# A General Method for Robust Bayesian Modeling

arXiv: https://arxiv.org/abs/1510.05078 · HTML: https://mlsanity.com/paper/1510.05078/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2015.

## Built on by (most cited first, 7 of 7)

- [On the Robustness to Misspecification of α-Posteriors and Their Variational Approximations](https://mlsanity.com/paper/2104.08324/) (2021)
- [Stochastic Approximation with Biased MCMC for Expectation Maximization](https://mlsanity.com/paper/2402.17870/) (2024)
- [Provably Scalable Black-Box Variational Inference with Structured Variational Families](https://mlsanity.com/paper/2401.10989/) (2024)
- [Predictive variational inference: Learn the predictively optimal posterior distribution](https://mlsanity.com/paper/2410.14843/) (2024)
- [Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecification](https://mlsanity.com/paper/2201.01973/) (2022)
- [A Bayesian Robust Regression Method for Corrupted Data Reconstruction](https://mlsanity.com/paper/2212.12787/) (2022)
- [Mode Collapse of Mean-Field Variational Inference](https://mlsanity.com/paper/2510.17063/) (2025)

## Abstract (arXiv)

Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case basis; examples include robust linear regression, robust mixture models, and bursty topic models. In this paper we develop a general approach to robust Bayesian modeling. We show how to turn an existing Bayesian model into a robust model, and then develop a generic strategy for computing with it. We use our method to study robust variants of several models, including linear regression, Poisson regression, logistic regression, and probabilistic topic models. We discuss the connections between our methods and existing approaches, especially empirical Bayes and James-Stein estimation.