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 .

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

The loss function being minimized is:

\frac{1}{1} \right) \right)$$ where: $$\begin{split}H_{\epsilon}(z) = \begin{cases} z^2, & \text {if } |z| < \epsilon, \\ 2\epsilon|z| - \epsilon^2, & \text{otherwise} \end{cases}\end{split}$$ ## Sources - [Hubber Regression](, Sci-Kit Learn User Guide - [Hubber Regressor](, Sci-Kit Documentation - [Robust Regression for Machine Learning in Python](, Machine Learning Mastery