Robust Learning of Mixtures of Gaussians

TL;DR

This paper presents a polynomial-time algorithm for robustly learning mixtures of two arbitrary high-dimensional Gaussians from corrupted samples, achieving small total variation error.

Contribution

It introduces a novel algorithm that efficiently learns Gaussian mixtures under adversarial corruption, resolving a key problem in robust statistics.

Findings

Successfully learns Gaussian mixtures with adversarial noise

Achieves error bounds polynomial in the corruption level

Operates efficiently in high-dimensional settings

Abstract

We resolve one of the major outstanding problems in robust statistics. In particular, if $X$ is an evenly weighted mixture of two arbitrary $d$-dimensional Gaussians, we devise a polynomial time algorithm that given access to samples from $X$ an $\eps$-fraction of which have been adversarially corrupted, learns $X$ to error $\poly(\eps)$ in total variation distance.