Implementation:Scikit learn Scikit learn HuberRegressor

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Robust Regression
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for L2-regularized linear regression that is robust to outliers using the Huber loss function provided by scikit-learn.

Description

HuberRegressor optimizes the squared loss for samples where |(y - Xw - c) / sigma| < epsilon and the absolute loss for samples where |(y - Xw - c) / sigma| > epsilon. The model parameters include coefficients w, intercept c, and scale sigma. The epsilon parameter controls the threshold between inlier (squared loss) and outlier (absolute loss) treatment, providing robustness to outliers while not completely ignoring their effect. The optimization is performed using scipy's L-BFGS-B solver.

Usage

Use HuberRegressor when your dataset contains outliers that would disproportionately affect ordinary least squares regression. It is particularly useful when you want a compromise between fully robust methods (like RANSAC) and standard least squares, maintaining sensitivity to most data while limiting the influence of outliers.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/linear_model/_huber.py

Signature

class HuberRegressor(LinearModel, RegressorMixin, BaseEstimator):
    def __init__(
        self,
        *,
        epsilon=1.35,
        max_iter=100,
        alpha=0.0001,
        warm_start=False,
        fit_intercept=True,
        tol=1e-05,
    ):

Import

from sklearn.linear_model import HuberRegressor

I/O Contract

Inputs

Name	Type	Required	Description
epsilon	float	No	Controls outlier classification threshold; must be >= 1 (default=1.35)
max_iter	int	No	Maximum number of L-BFGS-B iterations (default=100)
alpha	float	No	L2 regularization strength (default=0.0001)
warm_start	bool	No	Reuse previous solution as initialization (default=False)
fit_intercept	bool	No	Whether to fit the intercept (default=True)
tol	float	No	Convergence tolerance for the projected gradient (default=1e-05)

Outputs

Name	Type	Description
coef_	ndarray of shape (n_features,)	Feature coefficients
intercept_	float	Bias term in the linear model
scale_	float	Estimated scale parameter (sigma) of the Huber function
outliers_	ndarray of shape (n_samples,)	Boolean mask indicating samples classified as outliers
n_iter_	int	Number of iterations performed by the optimizer

Usage Examples

Basic Usage

from sklearn.linear_model import HuberRegressor
from sklearn.datasets import make_regression
import numpy as np

X, y = make_regression(n_samples=100, n_features=5, noise=10, random_state=42)
# Add outliers
y[0] = 1000
y[1] = -1000

model = HuberRegressor(epsilon=1.35)
model.fit(X, y)
print("Number of outliers:", model.outliers_.sum())
print("Coefficients:", model.coef_)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Robust_Regression