package sklearn

A decision tree regressor.

Read more in the :ref:`User Guide <tree>`.

Parameters ---------- criterion : 'mse', 'friedman_mse', 'mae', default='mse' The function to measure the quality of a split. Supported criteria are 'mse' for the mean squared error, which is equal to variance reduction as feature selection criterion and minimizes the L2 loss using the mean of each terminal node, 'friedman_mse', which uses mean squared error with Friedman's improvement score for potential splits, and 'mae' for the mean absolute error, which minimizes the L1 loss using the median of each terminal node.

.. versionadded:: 0.18 Mean Absolute Error (MAE) criterion.

splitter : 'best', 'random', default='best' The strategy used to choose the split at each node. Supported strategies are 'best' to choose the best split and 'random' to choose the best random split.

max_depth : int, default=None The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.

min_samples_split : int or float, default=2 The minimum number of samples required to split an internal node:

• If int, then consider `min_samples_split` as the minimum number.
• If float, then `min_samples_split` is a fraction and `ceil(min_samples_split * n_samples)` are the minimum number of samples for each split.

.. versionchanged:: 0.18 Added float values for fractions.

min_samples_leaf : int or float, default=1 The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least ``min_samples_leaf`` training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

• If int, then consider `min_samples_leaf` as the minimum number.
• If float, then `min_samples_leaf` is a fraction and `ceil(min_samples_leaf * n_samples)` are the minimum number of samples for each node.

.. versionchanged:: 0.18 Added float values for fractions.

min_weight_fraction_leaf : float, default=0.0 The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.

max_features : int, float or 'auto', 'sqrt', 'log2', default=None The number of features to consider when looking for the best split:

• If int, then consider `max_features` features at each split.
• If float, then `max_features` is a fraction and `int(max_features * n_features)` features are considered at each split.
• If 'auto', then `max_features=n_features`.
• If 'sqrt', then `max_features=sqrt(n_features)`.
• If 'log2', then `max_features=log2(n_features)`.
• If None, then `max_features=n_features`.

Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than ``max_features`` features.

random_state : int or RandomState, default=None If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`.

max_leaf_nodes : int, default=None Grow a tree with ``max_leaf_nodes`` in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.

min_impurity_decrease : float, default=0.0 A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

The weighted impurity decrease equation is the following::

N_t / N * (impurity - N_t_R / N_t * right_impurity

• N_t_L / N_t * left_impurity)

where ``N`` is the total number of samples, ``N_t`` is the number of samples at the current node, ``N_t_L`` is the number of samples in the left child, and ``N_t_R`` is the number of samples in the right child.

``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum, if ``sample_weight`` is passed.

.. versionadded:: 0.19

min_impurity_split : float, (default=1e-7) Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.

.. deprecated:: 0.19 ``min_impurity_split`` has been deprecated in favor of ``min_impurity_decrease`` in 0.19. The default value of ``min_impurity_split`` will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use ``min_impurity_decrease`` instead.

presort : deprecated, default='deprecated' This parameter is deprecated and will be removed in v0.24.

.. deprecated:: 0.22

ccp_alpha : non-negative float, default=0.0 Complexity parameter used for Minimal Cost-Complexity Pruning. The subtree with the largest cost complexity that is smaller than ``ccp_alpha`` will be chosen. By default, no pruning is performed. See :ref:`minimal_cost_complexity_pruning` for details.

.. versionadded:: 0.22

Attributes ---------- feature_importances_ : ndarray of shape (n_features,) The feature importances. The higher, the more important the feature. The importance of a feature is computed as the (normalized) total reduction of the criterion brought by that feature. It is also known as the Gini importance 4_.

max_features_ : int The inferred value of max_features.

n_features_ : int The number of features when ``fit`` is performed.

n_outputs_ : int The number of outputs when ``fit`` is performed.

tree_ : Tree The underlying Tree object. Please refer to ``help(sklearn.tree._tree.Tree)`` for attributes of Tree object and :ref:`sphx_glr_auto_examples_tree_plot_unveil_tree_structure.py` for basic usage of these attributes.

