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ENH Add Poisson, Gamma and Tweedie deviances to regression metrics (#14263)
* ENH add new metric Tweedie deviance * More improvements * A few more fixes * Fix doctest * Review comments * Add common metric tests * Add what's new entry * Fix symmetry check in metrics common tests * Fix test order determinism * Rename metric to mean_tweedie_deviance * Address review comments * Fix test_score_objects.py tests * Add Poisson and Gamma deviances * Fix doc link * Fix typo on what's new * Fix rst rendering
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‎doc/modules/classes.rst

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@@ -903,6 +903,9 @@ details.
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metrics.mean_squared_log_error
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metrics.median_absolute_error
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metrics.r2_score
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metrics.mean_poisson_deviance
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metrics.mean_gamma_deviance
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metrics.mean_tweedie_deviance
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Multilabel ranking metrics
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--------------------------

‎doc/modules/model_evaluation.rst

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@@ -91,6 +91,8 @@ Scoring Function
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'neg_mean_squared_log_error' :func:`metrics.mean_squared_log_error`
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'neg_median_absolute_error' :func:`metrics.median_absolute_error`
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'r2' :func:`metrics.r2_score`
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'neg_mean_poisson_deviance' :func:`metrics.mean_poisson_deviance`
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'neg_mean_gamma_deviance' :func:`metrics.mean_gamma_deviance`
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============================== ============================================= ==================================
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@@ -1957,6 +1959,76 @@ Here is a small example of usage of the :func:`r2_score` function::
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for an example of R² score usage to
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evaluate Lasso and Elastic Net on sparse signals.
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.. _mean_tweedie_deviance:
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Mean Poisson, Gamma, and Tweedie deviances
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------------------------------------------
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The :func:`mean_tweedie_deviance` function computes the `mean Tweedie
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deviance error
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<https://en.wikipedia.org/wiki/Tweedie_distribution#The_Tweedie_deviance>`_
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with power parameter `p`. This is a metric that elicits predicted expectation
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values of regression targets.
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Following special cases exist,
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- when `p=0` it is equivalent to :func:`mean_squared_error`.
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- when `p=1` it is equivalent to :func:`mean_poisson_deviance`.
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- when `p=2` it is equivalent to :func:`mean_gamma_deviance`.
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If :math:`\hat{y}_i` is the predicted value of the :math:`i`-th sample,
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and :math:`y_i` is the corresponding true value, then the mean Tweedie
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deviance error (D) estimated over :math:`n_{\text{samples}}` is defined as
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.. math::
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\text{D}(y, \hat{y}) = \frac{1}{n_\text{samples}}
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\sum_{i=0}^{n_\text{samples} - 1}
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\begin{cases}
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(y_i-\hat{y}_i)^2, & \text{for }p=0\text{ (Normal)}\\
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2(y_i \log(y/\hat{y}_i) + \hat{y}_i - y_i), & \text{for }p=1\text{ (Poisson)}\\
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2(\log(\hat{y}_i/y_i) + y_i/\hat{y}_i - 1), & \text{for }p=2\text{ (Gamma)}\\
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2\left(\frac{\max(y_i,0)^{2-p}}{(1-p)(2-p)}-
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\frac{y\,\hat{y}^{1-p}_i}{1-p}+\frac{\hat{y}^{2-p}_i}{2-p}\right),
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& \text{otherwise}
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\end{cases}
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Tweedie deviance is a homogeneous function of degree ``2-p``.
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Thus, Gamma distribution with `p=2` means that simultaneously scaling `y_true`
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and `y_pred` has no effect on the deviance. For Poisson distribution `p=1`
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the deviance scales linearly, and for Normal distribution (`p=0`),
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quadratically. In general, the higher `p` the less weight is given to extreme
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deviations between true and predicted targets.
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For instance, let's compare the two predictions 1.0 and 100 that are both
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50% of their corresponding true value.
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The mean squared error (``p=0``) is very sensitive to the
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prediction difference of the second point,::
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>>> from sklearn.metrics import mean_tweedie_deviance
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>>> mean_tweedie_deviance([1.0], [1.5], p=0)
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0.25
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>>> mean_tweedie_deviance([100.], [150.], p=0)
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2500.0
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If we increase ``p`` to 1,::
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>>> mean_tweedie_deviance([1.0], [1.5], p=1)
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0.18...
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>>> mean_tweedie_deviance([100.], [150.], p=1)
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18.9...
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the difference in errors decreases. Finally, by setting, ``p=2``::
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>>> mean_tweedie_deviance([1.0], [1.5], p=2)
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0.14...
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>>> mean_tweedie_deviance([100.], [150.], p=2)
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0.14...
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we would get identical errors. The deviance when `p=2` is thus only
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sensitive to relative errors.
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.. _clustering_metrics:
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Clustering metrics

