Robustly Learning a Gaussian: Getting Optimal Error, Efficiently

SODA '18: Symposium on Discrete Algorithms New Orleans Louisiana January, 2018, pp. 2683-2702, 2018.

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Abstract:

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise --- where an ε-fraction of our samples were chosen by an adversary. We give robust estimators that achieve estimation error O(ϵ) in the total variation distance, which is optimal up to a universal constant that is independen...More

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