See Also -------- DecisionTreeClassifier : A decision tree classifier.

Notes ----- The default values for the parameters controlling the size of the trees (e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and unpruned trees which can potentially be very large on some data sets. To reduce memory consumption, the complexity and size of the trees should be controlled by setting those parameter values.

The features are always randomly permuted at each split. Therefore, the best found split may vary, even with the same training data and ``max_features=n_features``, if the improvement of the criterion is identical for several splits enumerated during the search of the best split. To obtain a deterministic behaviour during fitting, ``random_state`` has to be fixed.

References ----------

.. 1 https://en.wikipedia.org/wiki/Decision_tree_learning

.. 2 L. Breiman, J. Friedman, R. Olshen, and C. Stone, 'Classification and Regression Trees', Wadsworth, Belmont, CA, 1984.

.. 3 T. Hastie, R. Tibshirani and J. Friedman. 'Elements of Statistical Learning', Springer, 2009.

.. 4 L. Breiman, and A. Cutler, 'Random Forests', https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm

Examples -------- >>> from sklearn.datasets import load_boston >>> from sklearn.model_selection import cross_val_score >>> from sklearn.tree import DecisionTreeRegressor >>> X, y = load_boston(return_X_y=True) >>> regressor = DecisionTreeRegressor(random_state=0) >>> cross_val_score(regressor, X, y, cv=10) ... # doctest: +SKIP ... array( 0.61..., 0.57..., -0.34..., 0.41..., 0.75..., 0.07..., 0.29..., 0.33..., -1.42..., -1.77...)

Return the index of the leaf that each sample is predicted as.

.. versionadded:: 0.17

Parameters ---------- X : array-like, sparse matrix of shape (n_samples, n_features) The input samples. Internally, it will be converted to ``dtype=np.float32`` and if a sparse matrix is provided to a sparse ``csr_matrix``.

check_input : bool, default=True Allow to bypass several input checking. Don't use this parameter unless you know what you do.

Returns ------- X_leaves : array-like of shape (n_samples,) For each datapoint x in X, return the index of the leaf x ends up in. Leaves are numbered within ``0; self.tree_.node_count)``, possibly with gaps in the numbering.

Compute the pruning path during Minimal Cost-Complexity Pruning.

See :ref:`minimal_cost_complexity_pruning` for details on the pruning process.

Parameters ---------- X : array-like, sparse matrix of shape (n_samples, n_features) The training input samples. Internally, it will be converted to ``dtype=np.float32`` and if a sparse matrix is provided to a sparse ``csc_matrix``.

y : array-like of shape (n_samples,) or (n_samples, n_outputs) The target values (class labels) as integers or strings.

sample_weight : array-like of shape (n_samples,), default=None Sample weights. If None, then samples are equally weighted. Splits that would create child nodes with net zero or negative weight are ignored while searching for a split in each node. Splits are also ignored if they would result in any single class carrying a negative weight in either child node.

Returns ------- ccp_path : Bunch Dictionary-like object, with attributes:

ccp_alphas : ndarray Effective alphas of subtree during pruning.

impurities : ndarray Sum of the impurities of the subtree leaves for the corresponding alpha value in ``ccp_alphas``.

Return the decision path in the tree.

.. versionadded:: 0.18

Parameters ---------- X : array-like, sparse matrix of shape (n_samples, n_features) The input samples. Internally, it will be converted to ``dtype=np.float32`` and if a sparse matrix is provided to a sparse ``csr_matrix``.

check_input : bool, default=True Allow to bypass several input checking. Don't use this parameter unless you know what you do.

Returns ------- indicator : sparse matrix of shape (n_samples, n_nodes) Return a node indicator CSR matrix where non zero elements indicates that the samples goes through the nodes.

