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技术 2022年11月20日
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一 背景

      首先举个例子:                         正样本(90)                       负样本(10)        模型1预测        正(90)                                正(10)模型2预测        正(70)负(20)                正(5)负(5)结论:       模型1准确率90%;       模型2 准确率75%             考虑对正负样本对预测能力,显然模型2要比模型1好,但对于这种正负样本分布不平衡对数据,准确率不能衡量分类器对好坏了,所以需要指标auc解决倾斜样本的评价问题。二分类混淆矩阵预测\实际       1            01                    TP          FP0                    FN          TN       TPR=TP/P=TP/TP+FN   直观1中猜对多少       FPR=FP/N=FP/FP+TN  直观0中猜错多少       Auc对横纵坐标分别为FPR和TPR,相对于y=x这条直线靠近左上角对分类器性能更好,所以模型2更优。                            TPR                            FPR模型1                 90/90=1                   10/10=1模型2                 70/90=0.78                5/10=0.5模型1和2的auc点位分别如下图所示,显然模型1更优: 

 二 研究现状        AUC直观概念,任意取一对正负样本,正样本score大于负样本对概率。        计算方法:正样本和负样本pair对,auc=预估正样本score大于负样本score的pair对数/总的pair对数。       E.g. 分别计算模型1和2对auc?四个样本label为y1=+1, y2=+1, y3=-1, y4=-1模型1的预测为 y1=0.9, y2=0.5, y3=0.2, y4=0.6模型2的预测为 y1=0.1, y2=0.9, y3=0.8, y4=0.2 <img 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×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" alt="" name="en-media:image/png:1a882bb59861bb07197c609b533b884c:none:none" width="282">解:         模型1: 正样本score大于负样本的pair包括(y1, y3), (y1, y4), (y2, y3),auc为3/4=0.75        模型2: 正样本score大于负样本的pair包括(y2, y3),(y2, y4),auc为2/4=0.5 计算参考paper:《 An introduction to ROC analysis 》(Tom Fawcett)方法:1按照score对样本排序;2依次对每个样本,label分对TP增1,否则FP增1。计算每个小梯形的面积。3累加所有样本,计算auc代码:  三 点击率模型auc计算方法        如上图,以两个分桶为例,每个分桶计算的AUC为图中的阴影部分。全局AUC部分需要补充P3部分的面积,等于前i-1个桶的sum(click)乘以每i个桶的noclick。       整体的AUC就是曲线下的面积除以曲线的起点、终点锚定矩型的面积。步骤1按照pctr聚合 sum_show和sum_clk;2样本按照pctr排序;3依次对每个样本,计算noclk和clk围成对小梯形对面积。       代码:    

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