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评估指标:ROC,AUC,Precision、Recall、F1-score

一、ROC,AUC

ROC(Receiver Operating Characteristic)曲线和AUC常被用来评价一个二值分类器(binary classifier)的优劣 。

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ROC曲线一般的横轴是FPR,纵轴是FPR。AUC为曲线下面的面积,作为评估指标,AUC值越大,说明模型越好。如下图:

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二、Precision、Recall、F1-score

Terminology and derivations
from a  confusion matrix
true positive (TP)
eqv. with hit
true negative (TN)
eqv. with correct rejection
false positive (FP)
eqv. with  false alarmType I error
false negative (FN)
eqv. with miss,  Type II error
sensitivity or  true positive rate (TPR)
eqv. with  hit raterecall

\mathit{TPR} = \frac {\mathit{TP}} {P} = \frac {\mathit{TP}} {\mathit{TP}+\mathit{FN}}

specificity (SPC) or  true negative rate (TNR)

\mathit{SPC} = \frac {\mathit{TN}} {N} = \frac {\mathit{TN}} {\mathit{FP} + \mathit{TN}}

precision or  positive predictive value (PPV)

\mathit{PPV} = \frac {\mathit{TP}} {\mathit{TP} + \mathit{FP}}

negative predictive value (NPV)

\mathit{NPV} = \frac {\mathit{TN}} {\mathit{TN} + \mathit{FN}}

fall-out or  false positive rate (FPR)

\mathit{FPR} = \frac {\mathit{FP}} {N} = \frac {\mathit{FP}} {\mathit{FP} + \mathit{TN}} = 1 - \mathit{SPC}

false discovery rate (fdr)

\mathit{FDR} = \frac {\mathit{FP}} {\mathit{FP} + \mathit{TP}} = 1 - \mathit{PPV}

miss rate or  false negative rate (FNR)

\mathit{FNR} = \frac {\mathit{FN}} {P} = \frac {\mathit{FN}} {\mathit{FN} + \mathit{TP}}

accuracy (ACC)

\mathit{ACC} = \frac {\mathit{TP} + \mathit{TN}} {P + N}

F1 score
is the  harmonic mean of  precision and  sensitivity

\mathit{F1} = \frac {2 \mathit{TP}} {2 \mathit{TP} + \mathit{FP} + \mathit{FN}}

Matthews correlation coefficient (MCC)

\frac{ TP \times TN - FP \times FN } {\sqrt{ (TP+FP) ( TP + FN ) ( TN + FP ) ( TN + FN ) } }

Informedness = Sensitivity + Specificity - 1
Markedness = Precision + NPV - 1

中文解释

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