Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics

TL;DR

This paper introduces a generalized Huber loss function using the log-exp transform, combining properties of absolute and quadratic losses, along with an efficient algorithm for its minimization in robust statistics.

Contribution

It presents a novel generalized Huber loss formulation and an efficient algorithm for its minimization, enhancing robustness in statistical learning.

Findings

The generalized Huber loss combines benefits of absolute and quadratic losses.

An efficient algorithm for minimizing the new loss is proposed.

Finding a centralizing metric with this loss is computationally feasible.

Abstract

We propose a generalized formulation of the Huber loss. We show that with a suitable function of choice, specifically the log-exp transform; we can achieve a loss function which combines the desirable properties of both the absolute and the quadratic loss. We provide an algorithm to find the minimizer of such loss functions and show that finding a centralizing metric is not that much harder than the traditional mean and median.