Robust Learning of Mixtures of Gaussians

07/12/2020

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by   Daniel M. Kane, et al.

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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 -fraction of which have been adversarially corrupted, learns X to error () in total variation distance.