;Support Vector Regression&#xff09;\u5728\u56de\u5f52\u95ee\u9898\u4e2d\u540c\u6837\u51fa\u8272\u3002<\/p>\n<p>\u6838\u5fc3\u533a\u522b&#xff1a;<\/p>\n<ul>\n<li>SVM\u5206\u7c7b&#xff1a;\u627e\u4e00\u6761\u201c\u6700\u5bbd\u7684\u7ebf\u201d\u5206\u9694\u4e24\u7c7b\u6837\u672c&#xff1b;<\/li>\n<li>SVR\u56de\u5f52&#xff1a;\u627e\u4e00\u6761\u201c\u5bb9\u9519\u7a7a\u95f4\u6700\u5927\u7684\u7ebf\u201d\u62df\u5408\u6837\u672c&#xff0c;\u5141\u8bb8\u6837\u672c\u5728\u4e00\u5b9a\u8303\u56f4\u5185\u201c\u4e0d\u8d34\u5408\u201d&#xff08;\u8fd9\u4e2a\u8303\u56f4\u53eb\u03b5-\u7ba1\u9053&#xff09;\u3002<\/li>\n<\/ul>\n<h3>\u4e8c\u3001SVR\u7684\u201c\u6838\u5fc3\u601d\u60f3\u201d&#xff1a;\u7ed9\u8bef\u5dee\u201c\u5212\u4e2a\u5bb9\u5fcd\u533a\u201d<\/h3>\n<p>\u4f20\u7edf\u56de\u5f52&#xff08;\u5982\u7ebf\u6027\u56de\u5f52&#xff09;\u8ffd\u6c42\u201c\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u5b8c\u5168\u4e00\u81f4\u201d&#xff0c;\u4f46\u73b0\u5b9e\u6570\u636e\u603b\u6709\u566a\u58f0&#xff0c;\u8fc7\u5ea6\u8ffd\u6c42\u7cbe\u786e\u53cd\u800c\u4f1a\u8fc7\u62df\u5408\u3002SVR\u53cd\u5176\u9053\u800c\u884c&#xff1a;\u5141\u8bb8\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u6709\u4e00\u5b9a\u8bef\u5dee&#xff08;\u03b5&#xff09;&#xff0c;\u53ea\u8981\u5728\u8fd9\u4e2a\u8303\u56f4\u5185&#xff0c;\u5c31\u4e0d\u7b97\u201c\u72af\u9519\u201d\u3002<\/p>\n<h4>1. \u03b5-\u4e0d\u654f\u611f\u635f\u5931\u51fd\u6570&#xff1a;\u8bef\u5dee\u5728\u03b5\u5185&#xff0c;\u5c31\u201c\u5f53\u6ca1\u770b\u89c1\u201d<\/h4>\n<p>SVR\u5b9a\u4e49\u4e86\u4e00\u4e2a\u201c\u5bbd\u5bb9\u201d\u7684\u635f\u5931\u51fd\u6570&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">L\u03b5(y,y^)&#061;max\u2061(0,\u2223y\u2212y^\u2223\u2212\u03b5)L_\\\\varepsilon(y, \\\\hat{y}) &#061; \\\\max(0, |y &#8211; \\\\hat{y}| &#8211; \\\\varepsilon)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">\u03b5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\">max<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">\u03b5<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u5f53\u9884\u6d4b\u8bef\u5dee<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2223y\u2212y^\u2223\u2264\u03b5|y &#8211; \\\\hat{y}| \\\\leq \\\\varepsilon<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">\u03b5<\/span><\/span><\/span><\/span><\/span>\u65f6&#xff0c;\u635f\u5931\u4e3a0&#xff08;\u4e0d\u60e9\u7f5a&#xff09;&#xff1b;<\/li>\n<li>\u5f53\u8bef\u5dee\u8d85\u8fc7\u03b5\u65f6&#xff0c;\u53ea\u60e9\u7f5a\u8d85\u8fc7\u7684\u90e8\u5206&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2223y\u2212y^\u2223\u2212\u03b5|y &#8211; \\\\hat{y}| &#8211; \\\\varepsilon<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">\u03b5<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u5f62\u8c61\u7406\u89e3&#xff1a;\u5c31\u50cf\u7ed9\u56de\u5f52\u66f2\u7ebf\u753b\u4e86\u4e00\u6761\u201c\u03b5\u5bbd\u5ea6\u7684\u7ba1\u9053\u201d&#xff0c;\u53ea\u8981\u6837\u672c\u70b9\u843d\u5728\u7ba1\u9053\u5185&#xff0c;\u5c31\u8ba4\u4e3a\u62df\u5408\u5408\u683c&#xff1b;\u53ea\u6709\u8dd1\u51fa\u7ba1\u9053\u7684\u70b9\u624d\u9700\u8981\u88ab\u201c\u62c9\u56de\u6765\u201d\u3002<\/p>\n<h4>2. \u652f\u6301\u5411\u91cf&#xff1a;\u51b3\u5b9a\u7ba1\u9053\u4f4d\u7f6e\u7684\u201c\u5173\u952e\u6837\u672c\u201d<\/h4>\n<p>SVR\u7684\u56de\u5f52\u66f2\u7ebf\u7531\u5c11\u6570\u8dd1\u51fa\u7ba1\u9053\u6216\u5728\u7ba1\u9053\u8fb9\u7f18\u7684\u6837\u672c\u51b3\u5b9a&#xff0c;\u8fd9\u4e9b\u6837\u672c\u53eb\u201c\u652f\u6301\u5411\u91cf\u201d&#xff1a;<\/p>\n<ul>\n<li>\u8dd1\u51fa\u7ba1\u9053\u7684\u6837\u672c&#xff1a;\u4f1a\u201c\u62c9\u201d\u66f2\u7ebf\u5411\u81ea\u5df1\u9760\u8fd1&#xff1b;<\/li>\n<li>\u7ba1\u9053\u8fb9\u7f18\u7684\u6837\u672c&#xff1a;\u5b9a\u4e49\u4e86\u7ba1\u9053\u7684\u8fb9\u754c&#xff1b;<\/li>\n<li>\u7ba1\u9053\u5185\u7684\u6837\u672c&#xff1a;\u5bf9\u66f2\u7ebf\u4f4d\u7f6e\u65e0\u5f71\u54cd&#xff08;\u53ef\u4ee5\u5ffd\u7565&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u8fd9\u5c31\u662fSVR\u9ad8\u6548\u7684\u539f\u56e0\u2014\u2014\u5b83\u53ea\u5173\u6ce8\u201c\u5173\u952e\u6837\u672c\u201d&#xff0c;\u4e0d\u7528\u8003\u8651\u6240\u6709\u6570\u636e\u3002<\/p>\n<h4>3. \u6838\u6280\u5de7&#xff1a;\u8ba9SVR\u641e\u5b9a\u975e\u7ebf\u6027\u5173\u7cfb<\/h4>\n<p>\u73b0\u5b9e\u4e2d&#xff0c;\u5f88\u591a\u6570\u636e\u662f\u975e\u7ebf\u6027\u7684&#xff08;\u6bd4\u5982<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">y&#061;sin\u2061(x)y &#061; \\\\sin(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u76f4\u63a5\u7528\u76f4\u7ebf\u62df\u5408\u6548\u679c\u5dee\u3002SVR\u901a\u8fc7\u6838\u51fd\u6570\u5c06\u4f4e\u7ef4\u6570\u636e\u6620\u5c04\u5230\u9ad8\u7ef4\u7a7a\u95f4&#xff0c;\u8ba9\u975e\u7ebf\u6027\u5173\u7cfb\u5728\u9ad8\u7ef4\u7a7a\u95f4\u53d8\u6210\u7ebf\u6027\u5173\u7cfb&#xff0c;\u518d\u7528\u7ebf\u6027\u56de\u5f52\u62df\u5408\u3002<\/p>\n<p>\u6700\u5e38\u7528\u7684\u6838\u51fd\u6570\u662fRBF&#xff08;\u5f84\u5411\u57fa\u51fd\u6570&#xff09;&#xff0c;\u5b83\u80fd\u5904\u7406\u51e0\u4e4e\u6240\u6709\u975e\u7ebf\u6027\u573a\u666f&#xff0c;\u516c\u5f0f&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">K(xi,xj)&#061;exp\u2061(\u2212\u03b3\u2223\u2223xi\u2212xj\u2223\u22232)K(x_i, x_j) &#061; \\\\exp(-\\\\gamma ||x_i &#8211; x_j||^2)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0556em\">\u03b3<\/span><span class=\"mord\">\u2223\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1502em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#xff08;\u03b3\u662f\u6838\u7cfb\u6570&#xff0c;\u63a7\u5236\u6620\u5c04\u7684\u590d\u6742\u5ea6&#xff09;<\/p>\n<h3>\u4e09\u3001SVR\u6838\u5fc3\u516c\u5f0f&#xff1a;\u4ece\u201c\u7ea6\u675f\u6761\u4ef6\u201d\u5230\u201c\u56de\u5f52\u66f2\u7ebf\u201d<\/h3>\n<h4>1. \u4f18\u5316\u76ee\u6807&#xff1a;\u8ba9\u7ba1\u9053\u5c3d\u53ef\u80fd\u5bbd&#xff0c;\u540c\u65f6\u60e9\u7f5a\u8d85\u754c\u6837\u672c<\/h4>\n<p>SVR\u7684\u76ee\u6807\u662f\u627e\u5230\u56de\u5f52\u51fd\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">f(x)&#061;w\u22c5\u03d5(x)&#043;bf(x) &#061; w \\\\cdot \\\\phi(x) &#043; b<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4445em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span>&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03d5(x)\\\\phi(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u662f\u6838\u51fd\u6570\u6620\u5c04&#xff09;&#xff0c;\u4f7f\u5f97&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">min\u2061w,b,\u03be,\u03be\u221712\u2223\u2223w\u2223\u22232&#043;C\u2211i&#061;1n(\u03bei&#043;\u03bei\u2217)\\\\min_{w,b,\\\\xi,\\\\xi^*} \\\\frac{1}{2}||w||^2 &#043; C \\\\sum_{i&#061;1}^n (\\\\xi_i &#043; \\\\xi_i^*)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.2097em;vertical-align: -0.8882em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -2.3479em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6183em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">min<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8882em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\">\u2223\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.9291em;vertical-align: -1.2777em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6514em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7387em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7ea6\u675f\u6761\u4ef6&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">{yi\u2212f(xi)\u2264\u03b5&#043;\u03beif(xi)\u2212yi\u2264\u03b5&#043;\u03bei\u2217\u03bei,\u03bei\u2217\u22650\\\\begin{cases}<br \/>\ny_i &#8211; f(x_i) \\\\leq \\\\varepsilon &#043; \\\\xi_i \\\\\\\\<br \/>\nf(x_i) &#8211; y_i \\\\leq \\\\varepsilon &#043; \\\\xi_i^* \\\\\\\\<br \/>\n\\\\xi_i, \\\\xi_i^* \\\\geq 0<br \/>\n\\\\end{cases}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 4.32em;vertical-align: -1.91em\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.35em\"><span class=\"\" style=\"top: -2.2em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"top: -2.192em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"\" style=\"height: 0.316em;width: 0.8889em\"><\/span><\/span><span class=\"\" style=\"top: -3.15em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"top: -4.292em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"\" style=\"height: 0.316em;width: 0.8889em\"><\/span><\/span><span class=\"\" style=\"top: -4.6em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a7<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.85em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.41em\"><span class=\"\" style=\"top: -4.41em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">\u03b5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.97em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">\u03b5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -1.53em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.91em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2223\u2223w\u2223\u22232||w||^2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u63a7\u5236\u7ba1\u9053\u5bbd\u5ea6&#xff08;\u8d8a\u5c0f\u8d8a\u5bbd&#xff09;&#xff1b;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u60e9\u7f5a\u7cfb\u6570&#xff08;C\u8d8a\u5927&#xff0c;\u5bf9\u8d85\u754c\u6837\u672c\u7684\u60e9\u7f5a\u8d8a\u91cd&#xff0c;\u6a21\u578b\u8d8a\u201c\u4e25\u683c\u201d&#xff09;&#xff1b;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bei,\u03bei\u2217\\\\xi_i, \\\\xi_i^*<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9531em;vertical-align: -0.2587em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u8d85\u754c\u6837\u672c\u7684\u8bef\u5dee&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bei\\\\xi_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">yiy_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5728\u7ba1\u9053\u4e0a\u65b9\u7684\u8d85\u754c&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bei\u2217\\\\xi_i^*<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9531em;vertical-align: -0.2587em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.046em\">\u03be<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.046em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u4e0b\u65b9&#xff09;\u3002<\/li>\n<\/ul>\n<h4>2. \u62c9\u683c\u6717\u65e5\u65b9\u6cd5\u6c42\u89e3&#xff1a;\u6700\u7ec8\u56de\u5f52\u66f2\u7ebf\u7531\u652f\u6301\u5411\u91cf\u51b3\u5b9a<\/h4>\n<p>\u901a\u8fc7\u62c9\u683c\u6717\u65e5\u4e58\u5b50\u6cd5\u548cKKT\u6761\u4ef6\u6c42\u89e3\u540e&#xff0c;\u56de\u5f52\u51fd\u6570\u53ef\u8868\u793a\u4e3a&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">f(x)&#061;\u2211i&#061;1n(\u03b1i\u2212\u03b1i\u2217)K(xi,x)&#043;bf(x) &#061; \\\\sum_{i&#061;1}^n (\\\\alpha_i &#8211; \\\\alpha_i^*) K(x_i, x) &#043; b<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.9291em;vertical-align: -1.2777em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6514em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0037em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7387em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0037em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b1i,\u03b1i\u2217\\\\alpha_i, \\\\alpha_i^*<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9474em;vertical-align: -0.2587em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0037em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.0037em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u62c9\u683c\u6717\u65e5\u4e58\u5b50&#xff0c;\u53ea\u6709\u652f\u6301\u5411\u91cf\u7684\u4e58\u5b50\u975e\u96f6&#xff08;\u666e\u901a\u6837\u672c\u7684\u4e58\u5b50\u4e3a0&#xff09;\u3002\u8fd9\u610f\u5473\u7740&#xff1a;SVR\u7684\u56de\u5f52\u66f2\u7ebf\u5b8c\u5168\u7531\u652f\u6301\u5411\u91cf\u51b3\u5b9a\u3002<\/p>\n<h3>\u56db\u3001\u4ee3\u7801\u5b9e\u6218&#xff1a;\u7528SVR\u62df\u5408\u975e\u7ebf\u6027\u6570\u636e&#xff08;\u9644\u53c2\u6570\u89e3\u8bfb&#xff09;<\/h3>\n<p>\u6211\u4eec\u7528\u201c\u6b63\u5f26\u66f2\u7ebf&#043;\u566a\u58f0\u201d\u6570\u636e&#xff08;\u5178\u578b\u7684\u975e\u7ebf\u6027\u5173\u7cfb&#xff09;&#xff0c;\u6f14\u793aSVR\u7684\u5b8c\u6574\u6d41\u7a0b&#xff0c;\u91cd\u70b9\u770b\u5b83\u5982\u4f55\u7528\u5c11\u6570\u652f\u6301\u5411\u91cf\u62df\u5408\u66f2\u7ebf\u3002<\/p>\n<h4>\u5b8c\u6574\u4ee3\u7801&#xff08;\u53ef\u76f4\u63a5\u8fd0\u884c&#xff09;<\/h4>\n<p><span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>svm <span class=\"token keyword\">import<\/span> SVR<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>metrics <span class=\"token keyword\">import<\/span> mean_squared_error<span class=\"token punctuation\">,<\/span> r2_score<\/p>\n<p><span class=\"token comment\"># \u8bbe\u7f6e\u4e2d\u6587\u663e\u793a<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>rcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#034;font.family&#034;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#034;SimHei&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;WenQuanYi Micro Hei&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;Heiti TC&#034;<\/span><span class=\"token punctuation\">]<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>rcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#034;axes.unicode_minus&#034;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">False<\/span>  <span class=\"token comment\"># \u8d1f\u53f7\u6b63\u5e38\u663e\u793a<\/span><\/p>\n<p><span class=\"token comment\"># &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/span><br \/>\n<span class=\"token comment\"># 1. \u751f\u6210\u975e\u7ebf\u6027\u6570\u636e&#xff08;\u6b63\u5f26\u66f2\u7ebf&#043;\u566a\u58f0&#xff09;<\/span><br \/>\n<span class=\"token comment\"># &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/span><br \/>\nnp<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">42<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u56fa\u5b9a\u968f\u673a\u79cd\u5b50<\/span><br \/>\nX <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>sort<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>rand<span class=\"token punctuation\">(<\/span><span class=\"token number\">1000<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> axis<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># x\u8303\u56f4&#xff1a;0-5&#xff0c;\u6392\u5e8f\u65b9\u4fbf\u7ed8\u56fe<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>sin<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>ravel<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span> np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>normal<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> X<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># y&#061;sin(x)&#043;\u566a\u58f0&#xff08;\u6a21\u62df\u771f\u5b9e\u6570\u636e&#xff09;<\/span><\/p>\n<p><span class=\"token comment\"># &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/span><br \/>\n<span class=\"token comment\"># 2. \u62df\u5408SVR\u6a21\u578b&#xff08;RBF\u6838&#xff0c;\u5904\u7406\u975e\u7ebf\u6027&#xff09;<\/span><br \/>\n<span class=\"token comment\"># &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/span><br \/>\n<span class=\"token comment\"># \u5173\u952e\u53c2\u6570&#xff1a;<\/span><br \/>\n<span class=\"token comment\"># &#8211; kernel&#061;&#039;rbf&#039;&#xff1a;\u5f84\u5411\u57fa\u6838&#xff0c;\u5904\u7406\u975e\u7ebf\u6027\u5173\u7cfb<\/span><br \/>\n<span class=\"token comment\"># &#8211; C&#061;100&#xff1a;\u60e9\u7f5a\u7cfb\u6570&#xff08;C\u8d8a\u5927&#xff0c;\u5bf9\u8d85\u754c\u6837\u672c\u60e9\u7f5a\u8d8a\u91cd&#xff09;<\/span><br \/>\n<span class=\"token comment\"># &#8211; gamma&#061;0.1&#xff1a;\u6838\u7cfb\u6570&#xff08;gamma\u8d8a\u5927&#xff0c;\u6a21\u578b\u8d8a\u5173\u6ce8\u5c40\u90e8\u6837\u672c&#xff09;<\/span><br \/>\n<span class=\"token comment\"># &#8211; epsilon&#061;0.1&#xff1a;\u8bef\u5dee\u5bb9\u5fcd\u8303\u56f4&#xff08;\u7ba1\u9053\u5bbd\u5ea6&#xff09;<\/span><br \/>\nsvr_rbf <span class=\"token operator\">&#061;<\/span> SVR<span class=\"token punctuation\">(<\/span>kernel<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;rbf&#039;<\/span><span class=\"token punctuation\">,<\/span> C<span class=\"token operator\">&#061;<\/span><span class=\"token number\">100<\/span><span class=\"token punctuation\">,<\/span> gamma<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> epsilon<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">)<\/span><br \/>\nsvr_rbf<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u8bad\u7ec3\u6a21\u578b<\/span><\/p>\n<p><span