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add Brier_score_loss to model validation doc #4804 #4964

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40 changes: 40 additions & 0 deletions doc/modules/model_evaluation.rst
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Expand Up @@ -1014,6 +1014,46 @@ set [0,1] has an error: ::
for an example of zero one loss usage to perform recursive feature
elimination with cross-validation.

.. _brier_score_loss:

Brier score loss
----------------

The :func:`brier_score_loss` function returns a score of the mean square difference
between the actual outcome and the predicted probability of the possible outcome.
The actual outcome has to be 1 or 0 (true or false), while the predicted probability
of the actual outcome happens can be value between 0 and 1. The brier score loss is
also between 0 to 1 and the lower the score (the mean square difference is smaller),
the more accurate the prediction is.

.. math::

BS = \frac{1}{N} \sum_{t=1}^{N}(f_t - o_t)^2

where : :math:`N` is the total number of predictions, :math:`f_t` is the predicted probablity of the actual outcome :math:`o_t`

>>> import numpy as np
>>> from sklearn.metrics import zero_one_loss
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you need to also import bier_score_loss

>>> y_true = np.array([0, 1, 1, 0])
>>> y_true_categorical = np.array(["spam", "ham", "ham", "spam"])
>>> y_prob = np.array([0.1, 0.9, 0.8, 0.3])
>>> brier_score_loss(y_true, y_prob)
0.25
>>> zero_one_loss(y_true, y_pred, normalize=False)
1
0.037...
>>> brier_score_loss(y_true, 1-y_prob, pos_label=0)
0.037...
>>> brier_score_loss(y_true_categorical, y_prob, pos_label="ham")
0.037...
>>> brier_score_loss(y_true, np.array(y_prob) > 0.5)
0.0

.. topic:: Example:

* See :ref:`example_calibration_plot_calibration.py`
for an example of Brier score loss usage to perform probability calibration of classifiers.


.. _multilabel_ranking_metrics:

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