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arXiv · 1702.07709

Computationally Efficient Robust Estimation of Sparse Functionals

Simon S. Du·Sivaraman Balakrishnan·Aarti Singh
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Abstract

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and possibly exceed the sample size. We consider the problem of robust estimation of sparse functionals, and provide a computationally and statistically efficient algorithm in the high-dimensional setting. Our theory identifies a unified set of deterministic conditions under which our algorithm guarantees accurate recovery. By further establishing that these deterministic conditions hold with high-probability for a wide range of statistical models, our theory applies to many problems of considerable interest including sparse mean and covariance estimation; sparse linear regression; and sparse generalized linear models.

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Simon S. Du, Sivaraman Balakrishnan, Aarti Singh. 2017-02-24. Computationally Efficient Robust Estimation of Sparse Functionals. https://arxiv.org/abs/1702.07709

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