ROC curve – ML – Yair Shinar

The ROC curve(relative operating characteristic curve), is a comparison of two operating characteristics (TPR and FPR) as the criterion changes (sensitivity as a function of fall-out).

The TPR(true positive rate) is also known as sensitivity, recall or probability of detection, it can be calculated as 1-miss rate(FNR).

$\mathrm {TPR} ={\frac {\mathrm {TP} }{P}}={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FN} }}=1-\mathrm {FNR}$

The FPR(false positive rate) A.K.A the fall-out or probability of false alarm, it can be calculated as 1-sensitivity(TNR).

$\mathrm {FPR} ={\frac {\mathrm {FP} }{N}}={\frac {\mathrm {FP} }{\mathrm {FP} +\mathrm {TN} }}=1-\mathrm {TNR}$

A receiver operating characteristic curve, is a graphical plot that illustrates the TPR) against the (FPR) at various threshold settings of a binary classifier system, and finding the max TPR against the min FPR value.

False positive rate (FPR)(α) = type I error = 1 − specificity
= FP / (FP + TN) = 180 / (180 + 1820) = 9%
False negative rate (FNR)(β) = type II error = 1 − sensitivity
= FN / (TP + FN) = 10 / (20 + 10) = 33%
True positive rate (TPR), Recall, Sensitivity, probability of detection
=Σ True positive/Σ Condition positive
Accuracy (ACC)
= Σ True positive + Σ True negative/Σ Total population
Precision
= Σ True positive/Σ Predicted condition positive

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