sklearn.ensemble
.GradientBoostingRegressor¶

class
sklearn.ensemble.
GradientBoostingRegressor
(*, loss='ls', learning_rate=0.1, n_estimators=100, subsample=1.0, criterion='friedman_mse', min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_depth=3, min_impurity_decrease=0.0, min_impurity_split=None, init=None, random_state=None, max_features=None, alpha=0.9, verbose=0, max_leaf_nodes=None, warm_start=False, validation_fraction=0.1, n_iter_no_change=None, tol=0.0001, ccp_alpha=0.0)[source]¶ Gradient Boosting for regression.
GB builds an additive model in a forward stagewise 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 User Guide.
 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_ratefloat, default=0.1
Learning rate shrinks the contribution of each tree by
learning_rate
. There is a tradeoff between learning_rate and n_estimators. n_estimatorsint, default=100
The number of boosting stages to perform. Gradient boosting is fairly robust to overfitting so a large number usually results in better performance.
 subsamplefloat, 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 parametern_estimators
. Choosingsubsample < 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.
New in version 0.18.
Deprecated since version 0.24:
criterion='mae'
is deprecated and will be removed in version 1.1 (renaming of 0.26). The correct way of minimizing the absolute error is to useloss='lad'
instead. min_samples_splitint 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 andceil(min_samples_split * n_samples)
are the minimum number of samples for each split.
Changed in version 0.18: Added float values for fractions.
 min_samples_leafint 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 andceil(min_samples_leaf * n_samples)
are the minimum number of samples for each node.
Changed in version 0.18: Added float values for fractions.
 min_weight_fraction_leaffloat, 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_depthint, 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_decreasefloat, 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, andN_t_R
is the number of samples in the right child.N
,N_t
,N_t_R
andN_t_L
all refer to the weighted sum, ifsample_weight
is passed.New in version 0.19.
 min_impurity_splitfloat, 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 since version 0.19:
min_impurity_split
has been deprecated in favor ofmin_impurity_decrease
in 0.19. The default value ofmin_impurity_split
has changed from 1e7 to 0 in 0.23 and it will be removed in 1.0 (renaming of 0.25). Usemin_impurity_decrease
instead. initestimator or ‘zero’, default=None
An estimator object that is used to compute the initial predictions.
init
has to provide fit and predict. If ‘zero’, the initial raw predictions are set to zero. By default aDummyEstimator
is used, predicting either the average target value (for loss=’ls’), or a quantile for the other losses. random_stateint, RandomState instance or None, 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 Glossary. 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 andint(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. alphafloat, default=0.9
The alphaquantile of the huber loss function and the quantile loss function. Only if
loss='huber'
orloss='quantile'
. verboseint, 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_nodesint, default=None
Grow trees with
max_leaf_nodes
in bestfirst fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes. warm_startbool, 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 the Glossary. validation_fractionfloat, 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.New in version 0.20.
 n_iter_no_changeint, 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 asidevalidation_fraction
size of the training data as validation and terminate training when validation score is not improving in all of the previousn_iter_no_change
numbers of iterations.New in version 0.20.
 tolfloat, default=1e4
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.New in version 0.20.
 ccp_alphanonnegative float, default=0.0
Complexity parameter used for Minimal CostComplexity Pruning. The subtree with the largest cost complexity that is smaller than
ccp_alpha
will be chosen. By default, no pruning is performed. See Minimal CostComplexity Pruning for details.New in version 0.22.
 Attributes
feature_importances_
ndarray of shape (n_features,)The impuritybased feature importances.
 oob_improvement_ndarray of shape (n_estimators,)
The improvement in loss (= deviance) on the outofbag samples relative to the previous iteration.
oob_improvement_[0]
is the improvement in loss of the first stage over theinit
estimator. Only available ifsubsample < 1.0
 train_score_ndarray of shape (n_estimators,)
The ith score
train_score_[i]
is the deviance (= loss) of the model at iterationi
on the inbag sample. Ifsubsample == 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 orloss.init_estimator
. estimators_ndarray of DecisionTreeRegressor of shape (n_estimators, 1)
The collection of fitted subestimators.
 n_classes_int
The number of classes, set to 1 for regressors.
Deprecated since version 0.24: Attribute
n_classes_
was deprecated in version 0.24 and will be removed in 1.1 (renaming of 0.26). n_estimators_int
The number of estimators as selected by early stopping (if
n_iter_no_change
is specified). Otherwise it is set ton_estimators
. n_features_int
The number of data features.
 max_features_int
The inferred value of max_features.
See also
HistGradientBoostingRegressor
Histogrambased Gradient Boosting Classification Tree.
sklearn.tree.DecisionTreeRegressor
A decision tree regressor.
sklearn.tree.RandomForestRegressor
A random forest regressor.
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.References
J. Friedman, Greedy Function Approximation: A Gradient Boosting Machine, The Annals of Statistics, Vol. 29, No. 5, 2001.
Friedman, Stochastic Gradient Boosting, 1999
T. Hastie, R. Tibshirani and J. Friedman. Elements of Statistical Learning Ed. 2, Springer, 2009.
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_test[1:2]) array([61...]) >>> reg.score(X_test, y_test) 0.4...
Methods
apply
(X)Apply trees in the ensemble to X, return leaf indices.
fit
(X, y[, sample_weight, monitor])Fit the gradient boosting model.
get_params
([deep])Get parameters for this estimator.
predict
(X)Predict regression target for X.
score
(X, y[, sample_weight])Return the coefficient of determination \(R^2\) of the prediction.
set_params
(**params)Set the parameters of this estimator.
Predict regression target at each stage for X.

