Robust polynomial regression up to the information theoretic limit

Abstract

We consider the problem of robust polynomial regression, where one receives samples (x_i, y_i) that are usually within of a polynomial y = p(x), but have a chance of being arbitrary adversarial outliers. Previously, it was known how to efficiently estimate p only when < 1 d. We give an algorithm that works for the entire feasible range of < 1/2, while simultaneously improving other parameters of the problem. We complement our algorithm, which gives a factor 2 approximation, with impossibility results that show, for example, that a 1.09 approximation is impossible even with infinitely many samples.

Tasks

Reproductions