Computationally Efficient Robust Estimation of Sparse Functionals
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.
Cite
@article{arxiv.1702.07709,
title = {Computationally Efficient Robust Estimation of Sparse Functionals},
author = {Simon S. Du and Sivaraman Balakrishnan and Aarti Singh},
journal= {arXiv preprint arXiv:1702.07709},
year = {2017}
}