class=\"token comment\"># \u9884\u6d4b<\/span><br \/>\ny_pred <span class=\"token operator\">&#061;<\/span> svr_rbf<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/span><br \/>\n<span class=\"token comment\"># 3. \u8bc4\u4f30\u6a21\u578b\u6027\u80fd<\/span><br \/>\n<span class=\"token comment\"># &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/span><br \/>\nmse <span class=\"token operator\">&#061;<\/span> mean_squared_error<span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u5747\u65b9\u8bef\u5dee&#xff08;\u8d8a\u5c0f\u8d8a\u597d&#xff09;<\/span><br \/>\nr2 <span class=\"token operator\">&#061;<\/span> r2_score<span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># R\u00b2&#xff08;\u8d8a\u63a5\u8fd11\u8d8a\u597d&#xff09;<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;\u5747\u65b9\u8bef\u5dee&#xff08;MSE&#xff09;&#xff1a;<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>mse<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;\u51b3\u5b9a\u7cfb\u6570&#xff08;R\u00b2&#xff09;&#xff1a;<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>r2<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u63a5\u8fd11&#xff0c;\u8bf4\u660e\u62df\u5408\u6548\u679c\u597d<\/span><\/p>\n<p><span class=\"token comment\"># &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/span><br \/>\n<span class=\"token comment\"># 4. \u53ef\u89c6\u5316&#xff1a;\u4ece\u56fe\u4e2d\u770b\u61c2SVR\u7684\u5de5\u4f5c\u539f\u7406<\/span><br \/>\n<span class=\"token comment\"># &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>figure<span class=\"token punctuation\">(<\/span>figsize<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">14<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u5b50\u56fe1&#xff1a;\u539f\u59cb\u6570\u636e\u4e0eSVR\u62df\u5408\u66f2\u7ebf<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>subplot<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>scatter<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;darkorange&#039;<\/span><span class=\"token punctuation\">,<\/span> alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.6<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;\u539f\u59cb\u6570\u636e&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;navy&#039;<\/span><span class=\"token punctuation\">,<\/span> lw<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;SVR\u62df\u5408\u66f2\u7ebf&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u753b\u51fa\u03b5-\u7ba1\u9053&#xff08;\u4e0a\u4e0b\u8fb9\u754c&#xff09;<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y_pred <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;green&#039;<\/span><span class=\"token punctuation\">,<\/span> linestyle<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;&#8211;&#039;<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;\u03b5\u4e0a\u8fb9\u754c&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y_pred <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;green&#039;<\/span><span class=\"token punctuation\">,<\/span> linestyle<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;&#8211;&#039;<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;\u03b5\u4e0b\u8fb9\u754c&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;x&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;y&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;SVR\u62df\u5408\u66f2\u7ebf\u4e0e\u03b5-\u7ba1\u9053&#039;<\/span><span class=\"token punctuation\">,<\/span> fontsize<span class=\"token operator\">&#061;<\/span><span class=\"token number\">14<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u5b50\u56fe2&#xff1a;\u6b8b\u5dee\u56fe&#xff08;\u8bef\u5dee\u5206\u5e03&#xff09;<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>subplot<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\nresiduals <span class=\"token operator\">&#061;<\/span> y <span class=\"token operator\">&#8211;<\/span> y_pred  <span class=\"token