Robust estimation algorithms don't need to know the corruption level

TL;DR

This paper introduces a universal meta technique that enhances robust estimation algorithms, enabling them to perform optimally without prior knowledge of the corruption level in data.

Contribution

It presents a geometric abstraction and a meta algorithm that remove the need for known corruption bounds in robust estimation.

Findings

Achieves near-optimal accuracy without corruption level bounds

Universal applicability to existing robust algorithms

Simplifies practical deployment of robust estimators

Abstract

Real data are rarely pure. Hence the past half-century has seen great interest in robust estimation algorithms that perform well even when part of the data is corrupt. However, their vast majority approach optimal accuracy only when given a tight upper bound on the fraction of corrupt data. Such bounds are not available in practice, resulting in weak guarantees and often poor performance. This brief note abstracts the complex and pervasive robustness problem into a simple geometric puzzle. It then applies the puzzle's solution to derive a universal meta technique that converts any robust estimation algorithm requiring a tight corruption-level upper bound to achieve its optimal accuracy into one achieving essentially the same accuracy without using any upper bounds.