3.2.3.3.6. sklearn.ensemble.GradientBoostingRegressor

class sklearn.ensemble.GradientBoostingRegressor(loss='ls', learning_rate=0.1, n_estimators=100, subsample=1.0, min_samples_split=2, min_samples_leaf=1, max_depth=3, init=None, random_state=None, max_features=None, alpha=0.9, verbose=0)

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.

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.

min_samples_split : integer, optional (default=2)

The minimum number of samples required to split an internal node.

min_samples_leaf : integer, optional (default=1)

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

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.

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.

See also

DecisionTreeRegressor, RandomForestRegressor

References

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

10. Friedman, Stochastic Gradient Boosting, 1999

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

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.
oob_score_	array, shape = [n_estimators]	Score of the training dataset obtained using an out-of-bag estimate. The i-th score oob_score_[i] is the deviance (= loss) of the model at iteration i on the out-of-bag sample. Deprecated: use oob_improvement_ instead.
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_: list of DecisionTreeRegressor		The collection of fitted sub-estimators.

Methods

decision_function(X)	Compute the decision function of X.
fit(X, y)	Fit the gradient boosting model.
get_params([deep])	Get parameters for this estimator.
predict(X)	Predict regression target for X.
score(X, y)	Returns the coefficient of determination R^2 of the prediction.
set_params(**params)	Set the parameters of this estimator.
staged_decision_function(X)	Compute decision function of X for each iteration.
staged_predict(X)	Predict regression target at each stage for X.

__init__(loss='ls', learning_rate=0.1, n_estimators=100, subsample=1.0, min_samples_split=2, min_samples_leaf=1, max_depth=3, init=None, random_state=None, max_features=None, alpha=0.9, verbose=0)

decision_function(X)

Compute the decision function of X.

Parameters :

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

The input samples.

Returns :

score : array, shape = [n_samples, k]

The decision function of the input samples. Classes are ordered by arithmetical order. Regression and binary classification are special cases with k == 1, otherwise k==n_classes.

feature_importances_

Return the feature importances (the higher, the more important the

feature).

Returns :feature_importances_ : array, shape = [n_features]

fit(X, y)

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 0, 1, ..., n_classes_-1

Returns :

self : object

Returns self.

get_params(deep=True)

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.

predict(X)

Predict regression target for X.

Parameters :

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

The input samples.

Returns :

y: array of shape = [n_samples] :

The predicted values.

score(X, y)

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, lower values are worse.

Parameters :

X : array-like, shape = (n_samples, n_features)

Test samples.

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

True values for X.

Returns :

score : float

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

set_params(**params)

Set the parameters of this estimator.

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

Returns :self :

staged_decision_function(X)

Compute decision function of X for each iteration.

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

Parameters :

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

The input samples.

Returns :

score : generator of array, shape = [n_samples, k]

The decision function of the input samples. Classes are ordered by arithmetical order. Regression and binary classification are special cases with k == 1, otherwise k==n_classes.

staged_predict(X)

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 of shape = [n_samples, n_features]

The input samples.

Returns :

y : array of shape = [n_samples]

The predicted value of the input samples.