‎doc/whats_new/v0.22.rst

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- |Feature| Added multiclass support to :func:`metrics.roc_auc_score`.
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:issue:`12789` by :user:`Kathy Chen <kathyxchen>`,
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:user:`Mohamed Maskani <maskani-moh>`, and :user:`Thomas Fan <thomasjpfan>`.
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- |Feature| Add :class:`metrics.mean_tweedie_deviance` measuring the
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Tweedie deviance for a power parameter ``p``. Also add mean Poisson deviance
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:class:`metrics.mean_poisson_deviance` and mean Gamma deviance
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:class:`metrics.mean_gamma_deviance` that are special cases of the Tweedie
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deviance for `p=1` and `p=2` respectively.
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:pr:`13938` by :user:`Christian Lorentzen <lorentzenchr>` and
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`Roman Yurchak`_.
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- |Enhancement| The parameter ``beta`` in :func:`metrics.fbeta_score` is
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updated to accept the zero and `float('+inf')` value.

‎sklearn/metrics/__init__.py

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from .regression import mean_squared_log_error
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from .regression import median_absolute_error
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from .regression import r2_score
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from .regression import mean_tweedie_deviance
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from .regression import mean_poisson_deviance
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from .regression import mean_gamma_deviance
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from .scorer import check_scoring
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'mean_absolute_error',
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'mean_squared_error',
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'mean_squared_log_error',
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'mean_poisson_deviance',
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'mean_gamma_deviance',
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'mean_tweedie_deviance',
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'median_absolute_error',
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'multilabel_confusion_matrix',
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'mutual_info_score',

