{"id":3065,"date":"2022-02-27T10:57:31","date_gmt":"2022-02-27T02:57:31","guid":{"rendered":"https:\/\/egonlin.com\/?p=3065"},"modified":"2022-02-27T11:01:04","modified_gmt":"2022-02-27T03:01:04","slug":"%e7%ac%ac%e4%b8%89%e8%8a%82%ef%bc%9a%e5%86%b3%e7%ad%96%e6%a0%91cart%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3065","title":{"rendered":"\u7b2c\u4e09\u8282\uff1a\u51b3\u7b56\u6811CART\u7b97\u6cd5"},"content":{"rendered":"<h1>\u51b3\u7b56\u6811CART\u7b97\u6cd5<\/h1>\n<p>&emsp;&emsp;\u51b3\u7b56\u6811C4.5\u7b97\u6cd5\u867d\u7136\u5bf9\u51b3\u7b56\u6811ID3\u7b97\u6cd5\u505a\u4e86\u5f88\u5927\u7684\u6539\u826f\uff0c\u4f46\u662f\u7f3a\u70b9\u4e5f\u662f\u5f88\u660e\u663e\u7684\uff0c\u65e0\u6cd5\u5904\u7406\u56de\u5f52\u95ee\u9898\u3001\u4f7f\u7528\u8f83\u4e3a\u590d\u6742\u7684\u71b5\u6765\u4f5c\u4e3a\u7279\u5f81\u9009\u62e9\u7684\u6807\u51c6\u3001\u751f\u6210\u7684\u51b3\u7b56\u6811\u662f\u4e00\u9897\u8f83\u4e3a\u590d\u6742\u7684\u591a\u53c9\u6811\u7ed3\u6784\uff0cCART\u7b97\u6cd5\u9488\u5bf9\u8fd9\u4e9b\u95ee\u9898\u53c8\u505a\u4e86\u8fdb\u4e00\u6b65\u7684\u4f18\u5316\u3002<\/p>\n<h1>\u51b3\u7b56\u6811CART\u7b97\u6cd5\u5b66\u4e60\u76ee\u6807<\/h1>\n<ol>\n<li>\u57fa\u5c3c\u6307\u6570\u548c\u71b5<\/li>\n<li>CART\u7b97\u6cd5\u5bf9\u8fde\u7eed\u503c\u548c\u7279\u5f81\u503c\u7684\u5904\u7406<\/li>\n<li>CART\u7b97\u6cd5\u526a\u679d<\/li>\n<li>\u51b3\u7b56\u6811CART\u7b97\u6cd5\u7684\u6b65\u9aa4<\/li>\n<li>\u51b3\u7b56\u6811CART\u7b97\u6cd5\u7684\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n<h1>\u51b3\u7b56\u6811CART\u7b97\u6cd5\u8be6\u89e3<\/h1>\n<p>&emsp;&emsp;CART\u7684\u82f1\u6587\u540d\u5168\u79f0\u662fclassification and regression tree\uff0c\u6240\u4ee5\u6709\u65f6\u5019\u4e5f\u628aCART\u79f0\u5b83\u4e3a\u5206\u7c7b\u56de\u5f52\u6811\uff0c\u5206\u7c7b\u56de\u5f52\u6811\u7531\u7279\u5f81\u9009\u62e9\u3001\u6811\u7684\u751f\u6210\u4ee5\u53ca\u526a\u679d\u7ec4\u6210\uff0c\u65e2\u53ef\u4ee5\u7528\u4e8e\u5206\u7c7b\u4e5f\u53ef\u4ee5\u7528\u4e8e\u56de\u5f52\u3002<\/p>\n<h2>\u57fa\u5c3c\u6307\u6570\u548c\u71b5<\/h2>\n<pre><code class=\"language-python\"># \u57fa\u5c3c\u6307\u6570\u548c\u71b5\u793a\u4f8b\u56fe\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\n%matplotlib inline\nfont = FontProperties(fname=&#039;\/Library\/Fonts\/Heiti.ttc&#039;)\n\np = np.arange(0.001, 1, 0.001)\ngini = 2*p*(1-p)\nentropy = -(p*np.log2(p) + (1-p)*np.log2(1-p))\/2\nerror = 1-np.max(np.vstack((p, 1-p)), 0)\nplt.plot(p, entropy, &#039;r-&#039;, label=&#039;\u57fa\u5c3c\u6307\u6570&#039;)\nplt.plot(p, gini, &#039;g-&#039;, label=&#039;\u71b5\u4e4b\u534a$(1\/2*H(p))$&#039;)\nplt.plot(p, error, &#039;b-&#039;, label=&#039;\u5206\u7c7b\u8bef\u5dee\u7387&#039;)\nplt.xlabel(&#039;p&#039;, fontproperties=font)\nplt.ylabel(&#039;\u635f\u5931&#039;, fontproperties=font)\nplt.legend(prop=font)\nplt.show()<\/code><\/pre>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/egonlin.com\/wp-content\/uploads\/2022\/02\/02-23-\u51b3\u7b56\u6811CART\u7b97\u6cd5_7_0.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  data-original=\"https:\/\/egonlin.com\/wp-content\/uploads\/2022\/02\/02-23-\u51b3\u7b56\u6811CART\u7b97\u6cd5_7_0.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" \/><\/div><\/p>\n<p>&emsp;&emsp;\u4e0a\u56fe\u53ef\u4ee5\u770b\u51fa\u4e8c\u5206\u7c7b\u95ee\u9898\u4e2d\u57fa\u5c3c\u6307\u6570\u548c\u71b5\u7684\u66f2\u7ebf\u975e\u5e38\u63a5\u8fd1\uff0c\u56e0\u6b64\u57fa\u5c3c\u6307\u6570\u53ef\u4ee5\u4f5c\u4e3a\u71b5\u7684\u4e00\u4e2a\u8fd1\u4f3c\u66ff\u4ee3\u3002\u800cCART\u7b97\u6cd5\u5c31\u662f\u4f7f\u7528\u4e86\u57fa\u5c3c\u6307\u6570\u6765\u9009\u62e9\u51b3\u7b56\u6811\u7684\u7279\u5f81\uff0c\u540c\u65f6\u4e3a\u4e86\u8fdb\u4e00\u6b65\u7b80\u5316\u57fa\u5c3c\u6307\u6570\u7684\u8ba1\u7b97\uff0cCART\u7b97\u6cd5\u6bcf\u6b21\u5bf9\u67d0\u4e2a\u7279\u5f81\u8fdb\u884c\u4e8c\u5206\uff0c\u56e0\u6b64CART\u7b97\u6cd5\u6784\u9020\u7684\u51b3\u7b56\u6811\u662f\u4e00\u9897\u4e8c\u53c9\u6811\u6a21\u578b\u3002<\/p>\n<h2>CART\u7b97\u6cd5\u5bf9\u8fde\u7eed\u503c\u7279\u5f81\u7684\u5904\u7406<\/h2>\n<p>&emsp;&emsp;CART\u7b97\u6cd5\u7c7b\u4f3c\u4e8eC4.5\u7b97\u6cd5\u5bf9\u8fde\u7eed\u503c\u7279\u5f81\u7684\u5904\u7406\uff0c\u53ea\u662fCART\u7b97\u6cd5\u4f7f\u7528\u57fa\u5c3c\u6307\u6570\u53d6\u4ee3\u4e86\u4fe1\u606f\u589e\u76ca\u6bd4\u5bf9\u8fde\u7eed\u503c\u505a\u4e86\u5904\u7406\u3002<\/p>\n<p>&emsp;&emsp;\u5047\u8bbe\u73b0\u6709\u4e00\u4e2a\u7279\u5f81$F$\u7684\u7279\u5f81\u503c\u4e3a\u8fde\u7eed\u503c\uff0c\u4ece\u5927\u5230\u5c0f\u6392\u5e8f\u4e3a$f_1,f_2,\\ldots,f_m$\uff0cCART\u7b97\u6cd5\u5bf9\u76f8\u90bb\u6837\u672c\u95f4\u7684\u7279\u5f81\u503c$f<em>i,f<\/em>{i+1}$\u53d6\u5e73\u5747\u6570\uff0c\u4e00\u5171\u53ef\u4ee5\u5f97\u5230$m-1$\u4e2a\u5212\u5206\u70b9\uff0c\u5176\u4e2d\u7b2c$j$\u4e2a\u5212\u5206\u70b9\u53ef\u4ee5\u8868\u793a\u4e3a<br \/>\n$$<br \/>\nS_j = {\\frac {f<em>i + f<\/em>{i+1}} {2}}<br \/>\n$$<br \/>\n\u5bf9\u4e8e\u8fd9$m-1$\u4e2a\u5212\u5206\u70b9\uff0c\u5206\u522b\u8ba1\u7b97\u4ee5\u8be5\u70b9\u4f5c\u4e3a\u4e8c\u5143\u5206\u7c7b\u70b9\u7684<strong>\u57fa\u5c3c\u6307\u6570<\/strong>\uff0c\u9009\u62e9<strong>\u57fa\u5c3c\u6307\u6570\u6700\u5c0f\u7684\u70b9<\/strong>\u4f5c\u4e3a\u8be5\u8fde\u7eed\u7279\u5f81\u7684\u4e8c\u5143\u79bb\u6563\u5206\u7c7b\u70b9\uff0c\u628a\u6539\u70b9\u8bb0\u4f5c$f_t$\uff0c\u5219\u7279\u5f81\u503c\u5c0f\u4e8e$f_t$\u7684\u70b9\u8bb0\u4f5c$c_1$\uff1b\u7279\u5f81\u503c\u5927\u4e8e$f_t$\u7684\u70b9\u8bb0\u4f5c$c_2$\uff0c\u8fd9\u6837\u5c31\u5b9e\u73b0\u4e86\u8fde\u7eed\u7279\u5f81\u503c\u7684\u79bb\u6563\u5316\u3002<\/p>\n<h2>CART\u7b97\u6cd5\u5bf9\u79bb\u6563\u503c\u7279\u5f81\u7684\u5904\u7406<\/h2>\n<p>&emsp;&emsp;CART\u7b97\u6cd5\u5bf9\u79bb\u6563\u503c\u7279\u5f81\u7684\u5904\u7406\u91c7\u7528\u7684\u662f\u4e0d\u505c\u7684\u4e8c\u5206\u79bb\u6563\u5316\u7279\u5f81\u7684\u601d\u60f3\u3002<\/p>\n<p>&emsp;&emsp;\u5047\u8bbe\u4e00\u4e2a\u8bad\u7ec3\u96c6$D$\u7684\u67d0\u4e2a\u7279\u5f81$F$\u6709$f_1,f_2,f_3$\u4e09\u79cd\u7c7b\u522b\u3002\u5982\u679c\u6211\u4eec\u4f7f\u7528\u7684\u662fID3\u7b97\u6cd5\u6216\u8005\u662fC4.5\u7b97\u6cd5\uff0c\u5219\u4f1a\u751f\u6210$3$\u4e2a\u5b50\u8282\u70b9\uff0c\u5373\u4e09\u53c9\u5b50\u8282\u70b9\uff0c\u4e5f\u56e0\u6b64\u5bfc\u81f4\u51b3\u7b56\u6811\u53d8\u6210\u4e00\u9897\u591a\u53c9\u6811\u3002\u4f46\u662fCART\u7b97\u6cd5\u4f1a\u57fa\u4e8e\u8fd9\u4e09\u4e2a\u7279\u5f81\u5f62\u6210$f_1$\u548c$f_2,f_3$\u3001$f_2$\u548c$f_1,f_3$\u3001$f_3$\u548c$f_1,f_2$\u8fd9\u4e09\u79cd\u7ec4\u5408\uff0c\u5e76\u4e14\u5728\u8fd9\u4e09\u4e2a\u7ec4\u5408\u4e2d\u627e\u5230\u57fa\u5c3c\u6307\u6570\u6700\u5c0f\u7684\u7ec4\u5408\uff0c\u7136\u540e\u751f\u6210\u4e8c\u53c9\u5b50\u8282\u70b9\u3002<\/p>\n<p>&emsp;&emsp;\u5047\u8bbe$f_1$\u548c$f_2,f_3$\u5728\u8fd9\u4e09\u8005\u4e2d\u57fa\u5c3c\u6307\u6570\u6700\u5c0f\uff0c\u5219\u751f\u6210\u7684\u4e8c\u53c9\u505a\u5b50\u8282\u70b9\u4e3a$f_1$\uff0c\u4e8c\u53c9\u