sklearn.linear_model.HuberRegressor¶

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

Linear regression model that is robust to outliers.

The Huber Regressor optimizes the squared loss for the samples where |(y - X'w) / sigma| < epsilon and the absolute loss for the samples where |(y - X'w) / sigma| > epsilon, where w and sigma are parameters to be optimized. The parameter sigma makes sure that if y is scaled up or down by a certain factor, one does not need to rescale epsilon to achieve the same robustness. Note that this does not take into account the fact that the different features of X may be of different scales.

This makes sure that the loss function is not heavily influenced by the outliers while not completely ignoring their effect.

Read more in the User Guide

New in version 0.18.

Parameters

epsilonfloat, greater than 1.0, default=1.35

The parameter epsilon controls the number of samples that should be classified as outliers. The smaller the epsilon, the more robust it is to outliers.

max_iterint, default=100

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

alphafloat, default=0.0001

Regularization parameter.

warm_startbool, default=False

This is useful if the stored attributes of a previously used model has to be reused. If set to False, then the coefficients will be rewritten for every call to fit. See the Glossary.

fit_interceptbool, default=True

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

tolfloat, default=1e-05

The iteration will stop when max{|proj g_i | i = 1, ..., n} <= tol where pg_i is the i-th component of the projected gradient.

Attributes

coef_array, shape (n_features,)

Features got by optimizing the Huber loss.

intercept_float

Bias.

scale_float

The value by which |y - X'w - c| is scaled down.

n_iter_int

Number of iterations that scipy.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 exceed max_iter. n_iter_ will now report at most max_iter.

outliers_array, shape (n_samples,)

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

References

1

Peter J. Huber, Elvezio M. Ronchetti, Robust Statistics Concomitant scale estimates, pg 172

2

Art B. Owen (2006), A robust hybrid of lasso and ridge regression. https://statweb.stanford.edu/~owen/reports/hhu.pdf

Examples

>>> import numpy as np
>>> from sklearn.linear_model import HuberRegressor, LinearRegression
>>> from sklearn.datasets import make_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...]

Methods

fit(X, y[, sample_weight])	Fit the model according to the given training data.
get_params([deep])	Get parameters for this estimator.
predict(X)	Predict using the linear model.
score(X, y[, sample_weight])	Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)	Set the parameters of this estimator.

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, where n_samples in the number of samples and n_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

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 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]¶

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 of y, disregarding the input features, would get a \(R^2\) score of 0.0.

Parameters

Xarray-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 with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

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

True values for X.

sample_weightarray-like 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 uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

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.

Examples using sklearn.linear_model.HuberRegressor¶