F-Beta Score (FBS)

The F-beta score is the weighted harmonic mean of precision and recall, reaching its optimal value at 1 and its worst value at 0.

The beta parameter determines the weight of recall 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).

\[F-beta = (1 + beta**2) * (precision * recall) / (beta**2 * precision + recall)\]

In the multi-class and multi-label case, this is the average of the FBS score of each class with weighting depending on the average parameter.

• Best possible score is 1.0, higher value is better. Range = [0, 1]

• https://neptune.ai/blog/evaluation-metrics-binary-classification

• https://scikit-learn.org/stable/modules/generated/sklearn.metrics.fbeta_score.html#sklearn.metrics.fbeta_score

Example:

from numpy import array
from permetrics.classification import ClassificationMetric

## For integer labels or categorical labels
y_true = [0, 1, 0, 0, 1, 0]
y_pred = [0, 1, 0, 0, 0, 1]

# y_true = ["cat", "ant", "cat", "cat", "ant", "bird", "bird", "bird"]
# y_pred = ["ant", "ant", "cat", "cat", "ant", "cat", "bird", "ant"]

cm = ClassificationMetric(y_true, y_pred)

print(cm.fbeta_score(average=None))
print(cm.fbeta_score(average="micro"))
print(cm.FBS(average="macro"))
print(cm.FBS(average="weighted"))