‎sklearn/metrics/regression.py

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# Manoj Kumar <manojkumarsivaraj334@gmail.com>
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# Michael Eickenberg <michael.eickenberg@gmail.com>
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# Konstantin Shmelkov <konstantin.shmelkov@polytechnique.edu>
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# Christian Lorentzen <lorentzen.ch@googlemail.com>
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# License: BSD 3 clause
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import numpy as np
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from scipy.special import xlogy
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import warnings
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from ..utils.validation import (check_array, check_consistent_length,
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"mean_squared_log_error",
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"median_absolute_error",
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"r2_score",
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"explained_variance_score"
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"explained_variance_score",
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"mean_tweedie_deviance",
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"mean_poisson_deviance",
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"mean_gamma_deviance",
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]
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def _check_reg_targets(y_true, y_pred, multioutput):
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def _check_reg_targets(y_true, y_pred, multioutput, dtype="numeric"):
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"""Check that y_true and y_pred belong to the same regression task
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Parameters
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Custom output weights if ``multioutput`` is array-like or
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just the corresponding argument if ``multioutput`` is a
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correct keyword.
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dtype: str or list, default="numeric"
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the dtype argument passed to check_array
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"""
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check_consistent_length(y_true, y_pred)
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y_true = check_array(y_true, ensure_2d=False)
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y_pred = check_array(y_pred, ensure_2d=False)
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y_true = check_array(y_true, ensure_2d=False, dtype=dtype)
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y_pred = check_array(y_pred, ensure_2d=False, dtype=dtype)
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if y_true.ndim == 1:
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y_true = y_true.reshape((-1, 1))
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if y_type == 'continuous-multioutput':
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raise ValueError("Multioutput not supported in max_error")
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return np.max(np.abs(y_true - y_pred))
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def mean_tweedie_deviance(y_true, y_pred, sample_weight=None, p=0):
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"""Mean Tweedie deviance regression loss.
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Read more in the :ref:`User Guide <mean_tweedie_deviance>`.
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Parameters
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----------
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y_true : array-like of shape (n_samples,)
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Ground truth (correct) target values.
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y_pred : array-like of shape (n_samples,)
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Estimated target values.
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sample_weight : array-like, shape (n_samples,), optional
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Sample weights.
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p : float, optional
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Tweedie power parameter. Either p ≤ 0 or p ≥ 1.
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The higher `p` the less weight is given to extreme
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deviations between true and predicted targets.
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- p < 0: Extreme stable distribution. Requires: y_pred > 0.
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- p = 0 : Normal distribution, output corresponds to
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mean_squared_error. y_true and y_pred can be any real numbers.
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- p = 1 : Poisson distribution. Requires: y_true ≥ 0 and y_pred > 0.
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- 1 < p < 2 : Compound Poisson distribution. Requires: y_true ≥ 0
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and y_pred > 0.
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- p = 2 : Gamma distribution. Requires: y_true > 0 and y_pred > 0.
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- p = 3 : Inverse Gaussian distribution. Requires: y_true > 0
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and y_pred > 0.
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- otherwise : Positive stable distribution. Requires: y_true > 0
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and y_pred > 0.
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Returns
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-------
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loss : float
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A non-negative floating point value (the best value is 0.0).
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Examples
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--------
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>>> from sklearn.metrics import mean_tweedie_deviance
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>>> y_true = [2, 0, 1, 4]
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>>> y_pred = [0.5, 0.5, 2., 2.]
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>>> mean_tweedie_deviance(y_true, y_pred, p=1)
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1.4260...
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"""
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y_type, y_true, y_pred, _ = _check_reg_targets(
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y_true, y_pred, None, dtype=[np.float64, np.float32])
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if y_type == 'continuous-multioutput':
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raise ValueError("Multioutput not supported in mean_tweedie_deviance")
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check_consistent_length(y_true, y_pred, sample_weight)
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if sample_weight is not None:
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sample_weight = column_or_1d(sample_weight)
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sample_weight = sample_weight[:, np.newaxis]
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message = ("Mean Tweedie deviance error with p={} can only be used on "
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.format(p))
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if p < 0:
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# 'Extreme stable', y_true any realy number, y_pred > 0
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if (y_pred <= 0).any():
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raise ValueError(message + "strictly positive y_pred.")
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dev = 2 * (np.power(np.maximum(y_true, 0), 2-p)/((1-p) * (2-p)) -
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y_true * np.power(y_pred, 1-p)/(1-p) +
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np.power(y_pred, 2-p)/(2-p))
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elif p == 0:
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# Normal distribution, y_true and y_pred any real number
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dev = (y_true - y_pred)**2
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elif p < 1:
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raise ValueError("Tweedie deviance is only defined for p<=0 and "
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"p>=1.")
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elif p == 1:
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# Poisson distribution, y_true >= 0, y_pred > 0
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if (y_true < 0).any() or (y_pred <= 0).any():
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raise ValueError(message + "non-negative y_true and strictly "
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"positive y_pred.")
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dev = 2 * (xlogy(y_true, y_true/y_pred) - y_true + y_pred)
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elif p == 2:
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# Gamma distribution, y_true and y_pred > 0
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if (y_true <= 0).any() or (y_pred <= 0).any():
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raise ValueError(message + "strictly positive y_true and y_pred.")
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dev = 2 * (np.log(y_pred/y_true) + y_true/y_pred - 1)
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else:
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if p < 2:
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# 1 < p < 2 is Compound Poisson, y_true >= 0, y_pred > 0
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if (y_true < 0).any() or (y_pred <= 0).any():
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raise ValueError(message + "non-negative y_true and strictly "
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"positive y_pred.")
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else:
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if (y_true <= 0).any() or (y_pred <= 0).any():
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raise ValueError(message + "strictly positive y_true and "
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"y_pred.")
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dev = 2 * (np.power(y_true, 2-p)/((1-p) * (2-p)) -
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y_true * np.power(y_pred, 1-p)/(1-p) +
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np.power(y_pred, 2-p)/(2-p))
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return np.average(dev, weights=sample_weight)
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def mean_poisson_deviance(y_true, y_pred, sample_weight=None):
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"""Mean Poisson deviance regression loss.
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Poisson deviance is equivalent to the Tweedie deviance with
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the power parameter `p=1`.
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Read more in the :ref:`User Guide <mean_tweedie_deviance>`.
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Parameters
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----------
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y_true : array-like of shape (n_samples,)
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Ground truth (correct) target values. Requires y_true ≥ 0.
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y_pred : array-like of shape (n_samples,)
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Estimated target values. Requires y_pred > 0.
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sample_weight : array-like, shape (n_samples,), optional
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Sample weights.
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Returns
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-------
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loss : float
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A non-negative floating point value (the best value is 0.0).
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Examples
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--------
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>>> from sklearn.metrics import mean_poisson_deviance
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>>> y_true = [2, 0, 1, 4]
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>>> y_pred = [0.5, 0.5, 2., 2.]
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>>> mean_poisson_deviance(y_true, y_pred)
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1.4260...
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"""
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return mean_tweedie_deviance(
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y_true, y_pred, sample_weight=sample_weight, p=1
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)
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def mean_gamma_deviance(y_true, y_pred, sample_weight=None):
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"""Mean Gamma deviance regression loss.
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Gamma deviance is equivalent to the Tweedie deviance with
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the power parameter `p=2`. It is invariant to scaling of
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the target variable, and mesures relative errors.
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Read more in the :ref:`User Guide <mean_tweedie_deviance>`.
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Parameters
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----------
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y_true : array-like of shape (n_samples,)
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Ground truth (correct) target values. Requires y_true > 0.
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y_pred : array-like of shape (n_samples,)
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Estimated target values. Requires y_pred > 0.
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sample_weight : array-like, shape (n_samples,), optional
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Sample weights.
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Returns
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-------
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loss : float
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A non-negative floating point value (the best value is 0.0).
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Examples
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--------
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>>> from sklearn.metrics import mean_gamma_deviance
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>>> y_true = [2, 0.5, 1, 4]
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>>> y_pred = [0.5, 0.5, 2., 2.]
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>>> mean_gamma_deviance(y_true, y_pred)
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1.0568...
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"""
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return mean_tweedie_deviance(
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y_true, y_pred, sample_weight=sample_weight, p=2
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)

