sklearn.inspection.partial_dependence(estimator, X, features, *, categorical_features=None, feature_names=None, response_method='auto', percentiles=(0.05, 0.95), grid_resolution=100, method='auto', kind='average')[source]

Partial dependence of features.

Partial dependence of a feature (or a set of features) corresponds to the average response of an estimator for each possible value of the feature.

Read more in the User Guide.


For GradientBoostingClassifier and GradientBoostingRegressor, the 'recursion' method (used by default) will not account for the init predictor of the boosting process. In practice, this will produce the same values as 'brute' up to a constant offset in the target response, provided that init is a constant estimator (which is the default). However, if init is not a constant estimator, the partial dependence values are incorrect for 'recursion' because the offset will be sample-dependent. It is preferable to use the 'brute' method. Note that this only applies to GradientBoostingClassifier and GradientBoostingRegressor, not to HistGradientBoostingClassifier and HistGradientBoostingRegressor.


A fitted estimator object implementing predict, predict_proba, or decision_function. Multioutput-multiclass classifiers are not supported.

X{array-like or dataframe} of shape (n_samples, n_features)

X is used to generate a grid of values for the target features (where the partial dependence will be evaluated), and also to generate values for the complement features when the method is ‘brute’.

featuresarray-like of {int, str}

The feature (e.g. [0]) or pair of interacting features (e.g. [(0, 1)]) for which the partial dependency should be computed.

categorical_featuresarray-like of shape (n_features,) or shape (n_categorical_features,), dtype={bool, int, str}, default=None

Indicates the categorical features.

  • None: no feature will be considered categorical;

  • boolean array-like: boolean mask of shape (n_features,)

    indicating which features are categorical. Thus, this array has the same shape has X.shape[1];

  • integer or string array-like: integer indices or strings

    indicating categorical features.

New in version 1.2.

feature_namesarray-like of shape (n_features,), dtype=str, default=None

Name of each feature; feature_names[i] holds the name of the feature with index i. By default, the name of the feature corresponds to their numerical index for NumPy array and their column name for pandas dataframe.

New in version 1.2.

response_method{‘auto’, ‘predict_proba’, ‘decision_function’}, default=’auto’

Specifies whether to use predict_proba or decision_function as the target response. For regressors this parameter is ignored and the response is always the output of predict. By default, predict_proba is tried first and we revert to decision_function if it doesn’t exist. If method is ‘recursion’, the response is always the output of decision_function.

percentilestuple of float, default=(0.05, 0.95)

The lower and upper percentile used to create the extreme values for the grid. Must be in [0, 1].

grid_resolutionint, default=100

The number of equally spaced points on the grid, for each target feature.

method{‘auto’, ‘recursion’, ‘brute’}, default=’auto’

The method used to calculate the averaged predictions:

  • 'recursion' is only supported for some tree-based estimators (namely GradientBoostingClassifier, GradientBoostingRegressor, HistGradientBoostingClassifier, HistGradientBoostingRegressor, DecisionTreeRegressor, RandomForestRegressor, ) when kind='average'. This is more efficient in terms of speed. With this method, the target response of a classifier is always the decision function, not the predicted probabilities. Since the 'recursion' method implicitly computes the average of the Individual Conditional Expectation (ICE) by design, it is not compatible with ICE and thus kind must be 'average'.

  • 'brute' is supported for any estimator, but is more computationally intensive.

  • 'auto': the 'recursion' is used for estimators that support it, and 'brute' is used otherwise.

Please see this note for differences between the 'brute' and 'recursion' method.

kind{‘average’, ‘individual’, ‘both’}, default=’average’

Whether to return the partial dependence averaged across all the samples in the dataset or one value per sample or both. See Returns below.

Note that the fast method='recursion' option is only available for kind='average'. Computing individual dependencies requires using the slower method='brute' option.

New in version 0.24.


Dictionary-like object, with the following attributes.

individualndarray of shape (n_outputs, n_instances, len(values[0]), len(values[1]), …)

The predictions for all the points in the grid for all samples in X. This is also known as Individual Conditional Expectation (ICE)

averagendarray of shape (n_outputs, len(values[0]), len(values[1]), …)

The predictions for all the points in the grid, averaged over all samples in X (or over the training data if method is ‘recursion’). Only available when kind='both'.

valuesseq 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.

n_outputs corresponds to the number of classes in a multi-class 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].

See also


Plot Partial Dependence.


Partial Dependence visualization.


>>> 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) 
(array([[-4.52...,  4.52...]]), [array([ 0.,  1.])])

Examples using sklearn.inspection.partial_dependence

Partial Dependence and Individual Conditional Expectation Plots

Partial Dependence and Individual Conditional Expectation Plots

Partial Dependence and Individual Conditional Expectation Plots