Precision and Recall

Accuracy and recall are two statistical metrics used to evaluate detection, classification, or information retrieval systems. They compare two sets: the set of items retrieved (or predicted positive) and the set of expected items (the reference or gold standard).

— Accuracy (positive predictive value) measures the reliability of the returned items.

— Recall (true positive rate or sensitivity) measures the system's ability to retrieve relevant items.

For an overview, the user can refer to the confusion matrix.

In information retrieval, precision is the ratio between the number of relevant items retrieved and the total number of items retrieved.

$$ \text{Precision}=\frac{|\{\text{Relevant items}\}\cap\{\text{Retrieved items}\}|}{|\{\text{Retrieved items}\}|} $$

Recall is the ratio between the number of relevant items retrieved and the total number of relevant items expected.

$$ \text{Recall}=\frac{|\{\text{Relevant items}\}\cap\{\text{Retrieved items}\}|}{|\{\text{Relevant items}\}|} $$

In statistics, the F-measure $ F_1 $ (or F-score) is the harmonic mean of precision $ P $ and recall $ R $, which penalizes imbalances between these two quantities.

$$ F = \frac{2 (P \times R)}{(P + R)} $$

The $ F_1 $ score ranges from 0 to 1: it is high (close to 1) only if both precision and recall are high.

The following diagram includes precision, recall, true positive (TP), false positive (FP), true negative (TN) and false negative (FN) (source wikipedia)