Bayesian Robustness: A Nonasymptotic Viewpoint

被引:2
|
作者
Bhatia, Kush [1 ]
Ma, Yi-An [2 ]
Dragan, Anca D. [3 ]
Bartlett, Peter L. [3 ,4 ]
Jordan, Michael I. [3 ,4 ]
机构
[1] Stanford Univ, Dept Comp Sci, Stanford, CA 94305 USA
[2] Univ Calif San Diego, Halicioglu Data Sci Inst, La Jolla, CA USA
[3] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA USA
[4] Univ Calif Berkeley, Dept Stat, Berkeley, CA USA
基金
美国国家科学基金会;
关键词
Huber contamination; MCMC methods; Robust statistics; CONVERGENCE;
D O I
10.1080/01621459.2023.2174121
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
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.
引用
收藏
页码:1112 / 1123
页数:12
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