523 lines
22 KiB
Python
523 lines
22 KiB
Python
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"""Partial dependence plots for regression and classification models."""
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# Authors: Peter Prettenhofer
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# Trevor Stephens
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# Nicolas Hug
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# License: BSD 3 clause
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from collections.abc import Iterable
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import warnings
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import numpy as np
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from scipy import sparse
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from scipy.stats.mstats import mquantiles
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from ..base import is_classifier, is_regressor
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from ..pipeline import Pipeline
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from ..utils.extmath import cartesian
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from ..utils import check_array
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from ..utils import check_matplotlib_support # noqa
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from ..utils import _safe_indexing
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from ..utils import _determine_key_type
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from ..utils import _get_column_indices
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from ..utils.validation import check_is_fitted
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from ..utils import Bunch
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from ..utils.validation import _deprecate_positional_args
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from ..tree import DecisionTreeRegressor
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from ..ensemble import RandomForestRegressor
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from ..exceptions import NotFittedError
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from ..ensemble._gb import BaseGradientBoosting
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from sklearn.ensemble._hist_gradient_boosting.gradient_boosting import (
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BaseHistGradientBoosting)
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__all__ = [
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'partial_dependence',
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]
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def _grid_from_X(X, percentiles, grid_resolution):
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"""Generate a grid of points based on the percentiles of X.
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The grid is a cartesian product between the columns of ``values``. The
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ith column of ``values`` consists in ``grid_resolution`` equally-spaced
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points between the percentiles of the jth column of X.
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If ``grid_resolution`` is bigger than the number of unique values in the
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jth column of X, then those unique values will be used instead.
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Parameters
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----------
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X : ndarray, shape (n_samples, n_target_features)
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The data.
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percentiles : tuple of floats
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The percentiles which are used to construct the extreme values of
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the grid. Must be in [0, 1].
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grid_resolution : int
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The number of equally spaced points to be placed on the grid for each
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feature.
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Returns
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-------
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grid : ndarray, shape (n_points, n_target_features)
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A value for each feature at each point in the grid. ``n_points`` is
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always ``<= grid_resolution ** X.shape[1]``.
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values : list of 1d ndarrays
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The values with which the grid has been created. The size of each
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array ``values[j]`` is either ``grid_resolution``, or the number of
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unique values in ``X[:, j]``, whichever is smaller.
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"""
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if not isinstance(percentiles, Iterable) or len(percentiles) != 2:
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raise ValueError("'percentiles' must be a sequence of 2 elements.")
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if not all(0 <= x <= 1 for x in percentiles):
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raise ValueError("'percentiles' values must be in [0, 1].")
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if percentiles[0] >= percentiles[1]:
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raise ValueError('percentiles[0] must be strictly less '
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'than percentiles[1].')
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if grid_resolution <= 1:
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raise ValueError("'grid_resolution' must be strictly greater than 1.")
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values = []
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for feature in range(X.shape[1]):
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uniques = np.unique(_safe_indexing(X, feature, axis=1))
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if uniques.shape[0] < grid_resolution:
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# feature has low resolution use unique vals
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axis = uniques
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else:
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# create axis based on percentiles and grid resolution
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emp_percentiles = mquantiles(
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_safe_indexing(X, feature, axis=1), prob=percentiles, axis=0
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)
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if np.allclose(emp_percentiles[0], emp_percentiles[1]):
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raise ValueError(
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'percentiles are too close to each other, '
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'unable to build the grid. Please choose percentiles '
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'that are further apart.')
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axis = np.linspace(emp_percentiles[0],
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emp_percentiles[1],
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num=grid_resolution, endpoint=True)
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values.append(axis)
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return cartesian(values), values
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def _partial_dependence_recursion(est, grid, features):
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averaged_predictions = est._compute_partial_dependence_recursion(grid,
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features)
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if averaged_predictions.ndim == 1:
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# reshape to (1, n_points) for consistency with
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# _partial_dependence_brute
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averaged_predictions = averaged_predictions.reshape(1, -1)
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return averaged_predictions
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def _partial_dependence_brute(est, grid, features, X, response_method):
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predictions = []
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averaged_predictions = []
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# define the prediction_method (predict, predict_proba, decision_function).
