机器学习之常见的性能度量

文章目录

1、简介
2、性能度量总结
3、参考文献

1、简介

本文是对论文《The Impact of Automated Parameter Optimization on Defect Prediction Models》涉及到的性能度量标准整理。

最初看这篇论文的时候，被震撼了好久。从101个数据集中，选取涉及多个语言、多个领域的18个数据集，用12个性能度量讨论现有流行机器学习分类器（模型）参数优化对性能的提升效果。整个实验过程严谨，这种震撼效果直到读到这个实验室2017年的一篇论文《An Empirical Comparison of Model Validation Techniques for Defect Prediction Models》才减弱，使用的方法是相同的，对比实验的设置也大同小异，像是流水线产品，留下了羡慕的泪水（这种综述类的论文只能领域里的专家才能发）。

2、性能度量总结

可以参考着这两篇博客一起看：
sklearn—评价指标大全
机器学习性能评估指标

指标很多都是根据二分类的混淆矩阵来的，混淆矩阵示例：

指标名称	计算公式	含义	参考文献
查准率(精确率Precision)	P = T P T P + F P P=\frac{TP}{TP+FP} P=TP+FPTP		[ 3 ] [3] [3]
查全率(召回率Recall) TPR	R = T P T P + F N R=\frac{TP}{TP+FN} R=TP+FNTP	正类(有缺陷的模块)被正确分类的比例	[ 3 ] [3] [3]
F m e a s u r e F_{measure} Fmeasure( F 1 F_{1} F1)	F = 2 × P × R P + R F=2 \times \frac{P \times R}{P+R} F=2×P+RP×R	查准率和查全率的调和平均值	[ 3 ] [3] [3]
特异度(Specify)TNR	S = T N T N + F P S=\frac{TN}{TN+FP} S=TN+FPTN	负类(无缺陷模块)被正确分类的比例
误报率FPR	F P R = F P T N + F P FPR=\frac{FP}{TN+FP} FPR=TN+FPFP	负类(无缺陷模块)被错误分类的比例	[ 4 ] [4] [4]
G m e a n G_{mean} Gmean	G − m e a n = R × S G-mean=\sqrt{R \times S} G−mean=R×S	R和S的几何平均数
G m e a s u r e G_{measure} Gmeasure	G m e a s u r e = 2 × p d × ( 1 − p f ) p d + ( 1 − p f ) G_{measure}=\frac{2 \times pd \times(1-pf)}{pd+(1-pf)} Gmeasure=pd+(1−pf)2×pd×(1−pf)	TPR和FPR的调和平均值，其中pd=TPR，pf=FPR
B a l a n c e Balance Balance	1 − ( 0 − p f ) 2 + ( 1 + p d ) 2 ) 2 1-\sqrt{\frac{\left.(0-p f)^{2}+(1+p d)^{2}\right)}{2}} 1−2(0−pf)2+(1+pd)2)	负类被误分类的比例，其中pd=TPR，pf=FPR	[ 5 ] [5] [5], [ 6 ] [6] [6]
马修斯系数(Matthews Correlation Coefficient, MCC)	M C C = T P × T N − F P × F N ( T P + F P ) ( T P + F N ) ( T N + F P ) ( T N + F N ) MCC=\frac{TP \times TN-FP \times FN}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}} MCC=(TP+FP)(TP+FN)(TN+FP)(TN+FN) TP×TN−FP×FN	实际分类与预测分类之间的相关系数	[ 7 ] [7] [7]
AUC		ROC曲线下的面积	[ 8 ] [8] [8]， [ 9 ] [9] [9]， [ 10 ] [10] [10]， [ 11 ] [11] [11]， [ 12 ] [12] [12]， [ 13 ] [13] [13]
Brier	1 N ∑ i = 1 N ( p i − y i ) 2 \frac{1}{N} \sum_{i=1}^{N}\left(p_{i}-y_{i}\right)^{2} N1i=1∑N(pi−yi)2	预测概率和结果之间的差距	[ 14 ] [14] [14]， [ 15 ] [15] [15]
LogLoss	l o g l o s s = − 1 N ∑ i = 1 N ( y i log ⁡ ( p i ) + ( 1 − y i ) log ⁡ ( 1 − p i ) ) logloss=-\frac{1}{N} \sum_{i=1}^{N}\left(y_{i} \log \left(p_{i}\right)+\left(1-y_{i}\right) \log \left(1-p_{i}\right)\right) logloss=−N1i=1∑N(yilog(pi)+(1−yi)log(1−pi))	分类损失函数

