# Bayesian Robustness: A Nonasymptotic Viewpoint

arXiv: https://arxiv.org/abs/1907.11826 · HTML: https://mlsanity.com/paper/1907.11826/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [A Bayesian Robust Regression Method for Corrupted Data Reconstruction](https://mlsanity.com/paper/2212.12787/) (2022)

## Abstract (arXiv)

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= tildeO(d/varepsilon_textsfacc) iterations, we can sample from pT such that dist(pT, p^*) ≤ varepsilon_textsfacc + tildeO(ε), where ε 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.