Confusion Matrix

Definition

	Predicted Positive (PP)	Predicted Negative (PN)
Actual Positive	True Positive (TP)	False Negative (FN)
Actual Negative	False Positive (FP)	True Negative (TN)

Metrics

Accuracy

Definition

$\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+\text{FN}}$

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Recall

Definition

$\frac{\text{TP}}{\text{TP}+\text{FN}}$

Recall, Sensitivity, or True positive rate means that the rate of correctly predicted cases out of all the actual positive cases..

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Precision

Definition

$\frac{\text{TP}}{\text{TP}+\text{FP}}$

Precision means that the rate of actually positive cases out of cases predicted as positive.

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Specificity

Definition

$\frac{\text{TN}}{\text{FP}+\text{TN}}$

Specificity means that the rate of correctly predicted cases out of all the actual negative cases.

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Type 1 Error

Definition

$\frac{\text{FP}}{\text{FP}+\text{TN}}$

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Type 2 Error

Definition

$\frac{\text{FN}}{\text{TP}+\text{FN}}$

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F-Score

Definition

F1 Score

$F_1=\frac{2}{{\text{recall}}^{-1}+{\text{precision}}^{-1}}=2\frac{\text{precision}\cdot \text{recall}}{\text{precision}+\text{recall}}$ The harmonic mean of Precision and Recall.

F-beta score

$F_{\beta }=(1+{\beta }^2)\frac{\text{precision}\cdot \text{recall}}{({\beta }^2\cdot \text{precision})+\text{recall}}$ where $\beta >0$

Recall is considered $\beta$ times as important as Precision.

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Positive Predictive Value

Definition

$\frac{\text{Sensitivity}\times \text{Prevalence}}{(\text{Sensitivity}\times \text{Prevalence})+((1-\text{Specificity})\times (1-\text{Prevalence}))}$ where $\text{Prevalence}=\frac{\text{positive cases}}{\text{total population}}$

Positive predictive value (in medical statistics and epidemiology) means that the rate of actually positive cases out of cases predicted as positive.

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