# Barycentric model aggregation in the Wasserstein space of distributions and a variational approach to consistency

arXiv: https://arxiv.org/abs/2507.11719 · HTML: https://mlsanity.com/paper/2507.11719/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 15 Jul 2025.

## Builds on (most cited first, 11 of 11)

- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning](https://mlsanity.com/paper/1708.01955/) (2017)
- [Wasserstein Regression](https://mlsanity.com/paper/2006.09660/) (2020)
- [Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms](https://mlsanity.com/paper/1805.09450/) (2018)
- [Bayesian Learning with Wasserstein Barycenters](https://mlsanity.com/paper/1805.10833/) (2018)
- [Wasserstein Regression with Empirical Measures and Density Estimation for Sparse Data](https://mlsanity.com/paper/2308.12540/) (2023)
- [Convergence of the k-Means Minimization Problem using Gamma-Convergence](https://mlsanity.com/paper/1501.01320/) (2015)
- [Projected Statistical Methods for Distributional Data on the Real Line with the Wasserstein Metric](https://mlsanity.com/paper/2101.09039/) (2021)
- [Ensemble distributional forecasting for insurance loss reserving](https://mlsanity.com/paper/2206.08541/) (2022)

## Abstract (arXiv)

We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters and develop a data-driven calibration framework in which the aggregation weights are statistically learned from empirical information associated with a target distribution. From a variational perspective based on Gamma-convergence, we establish consistency of the resulting aggregation scheme, showing that empirical minimizers converge to the minimizers of the actual problem, along with the associated barycentric estimators, under mild conditions. The performance of the proposed method is evaluated through synthetic experiments and illustrated on a real dataset from a temperature monitoring network of sensors.