F1-score

F1-score

The harmonic mean of precision and recall.

The F1 score combines precision and recall into one number using their harmonic mean:

F_{1} = \frac{2 \cdot precision \cdot recall}{precision + recall} = \frac{2 T P}{2 T P + F P + F N}

The harmonic mean is dominated by the smaller value, so F1 is only high when *both* are high. It ignores true negatives, which makes it suitable for imbalanced problems where TN is huge and uninformative.

The general $F_{β}$ weights recall $β$ times as much as precision: $F_{β} = (1 + β^{2}) \frac{P R}{β ^{2} P + R}$ . $F_{2}$ favours recall; $F_{0.5}$ favours precision.

Formula to remember

F_{1} = \frac{2 P R}{P + R}

Harmonic mean of precision P and recall R.

Quick check · +5 XP

Precision = 0.5 and recall = 1.0 give an F1 of…

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