RobULA: Efficient Sampling for Robust Bayesian Inference

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 RobULA, a robust variant of the Unadjusted Langevin Algorithm (ULA), and provide a finite-sample analysis of its sampling distribution. The key to our approach is combining a gradient-based sampling approach with a robust mean gradient estimator. In particular, we show that after T = Õ(d/εacc) iterations, we can sample from pT such that dist(pT , p∗) ≤ εacc + Õ( ), where is the fraction of corruptions.

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