Robust estimation via robust gradient estimation

• 成果类型: Article
• 署名作者: Prasad, Adarsh; Suggala, Arun Sai; Balakrishnan, Sivaraman; Ravikumar, Pradeep
• 署名单位: Carnegie Mellon University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12364
• 发表日期: 2020
• 页码: 601-627
• 关键词: high dimensions

摘要

We provide a new computationally efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models, under varied robustness settings, including in the classical Huber epsilon-contamination model, and in heavy-tailed settings. Our workhorse is a novel robust variant of gradient descent, and we provide conditions under which our gradient descent variant provides accurate estimators in a general convex risk minimization problem. We provide specific consequences of our theory for linear regression and logistic regression and for canonical parameter estimation in an exponential family. These results provide some of the first computationally tractable and provably robust estimators for these canonical statistical models. Finally, we study the empirical performance of our proposed methods on synthetic and real data sets, and we find that our methods convincingly outperform a variety of baselines.