Efficiently learning structured distributions from untrusted batches

We study the problem of list-decodable (robust) Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. In the former problem, we are given a set T of points in ⁿ with the promise that an α-fraction of ...

Let @@@@ be a class of probability distributions over the discrete domain [n] = {1,..., n}. We show that if @@@@ satisfies a rather general condition -- essentially, that each distribution in @@@@ can be well-approximated by a variable-width histogram ...

We give the first polynomial time algorithm for list-decodable covariance estimation. For any α > 0, our algorithm takes input a sample Y ⊆ ^d of size n≥ d^poly(1/α) obtained by adversarially corrupting an (1−α)n points in an i.i.d. sample X of size n ...