comment\"># \u6b8b\u5dee&#061;\u771f\u5b9e\u503c-\u9884\u6d4b\u503c<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>scatter<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> residuals<span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;red&#039;<\/span><span class=\"token punctuation\">,<\/span> alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.6<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;\u6b8b\u5dee&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>axhline<span class=\"token punctuation\">(<\/span>y<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;black&#039;<\/span><span class=\"token punctuation\">,<\/span> linestyle<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;&#8211;&#039;<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u6b8b\u5dee&#061;0\u53c2\u8003\u7ebf<\/span><br \/>\n<span class=\"token comment\"># \u6807\u51fa\u03b5\u8fb9\u754c&#xff08;\u6b8b\u5dee\u8d85\u8fc7\u00b10.1\u7684\u6837\u672c\u662f\u8d85\u754c\u6837\u672c&#xff09;<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>axhline<span class=\"token punctuation\">(<\/span>y<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;green&#039;<\/span><span class=\"token punctuation\">,<\/span> linestyle<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;&#8211;&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>axhline<span class=\"token punctuation\">(<\/span>y<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;green&#039;<\/span><span class=\"token punctuation\">,<\/span> linestyle<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;&#8211;&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;x&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u6b8b\u5dee&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u6b8b\u5dee\u5206\u5e03&#xff08;\u7eff\u8272\u7ebf\u4e3a\u03b5\u8fb9\u754c&#xff09;&#039;<\/span><span class=\"token punctuation\">,<\/span> fontsize<span class=\"token operator\">&#061;<\/span><span class=\"token number\">14<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u5b50\u56fe3&#xff1a;\u652f\u6301\u5411\u91cf&#xff08;\u51b3\u5b9a\u6a21\u578b\u7684\u5173\u952e\u6837\u672c&#xff09;<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>subplot<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>scatter<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;darkorange&#039;<\/span><span class=\"token punctuation\">,<\/span> alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.6<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;\u666e\u901a\u6837\u672c&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u652f\u6301\u5411\u91cf&#xff1a;\u7528\u7a7a\u5fc3\u9ed1\u6846\u6807\u8bb0<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>scatter<span class=\"token punctuation\">(<\/span><br \/>\n    X<span class=\"token punctuation\">[<\/span>svr_rbf<span class=\"token punctuation\">.<\/span>support_<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">[<\/span>svr_rbf<span class=\"token punctuation\">.<\/span>support_<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    facecolors<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;none&#039;<\/span><span class=\"token punctuation\">,<\/span> edgecolors<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;k&#039;<\/span><span class=\"token punctuation\">,<\/span> s<span class=\"token operator\">&#061;<\/span><span class=\"token number\">100<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;\u652f\u6301\u5411\u91cf&#039;<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;navy&#039;<\/span><span class=\"token punctuation\">,<\/span> lw<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;SVR\u62df\u5408\u66f2\u7ebf&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;x&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;y&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;\u652f\u6301\u5411\u91cf&#xff08;\u5171<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span><span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>svr_rbf<span class=\"token punctuation\">.