Performance metrics description

Quantities

\(\mathrm{TP}\)	-	number of true positive samples
\(\mathrm{TN}\)	-	number of true negative samples
\(\mathrm{FP}\)	-	number of false positive samples
\(\mathrm{FN}\)	-	number of false negative samples

Probabilities

\(P(+)\)	-	probability that the sample is positive
\(P(-)\)	-	probability that the sample is negative
\(P(C+)\)	-	probability that test classifies the sample as positive
\(P(C-)\)	-	probability that test classifies the sample as negative
\(P(A | B)\)	-	conditional probability: probability of A under the condition B

Precision

Probability that the sample is positive, given being classified as positive. Also known as PPV (Positive Predictive Value). $$\mathrm{PREC} = \frac{\mathrm{TP}}{\mathrm{TP} + \mathrm{FP}} = P(+ | C+)$$ See: Precision and recall on Wikipedia.

Recall

Probability that the test classifies sample as positive, given sample being positive. Also known as Sensitivity or TPR (True Positive Rate). $$\mathrm{REC} = \frac{\mathrm{TP}}{\mathrm{TP} + \mathrm{FN}} = P(C+ | +)$$ See: Precision and recall on Wikipedia.

Specificity

Probability that test classifies sample as negative, given sample being negative. Also known as TNR (True Negative Rate). $$\mathrm{SPEC} = \frac{\mathrm{TN}}{\mathrm{TN} + \mathrm{FP}} = P(C- | -)$$ See: Specificity and sensitivity on Wikipedia.

Negative predictive value

$$\mathrm{NPV} = \frac{\mathrm{TN}}{\mathrm{TN} + \mathrm{FN}} = P(- | C-)$$ See: Positive and negative predictive values on Wikipedia.

Accuracy

$$\mathrm{ACC} = \frac{\mathrm{TP} + \mathrm {TN}}{\mathrm{TP} + \mathrm{TN} + \mathrm{FP} + \mathrm{FN}}$$ See: Accuracy and precision on Wikipedia.

F₁

F₁ is a harmonic mean of Precision and Recall, which gives: $$\mathrm{F_1} = \frac{\mathrm{TP}}{\mathrm{TP} + \frac{1}{2} \left( \mathrm{FP} + \mathrm{FN} \right)}$$ See: F1 score on Wikipedia.

P₄

P₄ is a harmonic mean of Precision, Recall, Specificity and NPV which gives: $$\mathrm{P}_4 = \frac{4\cdot\mathrm{TP}\cdot\mathrm{TN}}{4\cdot\mathrm{TP}\cdot\mathrm{TN} + (\mathrm{TP} + \mathrm{TN}) \cdot (\mathrm{FP} + \mathrm{FN})}$$ See: P4 metric on Wikipedia.

Youden Index

$$\mathrm{J} = \mathrm{REC} + \mathrm{SPEC} - 1 = \frac{\mathrm{TP}}{\mathrm{TP} + \mathrm{FN}} + \frac{\mathrm{TN}}{\mathrm{TN} + \mathrm{FP}} - 1$$ See: Youden's statistic on Wikipedia.

Markedness

$$\mathrm{MK} = \mathrm{PREC} + \mathrm{NPV} - 1$$ See: Powers (2020) article.

MCC

MCC - Matthews correlation coefficient, also known as Phi coefficient. $$\mathrm{MCC} = \frac{\mathrm{TP} \times \mathrm{TN} - \mathrm{FP} \times \mathrm{FN}}{\sqrt{(\mathrm{TP} + \mathrm{FP}) (\mathrm{TP} + \mathrm{FN}) (\mathrm{TN} + \mathrm{FP}) (\mathrm{TN} + \mathrm{FN})}}$$ See: Phi coefficient on Wikipedia.