Computationally Efficient Robust Estimation of Sparse Functionals
arXiv:1702.07709
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.
References in corpus (6)
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- Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Model
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- Generative Adversarial Nets for Robust Scatter Estimation: A Proper Scoring Rule Perspective
- Robust High Dimensional Expectation Maximization Algorithm via Trimmed Hard Thresholding
- Robust Structured Statistical Estimation via Conditional Gradient Type Methods