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.
Ground truth (correct) target values.
Estimated targets as returned by a classifier.
Determines the weight of recall in the combined score.
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.
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.
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 weights.
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.
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.
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.
F-beta score is not implemented as a named scorer that can be passed to the scoring parameter of cross-validation tools directly: it requires to be wrapped with make_scorer so as to specify the value of beta. See examples for details.
References
[1]R. Baeza-Yates and B. Ribeiro-Neto (2011). Modern Information Retrieval. Addison Wesley, pp. 327-328.
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) 0.238 >>> fbeta_score(y_true, y_pred, average='micro', beta=0.5) 0.33 >>> fbeta_score(y_true, y_pred, average='weighted', beta=0.5) 0.238 >>> 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, ... ) 0.128
In order to use fbeta_scorer as a scorer, a callable scorer objects needs to be created first with make_scorer, passing the value for the beta parameter.
>>> from sklearn.metrics import fbeta_score, make_scorer
>>> ftwo_scorer = make_scorer(fbeta_score, beta=2)
>>> from sklearn.model_selection import GridSearchCV
>>> from sklearn.svm import LinearSVC
>>> grid = GridSearchCV(
... LinearSVC(dual="auto"),
... param_grid={'C': [1, 10]},
... scoring=ftwo_scorer,
... cv=5
... )
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