3.2.4.3.6. 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, presort='auto')[source]

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 User Guide.

Parameters:

loss : {‘ls’, ‘lad’, ‘huber’, ‘quantile’}, optional (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, optional (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.

max_depth : integer, optional (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.

criterion : string, optional (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.

min_samples_split : int, float, optional (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 percentage and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

Changed in version 0.18: Added float values for percentages.

min_samples_leaf : int, float, optional (default=1)

The minimum number of samples required to be at a leaf node:

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

Changed in version 0.18: Added float values for percentages.

min_weight_fraction_leaf : float, optional (default=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.

subsample : float, optional (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.

max_features : int, float, string or None, optional (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 percentage 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.

max_leaf_nodes : int or None, optional (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.

min_impurity_decrease : float, optional (default=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.

New in version 0.19.

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'.

init : BaseEstimator, None, optional (default=None)

An estimator object that is used to compute the initial predictions. init has to provide fit and predict. If None it uses loss.init_estimator.

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.

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.

random_state : int, RandomState instance or None, optional (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.

presort : bool or ‘auto’, optional (default=’auto’)

Whether to presort the data to speed up the finding of best splits in fitting. Auto mode by default will use presorting on dense data and default to normal sorting on sparse data. Setting presort to true on sparse data will raise an error.

New in version 0.17: optional parameter presort.

Attributes:

feature_importances_ : array, shape = [n_features]

The feature importances (the higher, the more important the feature).

oob_improvement_ : array, 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.

train_score_ : array, 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 : BaseEstimator

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

estimators_ : ndarray of DecisionTreeRegressor, shape = [n_estimators, 1]

The collection of fitted sub-estimators.

See also

DecisionTreeRegressor, RandomForestRegressor

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.

  1. Friedman, Stochastic Gradient Boosting, 1999

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

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]) Returns the coefficient of determination R^2 of the prediction.
set_params(**params) Set the parameters of this estimator.
staged_predict(X) Predict regression target at each stage for X.
__init__(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, presort='auto')[source]
apply(X)[source]

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

New in version 0.17.

Parameters:

X : array-like or sparse matrix, 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, 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.

feature_importances_
Return the feature importances (the higher, the more important the
feature).
Returns:feature_importances_ : array, shape = [n_features]
fit(X, y, sample_weight=None, monitor=None)[source]

Fit the gradient boosting model.

Parameters:

X : array-like, shape = [n_samples, n_features]

Training vectors, where n_samples is the number of samples and n_features is the number of features.

y : array-like, shape = [n_samples]

Target values (integers in classification, real numbers in regression) For classification, labels must correspond to classes.

sample_weight : array-like, shape = [n_samples] or 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, optional

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

Returns self.

get_params(deep=True)[source]

Get parameters for this estimator.

Parameters:

deep : boolean, optional

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.

n_features

DEPRECATED: Attribute n_features was deprecated in version 0.19 and will be removed in 0.21.

predict(X)[source]

Predict regression target for X.

Parameters:

X : array-like or sparse matrix, 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 : array of shape = [n_samples]

The predicted values.

score(X, y, sample_weight=None)[source]

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

The coefficient R^2 is defined as (1 - u/v), where u is the regression sum of squares ((y_true - y_pred) ** 2).sum() and v is the residual sum of squares ((y_true - y_true.mean()) ** 2).sum(). 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, shape = (n_samples, n_features)

Test samples.

y : array-like, shape = (n_samples) or (n_samples, n_outputs)

True values for X.

sample_weight : array-like, shape = [n_samples], optional

Sample weights.

Returns:

score : float

R^2 of self.predict(X) wrt. y.

set_params(**params)[source]

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.

Returns:self :
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 : array-like or sparse matrix, 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 array of shape = [n_samples]

The predicted value of the input samples.