HuberRegressor#

classsklearn.linear_model.HuberRegressor(*,epsilon=1.35,max_iter=100,alpha=0.0001,warm_start=False,fit_intercept=True,tol=1e-05)[source]#

L2-regularized linear regression model that is robust to outliers.

The Huber Regressor optimizes the squared loss for the samples where|(y-Xw-c)/sigma|<epsilon and the absolute loss for the sampleswhere|(y-Xw-c)/sigma|>epsilon, where the model coefficientsw, the interceptc and the scalesigma are parametersto be optimized. The parametersigma makes sure that ify is scaled upor down by a certain factor, one does not need to rescaleepsilon toachieve the same robustness. Note that this does not take into accountthe fact that the different features ofX may be of different scales.

The Huber loss function has the advantage of not being heavily influencedby the outliers while not completely ignoring their effect.

Read more in theUser Guide

Added in version 0.18.

Parameters:

epsilonfloat, default=1.35

The parameter epsilon controls the number of samples that should beclassified as outliers. The smaller the epsilon, the more robust it isto outliers. Epsilon must be in the range[1,inf).

max_iterint, default=100

Maximum number of iterations thatscipy.optimize.minimize(method="L-BFGS-B") should run for.

alphafloat, default=0.0001

Strength of the squared L2 regularization. Note that the penalty isequal toalpha*||w||^2.Must be in the range[0,inf).

warm_startbool, default=False

This is useful if the stored attributes of a previously used modelhas to be reused. If set to False, then the coefficients willbe rewritten for every call to fit.Seethe Glossary.

fit_interceptbool, default=True

Whether or not to fit the intercept. This can be set to Falseif the data is already centered around the origin.

tolfloat, default=1e-05

The iteration will stop whenmax{|projg_i|i=1,...,n} <=tolwhere pg_i is the i-th component of the projected gradient.

Attributes:

coef_array, shape (n_features,)

Features got by optimizing the L2-regularized Huber loss.

intercept_float

Bias.

scale_float

The value by which|y-Xw-c| is scaled down.

n_features_in_int

Number of features seen duringfit.

Added in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen duringfit. Defined only whenXhas feature names that are all strings.

Added in version 1.0.

n_iter_int

Number of iterations thatscipy.optimize.minimize(method="L-BFGS-B") has run for.

Changed in version 0.20:In SciPy <= 1.0.0 the number of lbfgs iterations may exceedmax_iter.n_iter_ will now report at mostmax_iter.

outliers_array, shape (n_samples,)

A boolean mask which is set to True where the samples are identifiedas outliers.

See also

RANSACRegressor

RANSAC (RANdom SAmple Consensus) algorithm.

TheilSenRegressor

Theil-Sen Estimator robust multivariate regression model.

SGDRegressor

Fitted by minimizing a regularized empirical loss with SGD.

References

[1]

Peter J. Huber, Elvezio M. Ronchetti, Robust StatisticsConcomitant scale estimates, p. 172

[2]

Art B. Owen (2006),A robust hybrid of lasso and ridge regression.

Examples

>>>importnumpyasnp>>>fromsklearn.linear_modelimportHuberRegressor,LinearRegression>>>fromsklearn.datasetsimportmake_regression>>>rng=np.random.RandomState(0)>>>X,y,coef=make_regression(...n_samples=200,n_features=2,noise=4.0,coef=True,random_state=0)>>>X[:4]=rng.uniform(10,20,(4,2))>>>y[:4]=rng.uniform(10,20,4)>>>huber=HuberRegressor().fit(X,y)>>>huber.score(X,y)-7.284>>>huber.predict(X[:1,])array([806.7200])>>>linear=LinearRegression().fit(X,y)>>>print("True coefficients:",coef)True coefficients: [20.4923...  34.1698...]>>>print("Huber coefficients:",huber.coef_)Huber coefficients: [17.7906... 31.0106...]>>>print("Linear Regression coefficients:",linear.coef_)Linear Regression coefficients: [-1.9221...  7.0226...]

fit(X,y,sample_weight=None)[source]#

Fit the model according to the given training data.

Parameters:

Xarray-like, shape (n_samples, n_features)

Training vector, wheren_samples is the number of samples andn_features is the number of features.

yarray-like, shape (n_samples,)

Target vector relative to X.

sample_weightarray-like, shape (n_samples,)

Weight given to each sample.

Returns:

selfobject

FittedHuberRegressor estimator.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please checkUser Guide on how the routingmechanism works.

Returns:

routingMetadataRequest

AMetadataRequest encapsulatingrouting information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True

If True, will return the parameters for this estimator andcontained subobjects that are estimators.

Returns:

paramsdict

Parameter names mapped to their values.

predict(X)[source]#

Predict using the linear model.

Parameters:

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.

Returns:

Carray, shape (n_samples,)

Returns predicted values.

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

Returncoefficient of determination on test data.

The coefficient of determination,\(R^2\), is defined as\((1 - \frac{u}{v})\), where\(u\) is the residualsum 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 themodel can be arbitrarily worse). A constant model that always predictsthe expected value ofy, disregarding the input features, would geta\(R^2\) score of 0.0.

Parameters:

Xarray-like of shape (n_samples, n_features)

Test samples. For some estimators this may be a precomputedkernel matrix or a list of generic objects instead with shape(n_samples,n_samples_fitted), wheren_samples_fittedis the number of samples used in the fitting for the estimator.

yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values forX.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

Returns:

scorefloat

\(R^2\) ofself.predict(X) w.r.t.y.

Notes

The\(R^2\) score used when callingscore on a regressor usesmultioutput='uniform_average' from version 0.23 to keep consistentwith default value ofr2_score.This influences thescore method of all the multioutputregressors (except forMultiOutputRegressor).

set_fit_request(*,sample_weight:bool|None|str='$UNCHANGED$')→HuberRegressor[source]#

Configure whether metadata should be requested to be passed to thefit method.

Note that this method is only relevant when this estimator is used as asub-estimator within ameta-estimator and metadata routing is enabledwithenable_metadata_routing=True (seesklearn.set_config).Please check theUser Guide on how the routingmechanism works.

The options for each parameter are:

• True: metadata is requested, and passed tofit if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it tofit.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing forsample_weight parameter infit.

Returns:

selfobject

The updated object.

set_params(**params)[source]#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects(such asPipeline). The latter haveparameters of the form<component>__<parameter> so that it’spossible to update each component of a nested object.

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

set_score_request(*,sample_weight:bool|None|str='$UNCHANGED$')→HuberRegressor[source]#

Configure whether metadata should be requested to be passed to thescore method.

Note that this method is only relevant when this estimator is used as asub-estimator within ameta-estimator and metadata routing is enabledwithenable_metadata_routing=True (seesklearn.set_config).Please check theUser Guide on how the routingmechanism works.

The options for each parameter are:

• True: metadata is requested, and passed toscore if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it toscore.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing forsample_weight parameter inscore.

Returns:

selfobject

The updated object.

Gallery examples#

HuberRegressor vs Ridge on dataset with strong outliers

HuberRegressor vs Ridge on dataset with strong outliers

Ridge coefficients as a function of the L2 Regularization

Ridge coefficients as a function of the L2 Regularization

Robust linear estimator fitting

Robust linear estimator fitting