package sklearn

Gradient Boosting for regression.

GB builds an additive model in a forward stage-wise fashion; it allows for the optimization of arbitrary differentiable loss functions. In each stage a regression tree is fit on the negative gradient of the given loss function.

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

Parameters ---------- loss : 'ls', 'lad', 'huber', 'quantile', default='ls' loss function to be optimized. 'ls' refers to least squares regression. 'lad' (least absolute deviation) is a highly robust loss function solely based on order information of the input variables. 'huber' is a combination of the two. 'quantile' allows quantile regression (use `alpha` to specify the quantile).

learning_rate : float, default=0.1 learning rate shrinks the contribution of each tree by `learning_rate`. There is a trade-off between learning_rate and n_estimators.

n_estimators : int, default=100 The number of boosting stages to perform. Gradient boosting is fairly robust to over-fitting so a large number usually results in better performance.

subsample : float, default=1.0 The fraction of samples to be used for fitting the individual base learners. If smaller than 1.0 this results in Stochastic Gradient Boosting. `subsample` interacts with the parameter `n_estimators`. Choosing `subsample < 1.0` leads to a reduction of variance and an increase in bias.

criterion : 'friedman_mse', 'mse', 'mae', default='friedman_mse' The function to measure the quality of a split. Supported criteria are 'friedman_mse' for the mean squared error with improvement score by Friedman, 'mse' for mean squared error, and 'mae' for the mean absolute error. The default value of 'friedman_mse' is generally the best as it can provide a better approximation in some cases.

.. versionadded:: 0.18

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_depth : int, default=3 maximum depth of the individual regression estimators. The maximum depth limits the number of nodes in the tree. Tune this parameter for best performance; the best value depends on the interaction of the input variables.

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=None 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`` has changed from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use ``min_impurity_decrease`` instead.

init : estimator or 'zero', default=None An estimator object that is used to compute the initial predictions. ``init`` has to provide :term:`fit` and :term:`predict`. If 'zero', the initial raw predictions are set to zero. By default a ``DummyEstimator`` is used, predicting either the average target value (for loss='ls'), or a quantile for the other losses.

random_state : int or RandomState, default=None Controls the random seed given to each Tree estimator at each boosting iteration. In addition, it controls the random permutation of the features at each split (see Notes for more details). It also controls the random spliting of the training data to obtain a validation set if `n_iter_no_change` is not None. Pass an int for reproducible output across multiple function calls. See :term:`Glossary <random_state>`.

max_features : 'auto', 'sqrt', 'log2', int or float, 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`.

Choosing `max_features < n_features` leads to a reduction of variance and an increase in bias.

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.

alpha : float, default=0.9 The alpha-quantile of the huber loss function and the quantile loss function. Only if ``loss='huber'`` or ``loss='quantile'``.

verbose : int, default=0 Enable verbose output. If 1 then it prints progress and performance once in a while (the more trees the lower the frequency). If greater than 1 then it prints progress and performance for every tree.

max_leaf_nodes : int, default=None Grow trees 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.

warm_start : bool, default=False When set to ``True``, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just erase the previous solution. See :term:`the Glossary <warm_start>`.

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

.. deprecated :: 0.22

validation_fraction : float, default=0.1 The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if ``n_iter_no_change`` is set to an integer.

.. versionadded:: 0.20

n_iter_no_change : int, default=None ``n_iter_no_change`` is used to decide if early stopping will be used to terminate training when validation score is not improving. By default it is set to None to disable early stopping. If set to a number, it will set aside ``validation_fraction`` size of the training data as validation and terminate training when validation score is not improving in all of the previous ``n_iter_no_change`` numbers of iterations.

.. versionadded:: 0.20

tol : float, default=1e-4 Tolerance for the early stopping. When the loss is not improving by at least tol for ``n_iter_no_change`` iterations (if set to a number), the training stops.

.. versionadded:: 0.20

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 impurity-based 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.