‎sklearn/metrics/scorer.py

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import numpy as np
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from . import (r2_score, median_absolute_error, max_error, mean_absolute_error,
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mean_squared_error, mean_squared_log_error, accuracy_score,
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mean_squared_error, mean_squared_log_error,
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mean_tweedie_deviance, accuracy_score,
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f1_score, roc_auc_score, average_precision_score,
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precision_score, recall_score, log_loss,
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balanced_accuracy_score, explained_variance_score,
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greater_is_better=False)
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neg_mean_absolute_error_scorer = make_scorer(mean_absolute_error,
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greater_is_better=False)
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neg_median_absolute_error_scorer = make_scorer(median_absolute_error,
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greater_is_better=False)
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neg_mean_poisson_deviance_scorer = make_scorer(
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mean_tweedie_deviance, p=1., greater_is_better=False
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)
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neg_mean_gamma_deviance_scorer = make_scorer(
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mean_tweedie_deviance, p=2., greater_is_better=False
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)
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# Standard Classification Scores
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accuracy_scorer = make_scorer(accuracy_score)
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neg_mean_absolute_error=neg_mean_absolute_error_scorer,
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neg_mean_squared_error=neg_mean_squared_error_scorer,
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neg_mean_squared_log_error=neg_mean_squared_log_error_scorer,
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neg_mean_poisson_deviance=neg_mean_poisson_deviance_scorer,
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neg_mean_gamma_deviance=neg_mean_gamma_deviance_scorer,
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accuracy=accuracy_scorer, roc_auc=roc_auc_scorer,
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roc_auc_ovr=roc_auc_ovr_scorer,
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roc_auc_ovo=roc_auc_ovo_scorer,

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