Build a decision tree regressor from the training set (X, y).

Parameters ---------- X : array-like, sparse matrix of shape (n_samples, n_features) The training input samples. Internally, it will be converted to ``dtype=np.float32`` and if a sparse matrix is provided to a sparse ``csc_matrix``.

y : array-like of shape (n_samples,) or (n_samples, n_outputs) The target values (real numbers). Use ``dtype=np.float64`` and ``order='C'`` for maximum efficiency.

sample_weight : array-like of shape (n_samples,), default=None Sample weights. If None, then samples are equally weighted. Splits that would create child nodes with net zero or negative weight are ignored while searching for a split in each node.

check_input : bool, default=True Allow to bypass several input checking. Don't use this parameter unless you know what you do.

X_idx_sorted : array-like of shape (n_samples, n_features), default=None The indexes of the sorted training input samples. If many tree are grown on the same dataset, this allows the ordering to be cached between trees. If None, the data will be sorted here. Don't use this parameter unless you know what to do.

Returns ------- self : DecisionTreeRegressor Fitted estimator.

Return the depth of the decision tree.

The depth of a tree is the maximum distance between the root and any leaf.

Returns ------- self.tree_.max_depth : int The maximum depth of the tree.

Return the number of leaves of the decision tree.

Returns ------- self.tree_.n_leaves : int Number of leaves.

Get parameters for this estimator.

Parameters ---------- deep : bool, default=True If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns ------- params : mapping of string to any Parameter names mapped to their values.

Predict class or regression value for X.

For a classification model, the predicted class for each sample in X is returned. For a regression model, the predicted value based on X is returned.

Parameters ---------- X : array-like, sparse matrix of shape (n_samples, n_features) The input samples. Internally, it will be converted to ``dtype=np.float32`` and if a sparse matrix is provided to a sparse ``csr_matrix``.

check_input : bool, default=True Allow to bypass several input checking. Don't use this parameter unless you know what you do.

Returns ------- y : array-like of shape (n_samples,) or (n_samples, n_outputs) The predicted classes, or the predict values.

Return the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - u/v), where u is the residual sum of squares ((y_true - y_pred) ** 2).sum() and v is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.

Parameters ---------- X : array-like of shape (n_samples, n_features) Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead, shape = (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

y : array-like of shape (n_samples,) or (n_samples, n_outputs) True values for X.

sample_weight : array-like of shape (n_samples,), default=None Sample weights.

Returns ------- score : float R^2 of self.predict(X) wrt. y.

Notes ----- The R2 score used when calling ``score`` on a regressor will use ``multioutput='uniform_average'`` from version 0.23 to keep consistent with :func:`~sklearn.metrics.r2_score`. This will influence the ``score`` method of all the multioutput regressors (except for :class:`~sklearn.multioutput.MultiOutputRegressor`). To specify the default value manually and avoid the warning, please either call :func:`~sklearn.metrics.r2_score` directly or make a custom scorer with :func:`~sklearn.metrics.make_scorer` (the built-in scorer ``'r2'`` uses ``multioutput='uniform_average'``).

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form ``<component>__<parameter>`` so that it's possible to update each component of a nested object.

Parameters ---------- **params : dict Estimator parameters.

Returns ------- self : object Estimator instance.

Attribute feature_importances_: get value or raise Not_found if None.

Attribute feature_importances_: get value as an option.

Attribute max_features_: get value or raise Not_found if None.

Attribute max_features_: get value as an option.

Attribute n_features_: get value or raise Not_found if None.

Attribute n_features_: get value as an option.

Attribute n_outputs_: get value or raise Not_found if None.

Attribute n_outputs_: get value as an option.

Attribute tree_: get value or raise Not_found if None.

Attribute tree_: get value as an option.

Print the object to a human-readable representation.

Print the object to a human-readable representation.

Pretty-print the object to a formatter.