apply
(X)[source]¶ Apply trees in the ensemble to X, return leaf indices.
New in version 0.17.
 Parameters
 X{arraylike, 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 sparsecsr_matrix
.
 Returns
 X_leavesarraylike 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.

property
feature_importances_
¶ The impuritybased 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: impuritybased feature importances can be misleading for high cardinality features (many unique values). See
sklearn.inspection.permutation_importance
as an alternative. Returns
 feature_importances_ndarray of shape (n_features,)
The values of this array sum to 1, unless all trees are single node trees consisting of only the root node, in which case it will be an array of zeros.

fit
(X, y, sample_weight=None, monitor=None)[source]¶ Fit the gradient boosting model.
 Parameters
 X{arraylike, 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 sparsecsr_matrix
. yarraylike of shape (n_samples,)
Target values (strings or integers in classification, real numbers in regression) For classification, labels must correspond to classes.
 sample_weightarraylike 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.
 monitorcallable, 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 argumentscallable(i, self, locals())
. If the callable returnsTrue
the fitting procedure is stopped. The monitor can be used for various things such as computing heldout estimates, early stopping, model introspect, and snapshoting.
 Returns
 selfobject

get_params
(deep=True)[source]¶ Get parameters for this estimator.
 Parameters
 deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
 Returns
 paramsdict
Parameter names mapped to their values.

predict
(X)[source]¶ Predict regression target for X.
 Parameters
 X{arraylike, 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 sparsecsr_matrix
.
 Returns
 yndarray of shape (n_samples,)
The predicted values.

score
(X, y, sample_weight=None)[source]¶ Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1  \frac{u}{v})\), 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 ofy
, disregarding the input features, would get a \(R^2\) score of 0.0. Parameters
 Xarraylike 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 with shape
(n_samples, n_samples_fitted)
, wheren_samples_fitted
is the number of samples used in the fitting for the estimator. yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for
X
. sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
\(R^2\) of
self.predict(X)
wrt.y
.
Notes
The \(R^2\) score used when calling
score
on a regressor usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).

set_params
(**params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as
Pipeline
). The latter have parameters of the form<component>__<parameter>
so that it’s possible to update each component of a nested object. Parameters
 **paramsdict
Estimator parameters.
 Returns
 selfestimator instance
Estimator instance.

staged_predict
(X)[source]¶ Predict regression target at each stage for X.
This method allows monitoring (i.e. determine error on testing set) after each stage.
 Parameters
 X{arraylike, 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 sparsecsr_matrix
.
 Returns
 ygenerator of ndarray of shape (n_samples,)
The predicted value of the input samples.