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Title: Outlier-Robust Sparse Estimation via Non-Convex Optimization
We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA. We develop novel and simple optimization formulations for these problems such that any approximate stationary point of the associated optimization problem yields a near-optimal solution for the underlying robust estimation task. As a corollary, we obtain that any first-order method that efficiently converges to stationarity yields an efficient algorithm for these tasks. The obtained algorithms are simple, practical, and succeed under broader distributional assumptions compared to prior work.  more » « less
Award ID(s):
2307106 2122628
NSF-PAR ID:
10387300
Author(s) / Creator(s):
; ; ; ; ;
Publisher / Repository:
Curran Associates
Date Published:
Journal Name:
Proceedings of the 36th Conference on Neural Information Processing Systems
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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