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Outlier-Robust Sparse Estimation via Non-Convex Optimization

Publication ,  Conference
Cheng, Y; Diakonikolas, I; Ge, R; Gupta, S; Kane, DM; Soltanolkotabi, M
Published in: Advances in Neural Information Processing Systems
January 1, 2022

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.

Duke Scholars

Published In

Advances in Neural Information Processing Systems

ISSN

1049-5258

Publication Date

January 1, 2022

Volume

35

Related Subject Headings

  • 4611 Machine learning
  • 1702 Cognitive Sciences
  • 1701 Psychology
 

Citation

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MLA
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Cheng, Y., Diakonikolas, I., Ge, R., Gupta, S., Kane, D. M., & Soltanolkotabi, M. (2022). Outlier-Robust Sparse Estimation via Non-Convex Optimization. In Advances in Neural Information Processing Systems (Vol. 35).
Cheng, Y., I. Diakonikolas, R. Ge, S. Gupta, D. M. Kane, and M. Soltanolkotabi. “Outlier-Robust Sparse Estimation via Non-Convex Optimization.” In Advances in Neural Information Processing Systems, Vol. 35, 2022.
Cheng Y, Diakonikolas I, Ge R, Gupta S, Kane DM, Soltanolkotabi M. Outlier-Robust Sparse Estimation via Non-Convex Optimization. In: Advances in Neural Information Processing Systems. 2022.
Cheng, Y., et al. “Outlier-Robust Sparse Estimation via Non-Convex Optimization.” Advances in Neural Information Processing Systems, vol. 35, 2022.
Cheng Y, Diakonikolas I, Ge R, Gupta S, Kane DM, Soltanolkotabi M. Outlier-Robust Sparse Estimation via Non-Convex Optimization. Advances in Neural Information Processing Systems. 2022.

Published In

Advances in Neural Information Processing Systems

ISSN

1049-5258

Publication Date

January 1, 2022

Volume

35

Related Subject Headings

  • 4611 Machine learning
  • 1702 Cognitive Sciences
  • 1701 Psychology