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if is_regressor(est):
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prediction_method = est.predict
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else:
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predict_proba = getattr(est, 'predict_proba', None)
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decision_function = getattr(est, 'decision_function', None)
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if response_method == 'auto':
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# try predict_proba, then decision_function if it doesn't exist
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prediction_method = predict_proba or decision_function
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else:
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prediction_method = (predict_proba if response_method ==
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'predict_proba' else decision_function)
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if prediction_method is None:
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if response_method == 'auto':
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raise ValueError(
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'The estimator has no predict_proba and no '
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'decision_function method.'
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)
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elif response_method == 'predict_proba':
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raise ValueError('The estimator has no predict_proba method.')
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else:
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raise ValueError(
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'The estimator has no decision_function method.')
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for new_values in grid:
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X_eval = X.copy()
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for i, variable in enumerate(features):
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if hasattr(X_eval, 'iloc'):
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X_eval.iloc[:, variable] = new_values[i]
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else:
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X_eval[:, variable] = new_values[i]
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try:
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# Note: predictions is of shape
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# (n_points,) for non-multioutput regressors
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# (n_points, n_tasks) for multioutput regressors
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# (n_points, 1) for the regressors in cross_decomposition (I think)
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# (n_points, 2) for binary classification
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# (n_points, n_classes) for multiclass classification
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pred = prediction_method(X_eval)
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predictions.append(pred)
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# average over samples
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averaged_predictions.append(np.mean(pred, axis=0))
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except NotFittedError as e:
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raise ValueError(
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"'estimator' parameter must be a fitted estimator") from e
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n_samples = X.shape[0]
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# reshape to (n_targets, n_instances, n_points) where n_targets is:
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# - 1 for non-multioutput regression and binary classification (shape is
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# already correct in those cases)
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# - n_tasks for multi-output regression
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# - n_classes for multiclass classification.
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predictions = np.array(predictions).T
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if is_regressor(est) and predictions.ndim == 2:
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# non-multioutput regression, shape is (n_instances, n_points,)
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predictions = predictions.reshape(n_samples, -1)
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elif is_classifier(est) and predictions.shape[0] == 2:
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# Binary classification, shape is (2, n_instances, n_points).
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# we output the effect of **positive** class
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predictions = predictions[1]
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predictions = predictions.reshape(n_samples, -1)
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# reshape averaged_predictions to (n_targets, n_points) where n_targets is:
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# - 1 for non-multioutput regression and binary classification (shape is
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# already correct in those cases)
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# - n_tasks for multi-output regression
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# - n_classes for multiclass classification.
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averaged_predictions = np.array(averaged_predictions).T
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if is_regressor(est) and averaged_predictions.ndim == 1:
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# non-multioutput regression, shape is (n_points,)
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averaged_predictions = averaged_predictions.reshape(1, -1)
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elif is_classifier(est) and averaged_predictions.shape[0] == 2:
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# Binary classification, shape is (2, n_points).
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# we output the effect of **positive** class
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averaged_predictions = averaged_predictions[1]
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averaged_predictions = averaged_predictions.reshape(1, -1)
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return averaged_predictions, predictions
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@_deprecate_positional_args
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def partial_dependence(estimator, X, features, *, response_method='auto',
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percentiles=(0.05, 0.95), grid_resolution=100,
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method='auto', kind='legacy'):
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"""Partial dependence of ``features``.
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Partial dependence of a feature (or a set of features) corresponds to
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the average response of an estimator for each possible value of the
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feature.
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Read more in the :ref:`User Guide <partial_dependence>`.
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.. warning::
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For :class:`~sklearn.ensemble.GradientBoostingClassifier` and
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:class:`~sklearn.ensemble.GradientBoostingRegressor`, the
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`'recursion'` method (used by default) will not account for the `init`
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predictor of the boosting process. In practice, this will produce
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the same values as `'brute'` up to a constant offset in the target
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response, provided that `init` is a constant estimator (which is the
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default). However, if `init` is not a constant estimator, the
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partial dependence values are incorrect for `'recursion'` because the
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offset will be sample-dependent. It is preferable to use the `'brute'`
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method. Note that this only applies to
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:class:`~sklearn.ensemble.GradientBoostingClassifier` and
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:class:`~sklearn.ensemble.GradientBoostingRegressor`, not to
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:class:`~sklearn.ensemble.HistGradientBoostingClassifier` and
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:class:`~sklearn.ensemble.HistGradientBoostingRegressor`.
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Parameters
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----------
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estimator : BaseEstimator
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A fitted estimator object implementing :term:`predict`,
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:term:`predict_proba`, or :term:`decision_function`.
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Multioutput-multiclass classifiers are not supported.
