F1Scores

F1 score is a performance metric used in binary classification to balance precision and recall. It is the harmonic mean of precision and recall, defined as F1 = 2 × (precision × recall) / (precision + recall). Precision equals TP / (TP + FP) and recall equals TP / (TP + FN), where TP, FP, and FN are true positives, false positives, and false negatives. The F1 score ranges from 0 to 1, with 1 indicating perfect precision and recall.

The F1 score is especially useful when the class distribution is imbalanced or when false positives and false negatives carry different costs. Unlike accuracy, F1 provides a single metric that accounts for both false positives and false negatives for the positive class.

For multiclass problems, F1 can be extended by computing per-class F1 scores and then aggregating. Common approaches are macro F1 (unweighted average of per-class F1s), micro F1 (global counts of TP, FP, FN across all classes), and weighted F1 (per-class F1 weighted by class support).

The metric can be generalized with the Fβ score, which weights recall more than precision when β > 1 and precision more when β < 1. F1 corresponds to β = 1, giving equal weight to precision and recall.

Limitations include sensitivity to the chosen threshold for converting scores to class labels and the fact that it ignores true negatives. It may also be misleading for very small classes or when the costs of false positives and false negatives vary significantly. Despite these caveats, the F1 score is a widely used, interpretable metric for evaluating classification performance.