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Bayesian Robustness: A Nonasymptotic Viewpoint
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DOI：10.1080/01621459.2023.2174121.png)
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摘要
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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.
Keyword:
Huber contamination
MCMC methods
Robust statistics
期刊
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IF:
3
论文数:
5.2K
被引数:
4.8W
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