<\/span>support_<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">\u4e2a&#xff0c;\u5f71\u54cd\u66f2\u7ebf\u5f62\u72b6&#xff09;&#039;<\/span><\/span><span class=\"token punctuation\">,<\/span> fontsize<span class=\"token operator\">&#061;<\/span><span class=\"token number\">14<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u5b50\u56fe4&#xff1a;\u6b8b\u5dee\u76f4\u65b9\u56fe&#xff08;\u770b\u8bef\u5dee\u662f\u5426\u968f\u673a&#xff09;<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>subplot<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>hist<span class=\"token punctuation\">(<\/span>residuals<span class=\"token punctuation\">,<\/span> bins<span class=\"token operator\">&#061;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;blue&#039;<\/span><span class=\"token punctuation\">,<\/span> edgecolor<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;black&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u6b8b\u5dee\u503c&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u9891\u6570&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u6b8b\u5dee\u76f4\u65b9\u56fe&#xff08;\u5e94\u63a5\u8fd1\u6b63\u6001\u5206\u5e03&#xff09;&#039;<\/span><span class=\"token punctuation\">,<\/span> fontsize<span class=\"token operator\">&#061;<\/span><span class=\"token number\">14<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>plt<span class=\"token punctuation\">.<\/span>tight_layout<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250812130952-689b3d207942c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>\u4e94\u3001\u7ed3\u679c\u89e3\u8bfb&#xff1a;SVR\u7684\u201c\u806a\u660e\u4e4b\u5904\u201d\u5728\u54ea&#xff1f;<\/h3>\n<h4>1. \u03b5-\u7ba1\u9053&#xff1a;\u7ed9\u8bef\u5dee\u201c\u7559\u4f59\u5730\u201d&#xff0c;\u907f\u514d\u8fc7\u62df\u5408<\/h4>\n<p>\u5b50\u56fe1\u4e2d&#xff0c;\u7eff\u8272\u865a\u7ebf\u662f\u03b5&#061;0.1\u7684\u7ba1\u9053\u8fb9\u754c&#xff0c;\u5927\u90e8\u5206\u6837\u672c\u843d\u5728\u7ba1\u9053\u5185&#xff08;\u635f\u5931\u4e3a0&#xff09;&#xff0c;\u53ea\u6709\u5c11\u6570\u6837\u672c\u8dd1\u51fa\u7ba1\u9053\u3002\u8fd9\u79cd\u201c\u5bbd\u5bb9\u201d\u8ba9SVR\u4e0d\u4f1a\u4e3a\u4e86\u8d34\u5408\u566a\u58f0\u800c\u626d\u66f2\u66f2\u7ebf&#xff0c;\u62df\u5408\u66f4\u7a33\u5065\u3002<\/p>\n<h4>2. \u652f\u6301\u5411\u91cf&#xff1a;\u5c11\u6570\u6837\u672c\u51b3\u5b9a\u66f2\u7ebf\u5f62\u72b6<\/h4>\n<p>\u5b50\u56fe3\u4e2d&#xff0c;\u7a7a\u5fc3\u9ed1\u6846\u6807\u8bb0\u7684\u662f\u652f\u6301\u5411\u91cf&#xff08;\u7ea6100\u4e2a&#xff0c;\u4ec5\u5360\u603b\u6837\u672c\u768410%&#xff09;\u3002\u53ef\u4ee5\u53d1\u73b0&#xff1a;<\/p>\n<ul>\n<li>\u652f\u6301\u5411\u91cf\u8981\u4e48\u662f\u8dd1\u51fa\u7ba1\u9053\u7684\u6837\u672c&#xff08;\u9700\u8981\u88ab\u201c\u62c9\u56de\u201d&#xff09;&#xff0c;\u8981\u4e48\u662f\u7ba1\u9053\u8fb9\u7f18\u7684\u6837\u672c&#xff08;\u5b9a\u4e49\u7ba1\u9053\u8fb9\u754c&#xff09;&#xff1b;<\/li>\n<li>\u62df\u5408\u66f2\u7ebf\u7684\u5f2f\u66f2\u5b8c\u5168\u7531\u8fd9\u4e9b\u652f\u6301\u5411\u91cf\u51b3\u5b9a&#xff0c;\u5176\u4ed6\u6837\u672c\u5bf9\u66f2\u7ebf\u65e0\u5f71\u54cd\u2014\u2014\u8fd9\u5c31\u662fSVR\u9ad8\u6548\u7684\u6838\u5fc3&#xff08;\u53ea\u5904\u7406\u5173\u952e\u6837\u672c&#xff09;\u3002<\/li>\n<\/ul>\n<h4>3. \u6b8b\u5dee\u5206\u6790&#xff1a;\u8bef\u5dee\u968f\u673a&#xff0c;\u8bf4\u660e\u6a21\u578b\u5408\u9002<\/h4>\n<p>\u5b50\u56fe2\u548c4\u663e\u793a&#xff1a;\u6b8b\u5dee\u56f4\u7ed50\u503c\u968f\u673a\u5206\u5e03&#xff0c;\u76f4\u65b9\u56fe\u63a5\u8fd1\u6b63\u6001\u5206\u5e03&#xff0c;\u6ca1\u6709\u660e\u663e\u8d8b\u52bf&#xff08;\u6bd4\u5982\u968fx\u589e\u5927\u800c\u589e\u5927&#xff09;\u3002\u8fd9\u8bf4\u660eSVR\u6355\u6349\u5230\u4e86\u6570\u636e\u7684\u4e3b\u8981\u89c4\u5f8b&#xff08;\u6b63\u5f26\u66f2\u7ebf&#xff09;&#xff0c;\u5269\u4e0b\u7684\u8bef\u5dee\u662f\u968f\u673a\u566a\u58f0&#xff0c;\u6a21\u578b\u62df\u5408\u5408\u7406\u3002<\/p>\n<h3>\u516d\u3001SVR\u53c2\u6570\u8c03\u4f18&#xff1a;3\u4e2a\u5173\u952e\u53c2\u6570\u51b3\u5b9a\u6548\u679c<\/h3>\n<p>SVR\u7684\u6027\u80fd\u4e25\u91cd\u4f9d\u8d56\u53c2\u6570&#xff0c;\u8fd93\u4e2a\u53c2\u6570\u5fc5\u987b\u638c\u63e1&#xff1a;<\/p>\n<table>\n<tr>\u53c2\u6570\u4f5c\u7528\u8c03\u4f18\u5efa\u8bae<\/tr>\n<tbody>\n<tr>\n