Daniil Dmitriev

Robust Mixture Learning when Outliers Overwhelm Small Groups We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly s...

We obtain information-theoretically optimal list size and recovery error, and provide empirical comparison with prior methods.

link: arxiv.org/abs/2407.15792

Joint with @raresbuhai.bsky.social, Stefan Tiegel, Alex Wolters, Gleb Novikov, @amartyasanyal.bsky.social, David Steurer, and Fanny Yang.

Our method works in the presence of large outliers if mixture components are spherical Gaussians, or, more generally, have bounded k-th sub-Gaussian moments.

We propose a reduction from the robust mixture learning problem to a well-studied list-decodable mean estimation problem.

When the number of outliers is negligible compared to the smallest component, existing algorithms recover all means with optimal errors.

However, when the fraction of outliers becomes larger than the smallest component, prior methods suffer both in recovery error and list size.

Excited to present at #NeurIPS2024 our work on robust mixture learning!

How hard is mixture learning when (a lot of) outliers are present? We show that it's easier than it seems!

Join us at the poster session (Wed, 16:30 PT, West Ballroom A-D #5710).

a typical day at Simons: read a paper in the morning, drink tea with all authors of the paper in the afternoon.