# Robustly Learning Mixtures of $k$ Arbitrary Gaussians

Ainesh Bakshi
He Jia
Pravesh K. Kothari
Santosh S. Vempala
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Abstract:

We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, 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...More

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