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arXiv · 1907.11826

Bayesian Robustness: A Nonasymptotic Viewpoint

Kush Bhatia·Yi-An Ma·Anca D. Dragan·Peter L. Bartlett·Michael I. Jordan
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Abstract

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 $T= \tilde{\mathcal{O}}(d/\varepsilon_{\textsf{acc}})$ iterations, we can sample from $p_T$ such that $\text{dist}(p_T, p^*) \leq \varepsilon_{\textsf{acc}} + \tilde{\mathcal{O}}(\epsilon)$, where $\epsilon$ is the fraction of corruptions. We corroborate our theoretical analysis with experiments on both synthetic and real-world data sets for mean estimation, regression and binary classification.

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Kush Bhatia, Yi-An Ma, Anca D. Dragan, Peter L. Bartlett, Michael I. Jordan. 2019-07-27. Bayesian Robustness: A Nonasymptotic Viewpoint. https://arxiv.org/abs/1907.11826

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