Outlier Robust Mean Estimation with Subgaussian Rates via Stability

• URL: http://arxiv.org/abs/2007.15618v2
• Date: Tue, 16 Mar 2021 15:58:25 GMT
• Title: Outlier Robust Mean Estimation with Subgaussian Rates via Stability
• Authors: Ilias Diakonikolas, Daniel M. Kane, Ankit Pensia
• Abstract summary: We study the problem of robust outlier high-dimensional mean estimation. We obtain first computationally efficient rate with subgaussian for outlier-robust mean estimation.
• Score: 46.03021473600576
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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