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X : {array-like or dataframe} of shape (n_samples, n_features)
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``X`` is used to generate a grid of values for the target
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``features`` (where the partial dependence will be evaluated), and
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also to generate values for the complement features when the
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`method` is 'brute'.
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features : array-like of {int, str}
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The feature (e.g. `[0]`) or pair of interacting features
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(e.g. `[(0, 1)]`) for which the partial dependency should be computed.
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response_method : {'auto', 'predict_proba', 'decision_function'}, \
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default='auto'
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Specifies whether to use :term:`predict_proba` or
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:term:`decision_function` as the target response. For regressors
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this parameter is ignored and the response is always the output of
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:term:`predict`. By default, :term:`predict_proba` is tried first
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and we revert to :term:`decision_function` if it doesn't exist. If
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``method`` is 'recursion', the response is always the output of
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:term:`decision_function`.
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percentiles : tuple of float, default=(0.05, 0.95)
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The lower and upper percentile used to create the extreme values
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for the grid. Must be in [0, 1].
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grid_resolution : int, default=100
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The number of equally spaced points on the grid, for each target
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feature.
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method : {'auto', 'recursion', 'brute'}, default='auto'
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The method used to calculate the averaged predictions:
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- `'recursion'` is only supported for some tree-based estimators
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(namely
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:class:`~sklearn.ensemble.GradientBoostingClassifier`,
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:class:`~sklearn.ensemble.GradientBoostingRegressor`,
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:class:`~sklearn.ensemble.HistGradientBoostingClassifier`,
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:class:`~sklearn.ensemble.HistGradientBoostingRegressor`,
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:class:`~sklearn.tree.DecisionTreeRegressor`,
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:class:`~sklearn.ensemble.RandomForestRegressor`,
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) when `kind='average'`.
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This is more efficient in terms of speed.
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With this method, the target response of a
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classifier is always the decision function, not the predicted
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probabilities. Since the `'recursion'` method implicitely computes
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the average of the Individual Conditional Expectation (ICE) by
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design, it is not compatible with ICE and thus `kind` must be
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`'average'`.
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- `'brute'` is supported for any estimator, but is more
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computationally intensive.
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- `'auto'`: the `'recursion'` is used for estimators that support it,
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and `'brute'` is used otherwise.
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Please see :ref:`this note <pdp_method_differences>` for
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differences between the `'brute'` and `'recursion'` method.
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kind : {'legacy', 'average', 'individual', 'both'}, default='legacy'
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Whether to return the partial dependence averaged across all the
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samples in the dataset or one line per sample or both.
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See Returns below.
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Note that the fast `method='recursion'` option is only available for
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`kind='average'`. Plotting individual dependencies requires using the
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slower `method='brute'` option.
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.. versionadded:: 0.24
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.. deprecated:: 0.24
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`kind='legacy'` is deprecated and will be removed in version 1.1.
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`kind='average'` will be the new default. It is intended to migrate
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from the ndarray output to :class:`~sklearn.utils.Bunch` output.
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Returns
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-------
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predictions : ndarray or :class:`~sklearn.utils.Bunch`
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- if `kind='legacy'`, return value is ndarray of shape (n_outputs, \
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len(values[0]), len(values[1]), ...)
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The predictions for all the points in the grid, averaged
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over all samples in X (or over the training data if ``method``
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is 'recursion').
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- if `kind='individual'`, `'average'` or `'both'`, return value is \
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:class:`~sklearn.utils.Bunch`
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Dictionary-like object, with the following attributes.
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individual : ndarray of shape (n_outputs, n_instances, \
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len(values[0]), len(values[1]), ...)
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The predictions for all the points in the grid for all
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samples in X. This is also known as Individual
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Conditional Expectation (ICE)
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average : ndarray of shape (n_outputs, len(values[0]), \
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len(values[1]), ...)
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The predictions for all the points in the grid, averaged
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over all samples in X (or over the training data if
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``method`` is 'recursion').
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Only available when kind='both'.
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values : seq of 1d ndarrays
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The values with which the grid has been created. The generated
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grid is a cartesian product of the arrays in ``values``.
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``len(values) == len(features)``. The size of each array
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``values[j]`` is either ``grid_resolution``, or the number of
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unique values in ``X[:, j]``, whichever is smaller.
