Fscores

Fscores, commonly written as F-scores, are a family of metrics used to evaluate the balance between precision and recall in binary classification and information retrieval tasks. Precision measures the proportion of retrieved items that are relevant, while recall measures the proportion of relevant items that are retrieved. The F-score combines these two aspects into a single value.

The general form is the F-beta score: F_beta = (1 + beta^2) * (precision * recall) / (beta^2 * precision + recall), where beta determines the weighting of recall relative to precision. When beta equals 1, the F1-score is the harmonic mean of precision and recall, giving equal weight to both. Values of beta less than 1 emphasize precision, while values greater than 1 emphasize recall. Common variants include F1, F0.5, and F2.

Fscores are widely used to evaluate classifiers, detectors, and search systems, especially when class distributions are imbalanced or when the costs of false positives and false negatives differ. They are threshold-dependent, since precision and recall change as the decision threshold changes.

Limitations include sensitivity to class prevalence and the potential to obscure performance on negatives or on specific subgroups. For example, high F-scores can be achieved by predicting a small positive class if both precision and recall are favorable, even if overall accuracy is low. As a result, F-scores are often reported alongside other metrics such as AUROC, AUPRC, MCC, and raw precision/recall.

See also: Precision, Recall, F1-score, F2-score, F-beta score.