Math @ Duke
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Publications [#356436] of Rong Ge
Papers Published
- Cheng, Y; Diakonikolas, I; Ge, R; Soltanolkotabi, M, High-dimensional robust mean estimation via gradient descent,
37th International Conference on Machine Learning, ICML 2020, vol. PartF168147-3
(January, 2020),
pp. 1746-1756, ISBN 9781713821120
(last updated on 2024/03/28)
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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