Hubber Regressor

The Hubber Regressor is a regressor that diminishes the weight of outliers when fitting the regression curve. Outliers are classified as such when their absolute error into the fitting curve is outside of a certain threshold, provided (not in absolute terms) by the parameter $ϵ$.

This makes de Hubber Regression a good choice to prevent bias against outliers, but without dismissing them completely.

The loss function being minimized is:

$$\underset{\omega ,\sigma }{\min }\sum _{i=1}^n\left(\sigma +H_{ϵ}\left(\frac{1}{1}\right)\right)$$

where:

$$\begin{array}{r}{H}_{ϵ}(z)=\{\begin{array}{ll}{z}^2,& \text{if }|z|<ϵ,\\ 2ϵ|z|-{ϵ}^2,& \text{otherwise}\end{array}\end{array}$$

Sources

• Hubber Regression, Sci-Kit Learn User Guide
• Hubber Regressor, Sci-Kit Documentation
• Robust Regression for Machine Learning in Python, Machine Learning Mastery