High-Dimensional Robust Mean Estimation via Gradient Descent

• URL: http://arxiv.org/abs/2005.01378v1
• Date: Mon, 4 May 2020 10:48:04 GMT
• Title: High-Dimensional Robust Mean Estimation via Gradient Descent
• Authors: Yu Cheng, Ilias Diakonikolas, Rong Ge, Mahdi Soltanolkotabi
• Abstract summary: We show that the problem of robust mean estimation in the presence of a constant adversarial fraction can be solved by gradient descent. Our work establishes an intriguing connection between the near non-lemma estimation and robust statistics.
• Score: 73.61354272612752
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with dimension-independent error guarantees for a range of natural distribution families. In this work, we show that a natural non-convex formulation of the problem can be solved directly by gradient descent. Our approach leverages a novel structural lemma, roughly showing that any approximate stationary point of our non-convex objective gives a near-optimal solution to the underlying robust estimation task. Our work establishes an intriguing connection between algorithmic high-dimensional robust statistics and non-convex optimization, which may have broader applications to other robust estimation tasks.

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