# Robust and Scalable Bayes via a Median of Subset Posterior Measures

arXiv: https://arxiv.org/abs/1403.2660 · HTML: https://mlsanity.com/paper/1403.2660/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2014.

## Built on by (most cited first, 8 of 8)

- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [Asynchronous and Distributed Data Augmentation for Massive Data Settings](https://mlsanity.com/paper/2109.08969/) (2021)
- [Robust probabilistic inference via a constrained transport metric](https://mlsanity.com/paper/2303.10085/) (2023)
- [Robust and Scalable Variational Bayes](https://mlsanity.com/paper/2504.12528/) (2025)
- [Robust Estimation in metric spaces: Achieving Exponential Concentration with a Fr'echet Median](https://mlsanity.com/paper/2504.14161/) (2025)
- [Divide-and-conquer methods for big data analysis](https://mlsanity.com/paper/2102.10771/) (2021)
- [A theoretical framework for M-posteriors: frequentist guarantees and robustness properties](https://mlsanity.com/paper/2510.01358/) (2025)
- [Robust Variational Bayes by Min-Max Median Aggregation](https://mlsanity.com/paper/2512.12676/) (2025)

## Abstract (arXiv)

We propose a novel approach to Bayesian analysis that is provably robust to outliers in the data and often has computational advantages over standard methods. Our technique is based on splitting the data into non-overlapping subgroups, evaluating the posterior distribution given each independent subgroup, and then combining the resulting measures. The main novelty of our approach is the proposed aggregation step, which is based on the evaluation of a median in the space of probability measures equipped with a suitable collection of distances that can be quickly and efficiently evaluated in practice. We present both theoretical and numerical evidence illustrating the improvements achieved by our method.