补充：

MCC：MCC本质上是一个描述实际分类与预测分类之间的相关系数，它的取值范围为[-1,1]，取值为1时表示对受试对象的完美预测，取值为0时表示预测的结果还不如随机预测的结果，-1是指预测分类和实际分类完全不一致；
Brier score： p i p_{i} pi是预测概率， y i y_{i} yi是真实的标签(0或者1)，取值范围是[0, 1]，0代表性能最好，1代表性能最差，0.25表示随机分类；
LogLoss： p i p_{i} pi是预测概率， y i y_{i} yi是真实的标签(0或者1)，Kaggle比赛的标准性能度量；

3、参考文献

[ 1 ] [1] [1]C. Tantithamthavorn, S. McIntosh, A. E. Hassan, and K. Matsumoto, “The Impact of Automated Parameter Optimization on Defect Prediction Models,” IEEE Trans. Softw. Eng., vol. 45, no. 7, pp. 683–711, Jul. 2019, doi: 10.1109/TSE.2018.2794977
[ 2 ] [2] [2]C. Tantithamthavorn, S. McIntosh, A. E. Hassan, and K. Matsumoto, “An Empirical Comparison of Model Validation Techniques for Defect Prediction Models,” IEEE Trans. Softw. Eng., vol. 43, no. 1, pp. 1–18, Jan. 2017, doi: 10.1109/TSE.2016.2584050.
[ 3 ] [3] [3]W. Fu, T. Menzies, and X. Shen, “Tuning for software analytics: is it really necessary?” Information and Software Technology, vol. 76, pp. 135–146.
[ 4 ] [4] [4]T. Menzies, J. Greenwald, and A. Frank, “Data Mining Static Code Attributes to Learn Defect Predictors,” IEEE Transactions on Software Engineering (TSE), vol. 33, no. 1, pp. 2–13, 2007.
[ 5 ] [5] [5]H. Zhang and X. Zhang, “Comments on “Data Min- ing Static Code Attributes to Learn Defect Predic- tors”,” IEEE Transactions on Software Engineering (TSE), vol. 33, no. 9, pp. 635–636, 2007.
[ 6 ] [6] [6]A. Tosun, “Ensemble of Software Defect Predictors: A Case Study,” in Proceedings of the International Sympo- sium on Empirical Software Engineering and Measurement (ESEM), 2008, pp. 318–320.
[ 7 ] [7] [7]M. Shepperd, D. Bowes, and T. Hall, “Researcher Bias: The Use of Machine Learning in Software Defect Prediction,” IEEE Transactions on Software Engineering (TSE), vol. 40, no. 6, pp. 603–616, 2014.
[ 8 ] [8] [8]S. den Boer, N. F. de Keizer, and E. de Jonge, “Performance of prognostic models in critically ill cancer patients - a review.” Critical care, vol. 9, no. 4, pp. R458–R463, 2005.
[ 9 ] [9] [9]F. E. Harrell Jr., Regression Modeling Strategies, 1st ed. Springer, 2002.
[ 10 ] [10] [10]J. Huang and C. X. Ling, “Using AUC and accuracy
in evaluating learning algorithms,” Transactions on Knowledge and Data Engineering, vol. 17, no. 3, pp. 299– 310, 2005.
[ 11 ] [11] [11]S. Lessmann, S. Member, B. Baesens, C. Mues, and S. Pietsch, “Benchmarking Classification Models for Software Defect Prediction: A Proposed Framework and Novel Findings,” IEEE Transactions on Software Engineering (TSE), vol. 34, no. 4, pp. 485–496, 2008.
[ 12 ] [12] [12]E. W. Steyerberg, Clinical prediction models: a practi- cal approach to development, validation, and updating. Springer Science & Business Media, 2008.
[ 13 ] [13] [13]E. W. Steyerberg, A. J. Vickers, N. R. Cook, T. Gerds, N. Obuchowski, M. J. Pencina, and M. W. Kattan, “Assessing the performance of prediction models: a framework for some traditional and novel measures,” Epidemiology, vol. 21, no. 1, pp. 128–138, 2010.
[ 14 ] [14] [14]G. W. Brier, “Verification of Forecasets Expressed in Terms of Probability,” Monthly Weather Review, vol. 78, no. 1, pp. 25–27, 1950.
[ 15 ] [15] [15]K. Rufibach, “Use of Brier score to assess binary predictions,” Journal of Clinical Epidemiology, vol. 63, no. 8, pp. 938–939, 2010.