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``n_outputs`` corresponds to the number of classes in a multi-class
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setting, or to the number of tasks for multi-output regression.
|
||
|
|
For classical regression and binary classification ``n_outputs==1``.
|
||
|
|
``n_values_feature_j`` corresponds to the size ``values[j]``.
|
||
|
|
|
||
|
|
values : seq of 1d ndarrays
|
||
|
|
The values with which the grid has been created. The generated grid
|
||
|
|
is a cartesian product of the arrays in ``values``. ``len(values) ==
|
||
|
|
len(features)``. The size of each array ``values[j]`` is either
|
||
|
|
``grid_resolution``, or the number of unique values in ``X[:, j]``,
|
||
|
|
whichever is smaller. Only available when `kind="legacy"`.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
plot_partial_dependence : Plot Partial Dependence.
|
||
|
|
PartialDependenceDisplay : Partial Dependence visualization.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> X = [[0, 0, 2], [1, 0, 0]]
|
||
|
|
>>> y = [0, 1]
|
||
|
|
>>> from sklearn.ensemble import GradientBoostingClassifier
|
||
|
|
>>> gb = GradientBoostingClassifier(random_state=0).fit(X, y)
|
||
|
|
>>> partial_dependence(gb, features=[0], X=X, percentiles=(0, 1),
|
||
|
|
... grid_resolution=2) # doctest: +SKIP
|
||
|
|
(array([[-4.52..., 4.52...]]), [array([ 0., 1.])])
|
||
|
|
"""
|
||
|
|
if not (is_classifier(estimator) or is_regressor(estimator)):
|
||
|
|
raise ValueError(
|
||
|
|
"'estimator' must be a fitted regressor or classifier."
|
||
|
|
)
|
||
|
|
|
||
|
|
if isinstance(estimator, Pipeline):
|
||
|
|
# TODO: to be removed if/when pipeline get a `steps_` attributes
|
||
|
|
# assuming Pipeline is the only estimator that does not store a new
|
||
|
|
# attribute
|
||
|
|
for est in estimator:
|
||
|
|
# FIXME: remove the None option when it will be deprecated
|
||
|
|
if est not in (None, 'drop'):
|
||
|
|
check_is_fitted(est)
|
||
|
|
else:
|
||
|
|
check_is_fitted(estimator)
|
||
|
|
|
||
|
|
if (is_classifier(estimator) and
|
||
|
|
isinstance(estimator.classes_[0], np.ndarray)):
|
||
|
|
raise ValueError(
|
||
|
|
'Multiclass-multioutput estimators are not supported'
|
||
|
|
)
|
||
|
|
|
||
|
|
# Use check_array only on lists and other non-array-likes / sparse. Do not
|
||
|
|
# convert DataFrame into a NumPy array.
|
||
|
|
if not(hasattr(X, '__array__') or sparse.issparse(X)):
|
||
|
|
X = check_array(X, force_all_finite='allow-nan', dtype=object)
|
||
|
|
|
||
|
|
accepted_responses = ('auto', 'predict_proba', 'decision_function')
|
||
|
|
if response_method not in accepted_responses:
|
||
|
|
raise ValueError(
|
||
|
|
'response_method {} is invalid. Accepted response_method names '
|
||
|
|
'are {}.'.format(response_method, ', '.join(accepted_responses)))
|
||
|
|
|
||
|
|
if is_regressor(estimator) and response_method != 'auto':
|
||
|
|
raise ValueError(
|
||
|
|
"The response_method parameter is ignored for regressors and "
|
||
|
|
"must be 'auto'."
|
||
|
|
)
|
||
|
|
|
||
|
|
accepted_methods = ('brute', 'recursion', 'auto')
|
||
|
|
if method not in accepted_methods:
|
||
|
|
raise ValueError(
|
||
|
|
'method {} is invalid. Accepted method names are {}.'.format(
|
||
|
|
method, ', '.join(accepted_methods)))
|
||
|
|
|
||
|
|
if kind != 'average' and kind != 'legacy':
|
||
|
|
if method == 'recursion':
|
||
|
|
raise ValueError(
|
||
|
|
"The 'recursion' method only applies when 'kind' is set "
|
||
|
|
"to 'average'"
|
||
|
|
)
|
||
|
|
method = 'brute'
|
||
|
|
|
||
|
|
if method == 'auto':
|
||
|
|
if (isinstance(estimator, BaseGradientBoosting) and
|
||
|
|
estimator.init is None):
|
||
|
|
method = 'recursion'
|
||
|
|
elif isinstance(estimator, (BaseHistGradientBoosting,
|
||
|
|
DecisionTreeRegressor,
|
||
|
|
RandomForestRegressor)):
|
||
|
|
method = 'recursion'
|
||
|
|
else:
|
||
|
|
method = 'brute'
|
||
|
|
|
||
|
|
if method == 'recursion':
|
||
|
|
if not isinstance(estimator,
|
||
|
|
(BaseGradientBoosting, BaseHistGradientBoosting,
|
||
|
|
DecisionTreeRegressor, RandomForestRegressor)):
|
||
|
|
supported_classes_recursion = (
|
||
|
|
'GradientBoostingClassifier',
|
||
|
|
'GradientBoostingRegressor',
|
||
|
|
'HistGradientBoostingClassifier',
|
||
|
|
'HistGradientBoostingRegressor',
|
||
|
|
'HistGradientBoostingRegressor',
|
||
|
|
'DecisionTreeRegressor',
|
||
|
|
'RandomForestRegressor',
|
||
|
|
)
|
||
|
|
raise ValueError(
|
||
|
|
"Only the following estimators support the 'recursion' "
|
||
|
|
"method: {}. Try using method='brute'."