Warning: impurity-based feature importances can be misleading for high cardinality features (many unique values). See :func:`sklearn.inspection.permutation_importance` as an alternative.

oob_improvement_ : ndarray of shape (n_estimators,) The improvement in loss (= deviance) on the out-of-bag samples relative to the previous iteration. ``oob_improvement_0`` is the improvement in loss of the first stage over the ``init`` estimator. Only available if ``subsample < 1.0``

train_score_ : ndarray of shape (n_estimators,) The i-th score ``train_score_i`` is the deviance (= loss) of the model at iteration ``i`` on the in-bag sample. If ``subsample == 1`` this is the deviance on the training data.

loss_ : LossFunction The concrete ``LossFunction`` object.

init_ : estimator The estimator that provides the initial predictions. Set via the ``init`` argument or ``loss.init_estimator``.

estimators_ : ndarray of DecisionTreeRegressor of shape (n_estimators, 1) The collection of fitted sub-estimators.

n_features_ : int The number of data features.

max_features_ : int The inferred value of max_features.

Notes ----- 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.

Examples -------- >>> from sklearn.datasets import make_regression >>> from sklearn.ensemble import GradientBoostingRegressor >>> from sklearn.model_selection import train_test_split >>> X, y = make_regression(random_state=0) >>> X_train, X_test, y_train, y_test = train_test_split( ... X, y, random_state=0) >>> reg = GradientBoostingRegressor(random_state=0) >>> reg.fit(X_train, y_train) GradientBoostingRegressor(random_state=0) >>> reg.predict(X_test1:2) array(-61...) >>> reg.score(X_test, y_test) 0.4...

See also -------- sklearn.ensemble.HistGradientBoostingRegressor, sklearn.tree.DecisionTreeRegressor, RandomForestRegressor

References ---------- J. Friedman, Greedy Function Approximation: A Gradient Boosting Machine, The Annals of Statistics, Vol. 29, No. 5, 2001.

J. Friedman, Stochastic Gradient Boosting, 1999

T. Hastie, R. Tibshirani and J. Friedman. Elements of Statistical Learning Ed. 2, Springer, 2009.

Return the index'th estimator in the ensemble.

Return iterator over estimators in the ensemble.

Apply trees in the ensemble to X, return leaf indices.

.. versionadded:: 0.17

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

Returns ------- X_leaves : array-like of shape (n_samples, n_estimators) For each datapoint x in X and for each tree in the ensemble, return the index of the leaf x ends up in each estimator.

Fit the gradient boosting model.

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``.

y : array-like of shape (n_samples,) Target values (strings or integers in classification, real numbers in regression) For classification, labels must correspond to classes.

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. In the case of classification, splits are also ignored if they would result in any single class carrying a negative weight in either child node.

monitor : callable, default=None The monitor is called after each iteration with the current iteration, a reference to the estimator and the local variables of ``_fit_stages`` as keyword arguments ``callable(i, self, locals())``. If the callable returns ``True`` the fitting procedure is stopped. The monitor can be used for various things such as computing held-out estimates, early stopping, model introspect, and snapshoting.

Returns ------- self : object

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 regression target for X.

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``.

Returns ------- y : ndarray of shape (n_samples,) The predicted 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 uses ``multioutput='uniform_average'`` from version 0.23 to keep consistent with default value of :func:`~sklearn.metrics.r2_score`. This influences the ``score`` method of all the multioutput regressors (except for :class:`~sklearn.multioutput.MultiOutputRegressor`).

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.

Predict regression target at each stage for X.

This method allows monitoring (i.e. determine error on testing set) after each stage.

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``.

Returns ------- y : generator of ndarray of shape (n_samples,) The predicted value of the input samples.

Attribute feature_importances_: get value or raise Not_found if None.

Attribute feature_importances_: get value as an option.

Attribute Warning: get value or raise Not_found if None.

Attribute Warning: get value as an option.

Attribute oob_improvement_: get value or raise Not_found if None.

Attribute oob_improvement_: get value as an option.

Attribute train_score_: get value or raise Not_found if None.

Attribute train_score_: get value as an option.

Attribute loss_: get value or raise Not_found if None.

Attribute loss_: get value as an option.

Attribute init_: get value or raise Not_found if None.

Attribute init_: get value as an option.

Attribute estimators_: get value or raise Not_found if None.

Attribute estimators_: 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 max_features_: get value or raise Not_found if None.

Attribute max_features_: 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.