# Scalable Bayes via Barycenter in Wasserstein Space

arXiv: https://arxiv.org/abs/1508.05880 · HTML: https://mlsanity.com/paper/1508.05880/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2015.

## Built on by (most cited first, 30 of 44)

- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization](https://mlsanity.com/paper/2102.01752/) (2021)
- [Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent](https://mlsanity.com/paper/2106.08502/) (2021)
- [Wasserstein barycenters are NP-hard to compute](https://mlsanity.com/paper/2101.01100/) (2021)
- [On Robust Optimal Transport: Computational Complexity and Barycenter Computation](https://mlsanity.com/paper/2102.06857/) (2021)
- [Wasserstein Iterative Networks for Barycenter Estimation](https://mlsanity.com/paper/2201.12245/) (2022)
- [The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification](https://mlsanity.com/paper/2204.12676/) (2022)
- [Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenters](https://mlsanity.com/paper/2305.16557/) (2023)
- [Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2210.06671/) (2022)
- [Estimating Barycenters of Distributions with Neural Optimal Transport](https://mlsanity.com/paper/2402.03828/) (2024)
- [Dimensionality Reduction for Wasserstein Barycenter](https://mlsanity.com/paper/2110.08991/) (2021)
- [Energy-Guided Continuous Entropic Barycenter Estimation for General Costs](https://mlsanity.com/paper/2310.01105/) (2023)
- [Doubly Regularized Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2303.11844/) (2023)
- [Many processors, little time: MCMC for partitions via optimal transport couplings](https://mlsanity.com/paper/2202.11258/) (2022)
- [SwISS: A Scalable Markov chain Monte Carlo Divide-and-Conquer Strategy](https://mlsanity.com/paper/2208.04080/) (2022)
- [Sliced Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2102.07115/) (2021)
- [Sampling From the Wasserstein Barycenter](https://mlsanity.com/paper/2105.01706/) (2021)
- [Generating Synthetic Datasets by Interpolating along Generalized Geodesics](https://mlsanity.com/paper/2306.06866/) (2023)
- [Wasserstein Geodesic Generator for Conditional Distributions](https://mlsanity.com/paper/2308.10145/) (2023)
- [Federated Variational Inference Methods for Structured Latent Variable Models](https://mlsanity.com/paper/2302.03314/) (2023)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [Approximate Algorithms For k-Sparse Wasserstein Barycenter With Outliers](https://mlsanity.com/paper/2404.13401/) (2024)
- [Asynchronous and Distributed Data Augmentation for Massive Data Settings](https://mlsanity.com/paper/2109.08969/) (2021)
- [Sobolev Gradient Ascent for Optimal Transport: Barycenter Optimization and Convergence Analysis](https://mlsanity.com/paper/2505.13660/) (2025)
- [Neural Estimation for Scaling Entropic Multimarginal Optimal Transport](https://mlsanity.com/paper/2506.00573/) (2025)
- [Schr"odinger Bridge Matching for Tree-Structured Costs and Entropic Wasserstein Barycentres](https://mlsanity.com/paper/2506.17197/) (2025)
- [Stability of Entropic Wasserstein Barycenters and application to random geometric graphs](https://mlsanity.com/paper/2210.10535/) (2022)
- [Improved learning theory for kernel distribution regression with two-stage sampling](https://mlsanity.com/paper/2308.14335/) (2023)
- [Robust and Scalable Variational Bayes](https://mlsanity.com/paper/2504.12528/) (2025)

## Abstract (arXiv)

Divide-and-conquer based methods for Bayesian inference provide a general approach for tractable posterior inference when the sample size is large. These methods divide the data into smaller subsets, sample from the posterior distribution of parameters in parallel on all the subsets, and combine posterior samples from all the subsets to approximate the full data posterior distribution. The smaller size of any subset compared to the full data implies that posterior sampling on any subset is computationally more efficient than sampling from the true posterior distribution. Since the combination step takes negligible time relative to sampling, posterior computations can be scaled to massive data by dividing the full data into a sufficiently large number of data subsets. One such approach relies on the geometry of posterior distributions estimated across different subsets and combines them through their barycenter in a Wasserstein space of probability measures. We provide theoretical guarantees on the accuracy of approximation that are valid in many applications. We show that the geometric method approximates the full data posterior distribution better than its competitors across diverse simulations and reproduces known results when applied to a movie ratings database.