|
||
|
|
.format(', '.join(supported_classes_recursion)))
|
||
|
|
if response_method == 'auto':
|
||
|
|
response_method = 'decision_function'
|
||
|
|
|
||
|
|
if response_method != 'decision_function':
|
||
|
|
raise ValueError(
|
||
|
|
"With the 'recursion' method, the response_method must be "
|
||
|
|
"'decision_function'. Got {}.".format(response_method)
|
||
|
|
)
|
||
|
|
|
||
|
|
if _determine_key_type(features, accept_slice=False) == 'int':
|
||
|
|
# _get_column_indices() supports negative indexing. Here, we limit
|
||
|
|
# the indexing to be positive. The upper bound will be checked
|
||
|
|
# by _get_column_indices()
|
||
|
|
if np.any(np.less(features, 0)):
|
||
|
|
raise ValueError(
|
||
|
|
'all features must be in [0, {}]'.format(X.shape[1] - 1)
|
||
|
|
)
|
||
|
|
|
||
|
|
features_indices = np.asarray(
|
||
|
|
_get_column_indices(X, features), dtype=np.int32, order='C'
|
||
|
|
).ravel()
|
||
|
|
|
||
|
|
grid, values = _grid_from_X(
|
||
|
|
_safe_indexing(X, features_indices, axis=1), percentiles,
|
||
|
|
grid_resolution
|
||
|
|
)
|
||
|
|
|
||
|
|
if method == 'brute':
|
||
|
|
averaged_predictions, predictions = _partial_dependence_brute(
|
||
|
|
estimator, grid, features_indices, X, response_method
|
||
|
|
)
|
||
|
|
|
||
|
|
# reshape predictions to
|
||
|
|
# (n_outputs, n_instances, n_values_feature_0, n_values_feature_1, ...)
|
||
|
|
predictions = predictions.reshape(
|
||
|
|
-1, X.shape[0], *[val.shape[0] for val in values]
|
||
|
|
)
|
||
|
|
else:
|
||
|
|
averaged_predictions = _partial_dependence_recursion(
|
||
|
|
estimator, grid, features_indices
|
||
|
|
)
|
||
|
|
|
||
|
|
# reshape averaged_predictions to
|
||
|
|
# (n_outputs, n_values_feature_0, n_values_feature_1, ...)
|
||
|
|
averaged_predictions = averaged_predictions.reshape(
|
||
|
|
-1, *[val.shape[0] for val in values])
|
||
|
|
|
||
|
|
if kind == 'legacy':
|
||
|
|
warnings.warn(
|
||
|
|
"A Bunch will be returned in place of 'predictions' from version"
|
||
|
|
" 1.1 (renaming of 0.26) with partial dependence results "
|
||
|
|
"accessible via the 'average' key. In the meantime, pass "
|
||
|
|
"kind='average' to get the future behaviour.",
|
||
|
|
FutureWarning
|
||
|
|
)
|
||
|
|
# TODO 1.1: Remove kind == 'legacy' section
|
||
|
|
return averaged_predictions, values
|
||
|
|
elif kind == 'average':
|
||
|
|
return Bunch(average=averaged_predictions, values=values)
|
||
|
|
elif kind == 'individual':
|
||
|
|
return Bunch(individual=predictions, values=values)
|
||
|
|
else: # kind='both'
|
||
|
|
return Bunch(
|
||
|
|
average=averaged_predictions, individual=predictions,
|
||
|
|
values=values,
|
||
|
|
)
|