fbeta_score

sklearn.metrics.fbeta_score(y_true, y_pred, *, beta, labels=None, pos_label=1, average='binary', sample_weight=None, zero_division='warn')

Compute the F-beta score.

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 represents the ratio of recall importance to precision importance. beta > 1 gives more weight to recall, while beta < 1 favors precision. For example, beta = 2 makes recall twice as important as precision, while beta = 0.5 does the opposite. Asymptotically, beta -> +inf considers only recall, and beta -> 0 only precision.

The formula for F-beta score is:

\[F_\beta = \frac{(1 + \beta^2) \text{tp}} {(1 + \beta^2) \text{tp} + \text{fp} + \beta^2 \text{fn}}\]

Where \(\text{tp}\) is the number of true positives, \(\text{fp}\) is the number of false positives, and \(\text{fn}\) is the number of false negatives.

Support beyond term:binary targets is achieved by treating multiclass and multilabel data as a collection of binary problems, one for each label. For the binary case, setting average='binary' will return F-beta score for pos_label. If average is not 'binary', pos_label is ignored and F-beta score for both classes are computed, then averaged or both returned (when average=None). Similarly, for multiclass and multilabel targets, F-beta score for all labels are either returned or averaged depending on the average parameter. Use labels specify the set of labels to calculate F-beta score for.

Read more in the User Guide.

Parameters:

y_true1d array-like, or label indicator array / sparse matrix

Ground truth (correct) target values.

y_pred1d array-like, or label indicator array / sparse matrix

Estimated targets as returned by a classifier.

betafloat

Determines the weight of recall in the combined score.

labelsarray-like, default=None

The set of labels to include when average != 'binary', and their order if average is None. Labels present in the data can be excluded, for example in multiclass classification to exclude a “negative class”. Labels not present in the data can be included and will be “assigned” 0 samples. For multilabel targets, labels are column indices. By default, all labels in y_true and y_pred are used in sorted order.

Changed in version 0.17: Parameter labels improved for multiclass problem.

pos_labelint, float, bool or str, default=1

The class to report if average='binary' and the data is binary, otherwise this parameter is ignored. For multiclass or multilabel targets, set labels=[pos_label] and average != 'binary' to report metrics for one label only.

average{‘micro’, ‘macro’, ‘samples’, ‘weighted’, ‘binary’} or None, default=’binary’

This parameter is required for multiclass/multilabel targets. If None, the metrics for each class are returned. Otherwise, this determines the type of averaging performed on the data:

'binary':

Only report results for the class specified by pos_label. This is applicable only if targets (y_{true,pred}) are binary.

'micro':

Calculate metrics globally by counting the total true positives, false negatives and false positives.

'macro':

Calculate metrics for each label, and find their unweighted mean. This does not take label imbalance into account.

'weighted':

Calculate metrics for each label, and find their average weighted by support (the number of true instances for each label). This alters ‘macro’ to account for label imbalance; it can result in an F-score that is not between precision and recall.

'samples':

Calculate metrics for each instance, and find their average (only meaningful for multilabel classification where this differs from accuracy_score).

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

zero_division{“warn”, 0.0, 1.0, np.nan}, default=”warn”

Sets the value to return when there is a zero division, i.e. when all predictions and labels are negative.

Notes:

• If set to “warn”, this acts like 0, but a warning is also raised.

• If set to np.nan, such values will be excluded from the average.

Added in version 1.3: np.nan option was added.

Returns:

fbeta_scorefloat (if average is not None) or array of float, shape = [n_unique_labels]

F-beta score of the positive class in binary classification or weighted average of the F-beta score of each class for the multiclass task.

See also

precision_recall_fscore_support

Compute the precision, recall, F-score, and support.

multilabel_confusion_matrix

Compute a confusion matrix for each class or sample.

Notes

When true positive + false positive + false negative == 0, f-score returns 0.0 and raises UndefinedMetricWarning. This behavior can be modified by setting zero_division.

References

[1]

R. Baeza-Yates and B. Ribeiro-Neto (2011). Modern Information Retrieval. Addison Wesley, pp. 327-328.

[2]

Wikipedia entry for the F1-score.

Examples

>>> import numpy as np
>>> from sklearn.metrics import fbeta_score
>>> y_true = [0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 2, 1, 0, 0, 1]
>>> fbeta_score(y_true, y_pred, average='macro', beta=0.5)
0.23...
>>> fbeta_score(y_true, y_pred, average='micro', beta=0.5)
0.33...
>>> fbeta_score(y_true, y_pred, average='weighted', beta=0.5)
0.23...
>>> fbeta_score(y_true, y_pred, average=None, beta=0.5)
array([0.71..., 0.        , 0.        ])
>>> y_pred_empty = [0, 0, 0, 0, 0, 0]
>>> fbeta_score(y_true, y_pred_empty,
...             average="macro", zero_division=np.nan, beta=0.5)
0.12...