<td>C<\/td>\n<td>\u60e9\u7f5a\u7cfb\u6570&#xff08;C\u8d8a\u5927&#xff0c;\u5bf9\u8d85\u754c\u6837\u672c\u60e9\u7f5a\u8d8a\u91cd&#xff09;<\/td>\n<td>\u592a\u5c0f\u2192\u6b20\u62df\u5408&#xff08;\u7ba1\u9053\u592a\u5bbd&#xff0c;\u5ffd\u7565\u91cd\u8981\u6837\u672c&#xff09;&#xff1b;\u592a\u5927\u2192\u8fc7\u62df\u5408&#xff08;\u5bf9\u566a\u58f0\u654f\u611f&#xff09;&#xff0c;\u901a\u5e38\u4ece1\u300110\u3001100\u8bd5\u8d77\u3002<\/td>\n<\/tr>\n<tr>\n<td>gamma<\/td>\n<td>RBF\u6838\u7cfb\u6570&#xff08;gamma\u8d8a\u5927&#xff0c;\u6a21\u578b\u8d8a\u5173\u6ce8\u5c40\u90e8\u6837\u672c&#xff09;<\/td>\n<td>\u592a\u5c0f\u2192\u6a21\u578b\u592a\u201c\u7c97\u7cd9\u201d&#xff08;\u6b20\u62df\u5408&#xff09;&#xff1b;\u592a\u5927\u2192\u8fc7\u62df\u5408&#xff08;\u53ea\u5173\u6ce8\u9644\u8fd1\u6837\u672c&#xff09;&#xff0c;\u901a\u5e38\u4ece0.1\u30011\u300110\u8bd5\u8d77\u3002<\/td>\n<\/tr>\n<tr>\n<td>epsilon<\/td>\n<td>\u8bef\u5dee\u5bb9\u5fcd\u8303\u56f4&#xff08;\u03b5\u8d8a\u5927&#xff0c;\u7ba1\u9053\u8d8a\u5bbd&#xff0c;\u5141\u8bb8\u7684\u8bef\u5dee\u8d8a\u5927&#xff09;<\/td>\n<td>\u6839\u636e\u6570\u636e\u566a\u58f0\u7a0b\u5ea6\u8c03\u6574&#xff1a;\u566a\u58f0\u5927\u2192\u03b5\u5927&#xff08;\u59820.2&#xff09;&#xff0c;\u566a\u58f0\u5c0f\u2192\u03b5\u5c0f&#xff08;\u59820.01&#xff09;\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>\u4e03\u3001SVR\u7684\u201c\u9ad8\u5149\u65f6\u523b\u201d\u4e0e\u201c\u8f6f\u808b\u201d<\/h3>\n<h4>\u9002\u5408\u7528SVR\u7684\u573a\u666f&#xff1a;<\/h4>\n<li>\u975e\u7ebf\u6027\u6570\u636e&#xff1a;\u901a\u8fc7RBF\u6838\u8f7b\u677e\u5904\u7406\u66f2\u7ebf\u5173\u7cfb&#xff08;\u5982\u80a1\u4ef7\u3001\u6b63\u5f26\u6ce2&#xff09;&#xff1b;<\/li>\n<li>\u9ad8\u7ef4\u7279\u5f81&#xff1a;\u5373\u4f7f\u7279\u5f81\u6bd4\u6837\u672c\u591a&#xff08;\u59821000\u4e2a\u7279\u5f81&#xff0c;100\u4e2a\u6837\u672c&#xff09;&#xff0c;\u4e5f\u80fd\u7a33\u5b9a\u62df\u5408&#xff1b;<\/li>\n<li>\u5c0f\u6837\u672c\u6570\u636e&#xff1a;\u53ea\u9760\u652f\u6301\u5411\u91cf\u5efa\u6a21&#xff0c;\u5c0f\u6837\u672c\u4e5f\u80fd\u6709\u597d\u6548\u679c\u3002<\/li>\n<h4>\u4e0d\u9002\u5408\u7684\u573a\u666f&#xff1a;<\/h4>\n<li>\u8d85\u5927\u6837\u672c&#xff1a;\u6837\u672c\u8d85\u8fc710\u4e07\u65f6&#xff0c;\u8bad\u7ec3\u901f\u5ea6\u6162&#xff08;\u652f\u6301\u5411\u91cf\u53ef\u80fd\u592a\u591a&#xff09;&#xff1b;<\/li>\n<li>\u5f3a\u7ebf\u6027\u5173\u7cfb&#xff1a;\u7528\u7ebf\u6027\u56de\u5f52\u66f4\u7b80\u5355\u9ad8\u6548&#xff0c;\u6ca1\u5fc5\u8981\u7528SVR&#xff1b;<\/li>\n<li>\u89e3\u91ca\u6027\u8981\u6c42\u9ad8&#xff1a;SVR\u7684\u56de\u5f52\u66f2\u7ebf\u7531\u6838\u51fd\u6570\u548c\u652f\u6301\u5411\u91cf\u51b3\u5b9a&#xff0c;\u96be\u4ee5\u7528\u201c\u7279\u5f81\u2192\u7cfb\u6570\u201d\u89e3\u91ca\u3002<\/li>\n<h3>\u603b\u7ed3&#xff1a;SVR\u7684\u6838\u5fc3\u4ef7\u503c\u2014\u2014\u201c\u6293\u5173\u952e&#xff0c;\u5bb9\u8bef\u5dee\u201d<\/h3>\n<p>SVR\u4e4b\u6240\u4ee5\u5f3a\u5927&#xff0c;\u5728\u4e8e\u5b83\u7684\u201c\u667a\u6167\u201d&#xff1a;<\/p>\n<ul>\n<li>\u6293\u5173\u952e&#xff1a;\u53ea\u9760\u5c11\u6570\u652f\u6301\u5411\u91cf\u5efa\u6a21&#xff0c;\u9ad8\u6548\u4e14\u6297\u8fc7\u62df\u5408&#xff1b;<\/li>\n<li>\u5bb9\u8bef\u5dee&#xff1a;\u901a\u8fc7\u03b5-\u7ba1\u9053\u5141\u8bb8\u5408\u7406\u8bef\u5dee&#xff0c;\u4e0d\u88ab\u566a\u58f0\u5e26\u504f&#xff1b;<\/li>\n<li>\u6838\u6280\u5de7&#xff1a;\u8f7b\u677e\u641e\u5b9a\u975e\u7ebf\u6027&#xff0c;\u4e0d\u7528\u624b\u52a8\u8bbe\u8ba1\u9ad8\u6b21\u9879\u3002<\/li>\n<\/ul>\n<p>\u5f53\u4f60\u9047\u5230\u975e\u7ebf\u6027\u3001\u9ad8\u7ef4\u3001\u5c0f\u6837\u672c\u7684\u56de\u5f52\u95ee\u9898&#xff0c;\u4e0d\u59a8\u8bd5\u8bd5SVR\u2014\u2014\u5b83\u53ef\u80fd\u6bd4\u590d\u6742\u7684\u6df1\u5ea6\u5b66\u4e60\u66f4\u7b80\u5355\u3001\u66f4\u7a33\u5065\u3002<\/p>\n<p>\u4f60\u5728\u9879\u76ee\u4e2d\u7528SVR\u89e3\u51b3\u8fc7\u54ea\u4e9b\u95ee\u9898&#xff1f;\u53c2\u6570\u8c03\u4f18\u6709\u4ec0\u4e48\u6280\u5de7&#xff1f;\u8bc4\u8bba\u533a\u804a\u804a&#xff5e;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb795\u6b21\uff0c\u70b9\u8d5e23\u6b21\uff0c\u6536\u85cf11\u6b21\u3002\u6458\u8981\uff1a\u6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