Outlier Robust Mean Estimation with Subgaussian Rates via Stability

NeurIPS 2020

Outlier Robust Mean Estimation with Subgaussian Rates via Stability

Dec 06, 2020
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We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions. We consider a standard stability condition from the recent robust statistics literature and prove that, except with exponentially small failure probability, there exists a large fraction of the inliers satisfying this condition. As a corollary, it follows that a number of recently developed algorithms for robust mean estimation, including iterative filtering and non-convex gradient descent, give optimal error estimators with (near-)subgaussian rates. Previous analyses of these algorithms gave significantly suboptimal rates. As a corollary of our approach, we obtain the first computationally efficient algorithm with subgaussian rate for outlier-robust mean estimation in the strong contamination model under a finite covariance assumption. Speakers: Ilias Diakonikolas, Daniel M Kane, Ankit Pensia

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