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=1e05)[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="LBFGSB")
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=1e05
The iteration will stop when
max{proj g_i  i = 1, ..., n}
<=tol
where pg_i is the ith 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="LBFGSB")
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 mostmax_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
 Xarraylike, shape (n_samples, n_features)
Training vector, where n_samples in the number of samples and n_features is the number of features.
 yarraylike, shape (n_samples,)
Target vector relative to X.
 sample_weightarraylike, 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
 Xarraylike 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 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.