Bayesian Robustness: A Nonasymptotic Viewpoint.

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 / ε acc) iterations, we can sample from p_T such that dist (p T , p *) ≤ ε acc + O ˜ (ϵ) , where ϵ 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. for this article are available online. [ABSTRACT FROM AUTHOR]