F05 Score

The F0.5 Score (also called the F-beta score) is a measure of a test's accuracy that considers both precision and recall. It is a type of F score that weighs recall lower than precision (by applying more weight to false positives).

The general formula for F-beta score is:

F-beta = (1 + beta^2) (precision . recall) / ((beta^2 . precision) + recall)

When beta is 0.5, we get the F0.5 score formula:

F0.5 = 1.25 (precision . recall) / (0.25 . precision + recall)

The F0.5 score is used when you want to tune your model towards precision. That is, when you want to minimize false positives.

If you have a classification problem where false positives are more detrimental than false negatives, the F0.5 score might be the best metric to use. It gives more importance to precision than recall.

On the other hand, if false negatives are more important, you would give more importance to recall, and use an F2 score instead (beta=2). The traditional F1 score (beta=1) considers precision and recall equally important.

Note: The beta parameter determines the weight of precision in the combined score. beta < 1 lends more weight to precision, while beta > 1 favors recall. beta -> 0 considers only precision, beta -> inf only recall.