Robustly Learning Mixtures of k Arbitrary Gaussians [article]

Ainesh Bakshi, Ilias Diakonikolas, He Jia, Daniel M. Kane, Pravesh K. Kothari, Santosh S. Vempala
2021 arXiv   pre-print
We give a polynomial-time algorithm for the problem of robustly estimating a mixture of k arbitrary Gaussians in ℝ^d, for any fixed k, in the presence of a constant fraction of arbitrary corruptions. This resolves the main open problem in several previous works on algorithmic robust statistics, which addressed the special cases of robustly estimating (a) a single Gaussian, (b) a mixture of TV-distance separated Gaussians, and (c) a uniform mixture of two Gaussians. Our main tools are an
more » ... t partial clustering algorithm that relies on the sum-of-squares method, and a novel tensor decomposition algorithm that allows errors in both Frobenius norm and low-rank terms.
arXiv:2012.02119v3 fatcat:2j6gb5iax5anfeamjfuiwwof3i