Bayesian Robustness: A Nonasymptotic Viewpoint

• 成果类型: Article
• 署名作者: Bhatia, Kush; Ma, Yi-An; Dragan, Anca D.; Bartlett, Peter L.; Jordan, Michael I.
• 署名单位: Stanford University; University of California System; University of California San Diego; University of California System; University of California Berkeley; University of California System; University of California Berkeley
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2174121
• 发表日期: 2024
• 页码: 1112-1123
• 关键词: convergence

摘要

We study the problem of robustly estimating the posterior distribution for the setting where observed data can be contaminated with potentially adversarial outliers. We propose Rob-ULA, a robust variant of the Unadjusted Langevin Algorithm (ULA), and provide a finite-sample analysis of its sampling distribution. In particular, we show that after T = O (d/eacc) iterations, we can sample from pT such that dist(pT, p*) = e(acc) + O(e), where e is the fraction of corruptions and dist represents the squared 2-Wasserstein distance metric. Our results for the class of posteriors p* which satisfy log-concavity and smoothness assumptions. We corroborate our theoretical analysis with experiments on both synthetic and real-world datasets for mean estimation, regression and binary classification. Supplementary materials for this article are available online.