53f3\u5b50\u8282\u70b9\u4e3a$f_2,f_3$\u3002\u7531\u4e8e\u53f3\u5b50\u8282\u70b9\u5e76\u6ca1\u6709\u88ab\u5b8c\u5168\u5206\u5f00\uff0c\u56e0\u6b64\u5728\u4e4b\u540e\u4f1a\u7ee7\u7eed\u6c42\u51fa$f_2$\u548c$f_3$\u7684\u57fa\u5c3c\u6307\u6570\uff0c\u7136\u540e\u627e\u5230\u6700\u5c0f\u7684\u57fa\u5c3c\u6307\u6570\u6765\u5212\u5206\u7279\u5f81$F$\u3002<\/p>\n<h2>CART\u7b97\u6cd5\u526a\u679d<\/h2>\n<p>&emsp;&emsp;\u56de\u5f52CART\u6811\u548c\u5206\u7c7bCART\u6811\u526a\u679d\u7b56\u7565\u9664\u4e86\u5728\u7279\u5f81\u9009\u62e9\u7684\u65f6\u5019\u4e00\u4e2a\u4f7f\u7528\u4e86\u5747\u65b9\u8bef\u5dee\uff0c\u53e6\u4e00\u4e2a\u4f7f\u7528\u4e86\u57fa\u5c3c\u6307\u6570\uff0c\u5176\u4ed6\u5185\u5bb9\u90fd\u4e00\u6837\u3002<\/p>\n<p>&emsp;&emsp;\u65e0\u8bba\u662fC4.5\u7b97\u6cd5\u8fd8\u662fCART\u7b97\u6cd5\u5f62\u6210\u7684\u51b3\u7b56\u6811\u90fd\u5f88\u5bb9\u6613\u5bf9\u8bad\u7ec3\u96c6\u8fc7\u62df\u5408\uff0c\u56e0\u6b64\u53ef\u4ee5\u4f7f\u7528\u526a\u679d\u7684\u65b9\u5f0f\u89e3\u51b3\u8fc7\u62df\u5408\u95ee\u9898\uff0c\u8fd9\u7c7b\u4f3c\u4e8e\u7ebf\u6027\u56de\u5f52\u4e2d\u7684\u6b63\u5219\u5316\u3002<\/p>\n<p>&emsp;&emsp;CART\u7b97\u6cd5\u91c7\u7528\u7684\u4e8b\u540e\u526a\u679d\u6cd5\uff0c\u5373\u5148\u751f\u6210\u51b3\u7b56\u6811\uff0c\u7136\u540e\u4ea7\u751f\u6240\u6709\u53ef\u80fd\u7684\u526a\u679d\u540e\u7684CART\u6811\uff0c\u7136\u540e\u4f7f\u7528\u4ea4\u53c9\u9a8c\u8bc1\u6765\u68c0\u9a8c\u5404\u79cd\u526a\u679d\u7684\u6548\u679c\uff0c\u9009\u62e9\u8fd4\u56de\u6cdb\u5316\u80fd\u529b\u6700\u597d\u7684\u526a\u679d\u65b9\u6cd5\u3002\u5373CART\u6811\u7684\u526a\u679d\u65b9\u6cd5\u53ef\u5206\u4e3a\u4e24\u6b65\uff1a<\/p>\n<ol>\n<li>\u4f7f\u7528\u539f\u59cb\u7684\u51b3\u7b56\u6811$T_0$\u4ece\u5b83\u7684\u5e95\u7aef\u5f00\u59cb\u4e0d\u65ad\u526a\u679d\uff0c\u76f4\u5230$T_0$\u7684\u6839\u8282\u70b9\u751f\u6210\u4e00\u4e2a\u5b50\u6811\u5e8f\u5217${T_0,T_1,\\ldots,T_n}$<\/li>\n<li>\u901a\u8fc7\u4ea4\u53c9\u9a8c\u8bc1\u6cd5\u9009\u62e9\u6cdb\u5316\u80fd\u529b\u6700\u597d\u7684\u526a\u679d\u540e\u7684\u6811\u4f5c\u4e3a\u6700\u7ec8\u7684CART\u6811\uff0c\u5373\u6700\u4f18\u5b50\u6811<\/li>\n<\/ol>\n<h3>\u751f\u6210\u526a\u679d\u540e\u7684\u51b3\u7b56\u6811<\/h3>\n<p>&emsp;&emsp;\u5728\u526a\u679d\u8fc7\u7a0b\u4e2d\uff0c\u5b50\u6811$T$\u7684\u635f\u5931\u51fd\u6570\u4e3a<br \/>\n$$<br \/>\nC_\\alpha(T) = C(T) + \\alpha|T|<br \/>\n$$<br \/>\n\u5176\u4e2d$T$\u662f\u4efb\u610f\u5b50\u6811\uff0c$\\alpha \\quad \\alpha\\geq0$\u4e3a\u6b63\u5219\u5316\u53c2\u6570\uff0c\u5b83\u6743\u8861\u8bad\u7ec3\u6570\u636e\u7684\u62df\u5408\u7a0b\u5ea6\u4e0e\u6a21\u578b\u7684\u590d\u6742\u5ea6\uff1b$C(T)$\u662f\u8bad\u7ec3\u6570\u636e\u7684\u9884\u6d4b\u8bef\u5dee\uff08\u5206\u7c7b\u6811\u4f7f\u7528\u57fa\u5c3c\u6307\u6570\u5ea6\u91cf\uff0c\u56de\u5f52\u6811\u4f7f\u7528\u5747\u65b9\u5dee\u5ea6\u91cf\uff09\uff0c$|T|$\u662f\u5b50\u6811$T$\u7684\u53f6\u5b50\u8282\u70b9\u7684\u6570\u91cf\u3002<\/p>\n<p>&emsp;&emsp;\u5f53$\\alpha=0$\u65f6\u6ca1\u6709\u6b63\u5219\u5316\uff0c\u5373\u539f\u59cb\u7684\u51b3\u7b56\u6811\u4e3a\u6700\u4f18\u5b50\u6811\uff1b\u5f53$\\alpha$\u9010\u6e10\u589e\u5927\u65f6\uff0c\u5219\u6b63\u5219\u5316\u5f3a\u5ea6\u8d8a\u5927\uff0c\u751f\u6210\u7684\u6700\u4f18\u5b50\u6811\u76f8\u6bd4\u8f83\u539f\u751f\u7684\u5b50\u6811\u5c31\u8d8a\u5c0f\uff1b\u5f53$\\alpha=\\infty$\u65f6\uff0c\u5373\u6b63\u5219\u5316\u5f3a\u5ea6\u8fbe\u5230\u6700\u5927\uff0c\u6b64\u65f6\u7531\u539f\u59cb\u7684\u51b3\u7b56\u6811\u7684\u6839\u8282\u70b9\u7ec4\u6210\u7684\u5355\u8282\u70b9\u6811\u4e3a\u6700\u4f18\u5b50\u6811\u3002\u56e0\u6b64\u5bf9\u4e8e\u56fa\u5b9a\u7684$\\alpha$\uff0c\u4ece\u5b50\u6811\u7684\u635f\u5931\u51fd\u6570\u4e2d\u53ef\u4ee5\u770b\u51fa\u4e00\u5b9a\u5b58\u5728\u4f7f\u635f\u5931\u51fd\u6570$C_\\alpha(T)$\u6700\u5c0f\u7684\u552f\u4e00\u5b50\u6811$T_a$\uff0c$T_a$\u5728\u635f\u5931\u51fd\u6570\u6700\u5c0f\u7684\u610f\u4e49\u4e0b\u662f\u6700\u4f18\u7684\u3002<\/p>\n<p>&emsp;&emsp;\u53ef\u4ee5\u9012\u5f52\u7684\u65b9\u6cd5\u5bf9\u4e66\u8fdb\u884c\u526a\u679d\u3002\u5c06$\\alpha$\u4ece\u5c0f\u589e\u5927\uff0c$0=\\alpha_0&lt;\\alpha_1&lt;\\cdots\\alpha_n&lt;+\\infty$\uff0c\u4ea7\u751f\u4e00\u7cfb\u5217\u7684\u533a\u95f4$[\\alpha<em>i,\\alpha<\/em>{i+1}),i=0,1,\\ldots,n$\uff1b\u526a\u679d\u5f97\u5230\u7684\u5b50\u5e8f\u5217\u5bf9\u5e94\u7740\u533a\u95f4$\\alpha{\\in}{[\\alpha<em>i,\\alpha<\/em>{i+1})}$\u7684\u6700\u4f18\u5b50\u6811\u5e8f\u5217${T_0,T_1,\\ldots,T_n}$(\u6ce8\uff1a\u6bcf\u4e2a\u533a\u95f4\u5185\u662f\u6709\u53ef\u80fd\u6709\u591a\u4e2a\u5b50\u6811\u7684)\uff0c\u5e8f\u5217\u4e2d\u7684\u5b50\u6811\u662f\u5d4c\u5957\u7684\u3002<\/p>\n<p>&emsp;&emsp;\u4ece\u539f\u59cb\u7684\u51b3\u7b56\u6811$T_0$\u5f00\u59cb\u526a\u679d\uff0c\u5bf9$T<em>0$\u7684\u4efb\u610f\u5185\u90e8\u8282\u70b9$t$\uff0c\u4ee5$t$\u4e3a\u5355\u7ed3\u70b9\u6811\u7684\u635f\u5931\u51fd\u6570\u662f<br \/>\n$$<br \/>\nC<\/em>\\alpha(t) = C(t) + \\alpha<br \/>\n$$<br \/>\n\u4ee5$t$\u4e3a\u6839\u8282\u70b9\u7684\u5b50\u6811$T<em>t$\u7684\u635f\u5931\u51fd\u6570\u662f<br \/>\n$$<br \/>\nC<\/em>\\alpha(T_t) = C(T_t) + \\alpha|T<em>t|<br \/>\n$$<br \/>\n&emsp;&emsp;\u5f53$\\alpha=0$\u4ee5\u53ca$\\alpha$\u5145\u5206\u5c0f\u65f6\uff08\u6700\u4f18\u5b50\u6811\u4e3a\u539f\u59cb\u7684\u51b3\u7b56\u6811\uff09\uff0c\u6709\u4e0d\u7b49\u5f0f<br \/>\n$$<br \/>\nC<\/em>\\alpha(T<em>t) &lt; C<\/em>\\alpha(t)<br \/>\n$$<br \/>\n&emsp;&emsp;\u5f53$\\alpha$\u589e\u5927\u65f6\uff0c\u5728\u67d0\u4e00$\\alpha$\u6709<br \/>\n$$<br \/>\nC_\\alpha(T<em>t) = C<\/em>\\alpha(t)<br \/>\n$$<br \/>\n&emsp;&emsp;\u5f53$\\alpha$\u7ee7\u7eed\u589e\u5927\u65f6\uff08\u6700\u4f18\u5b50\u6811\u4e3a\u6839\u8282\u70b9\u7ec4\u6210\u7684\u5355\u8282\u70b9\u6811\uff09\uff0c\u6709<br \/>\n$$<br \/>\nC_\\alpha(T<em>t) &gt; C<\/em>\\alpha(t)<br \/>\n$$<br \/>\n\u5e76\u4e14\u53ea\u8981\u5f53$\\alpha = {\\frac {C(t)-C(T_t)} {|T_t|-1} }$(\u6ce8\uff1a\u5f53$T_t$\u548c$t$\u6709\u76f8\u540c\u7684\u635f\u5931\u51fd\u6570\u65f6\u8be5\u516c\u5f0f\u7531$t$\u548c$T_t$\u7684\u635f\u5931\u51fd\u6570\u8054\u7acb\u5f97\u5230)\u3002\u7531\u4e8e$t$\u7684\u8282\u70b9\u5c11\uff0c\u56e0\u6b64$t$\u6bd4$T_t$\u66f4\u53ef\u53d6\uff0c\u56e0\u6b64\u53ef\u4ee5\u5bf9\u5b50\u6811$T_t$\u526a\u679d\uff0c\u4e5f\u5c31\u662f\u5c06\u5b83\u7684\u5b50\u8282\u70b9\u5168\u90e8\u526a\u6389\uff0c\u53d8\u4e3a\u4e00\u4e2a\u53f6\u5b50\u8282\u70b9$t$\u3002<\/p>\n<h3>\u9009\u62e9\u6700\u4f18\u5b50\u6811<\/h3>\n<p><\/p><div id=\"rml_readmorelogin_placeholder\" style=\"position:relative;\"><div id=\"rml_fade_content\" style=\"position: absolute;\r\ntop:-10em;\r\nwidth:100%;\r\nheight:10em;\r\nbackground: -webkit-linear-gradient(rgba(255, 255, 255, 0) 0%,#ffffff 100%);\r\nbackground-image: -moz-linear-gradient(rgba(255, 255, 255, 0) 0%,#ffffff 100%);\r\nbackground-image: -o-linear-gradient(rgba(255, 255, 255, 0) 0%,#ffffff 100%);\r\nbackground-image: 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