Outlier-resilient model fitting via percentile losses: Methods for general and convex residuals

TL;DR

This paper introduces methods for robust model fitting that are resilient to outliers by using percentile optimization, applicable to general and convex residuals, and demonstrates improved outlier tolerance over standard methods.

Contribution

It develops new properties and methods for solving percentile-based robust fitting problems for both general and convex residuals, extending theoretical validation.

Findings

Methods endure higher outlier percentages than standard estimates.

Properties enable solving non-smooth, non-convex percentile problems.

Broader theoretical validation for existing robust methods.

Abstract

We consider the problem of robustly fitting a model to data that includes outliers by formulating a percentile optimization problem. This problem is non-smooth and non-convex, hence hard to solve. We derive properties that the minimizers of such problems must satisfy. These properties lead to methods that solve the percentile formulation both for general residuals and for convex residuals. The methods fit the model to subsets of the data, and then extract the solution of the percentile formulation from these partial fits. As illustrative simulations show, such methods endure higher outlier percentages, when compared with standard robust estimates. Additionally, the derived properties provide a broader and alternative theoretical validation for existing robust methods, whose validity was previously limited to specific forms of the residuals.