On the exact minimization of saturated loss functions for robust regression and subspace estimation

TL;DR

This paper presents an exact polynomial-time algorithm for robust regression and subspace estimation by reformulating the problem as a classification task, outperforming traditional methods like RANSAC in accuracy.

Contribution

It introduces a novel polynomial-time algorithm for minimizing saturated loss functions in robust regression and subspace estimation, improving accuracy over existing sampling-based methods.

Findings

Exact polynomial-time algorithm developed

Algorithm outperforms RANSAC in accuracy

Approximate variants offer practical benefits

Abstract

This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with polynomial time-complexity with respect to the number of data can be devised for robust regression and subspace estimation. This result is obtained by adopting a classification point of view and relating the problems to the search for a linear model that can approximate the maximal number of points with a given error. Approximate variants of the algorithms based on ramdom sampling are also discussed and experiments show that it offers an accuracy gain over the traditional RANSAC for a similar algorithmic simplicity.