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Outlier-Robust Sparse Estimation via Non-Convex Optimization
Yu Cheng · Ilias Diakonikolas · Rong Ge · Shivam Gupta · Daniel Kane · Mahdi Soltanolkotabi

Tue Nov 29 09:00 AM -- 11:00 AM (PST) @ Hall J #722

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.

Author Information

Yu Cheng (Brown University)
Ilias Diakonikolas (University of Wisconsin-Madison)
Rong Ge (Duke University)
Shivam Gupta (University of Texas, Austin)
Daniel Kane (UCSD)
Mahdi Soltanolkotabi (University of Southern California)

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