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

TL;DR

This paper introduces a Wasserstein barycentric model aggregation method with a variational approach, demonstrating its consistency and effectiveness through synthetic and real temperature data experiments.

Contribution

It develops a data-driven calibration framework for Wasserstein barycenter aggregation and proves its statistical consistency using a variational perspective.

Findings

Empirical minimizers converge to true minimizers under mild conditions.

The method performs well on synthetic data and real temperature sensor data.

The approach provides a consistent and interpretable model aggregation framework.

Abstract

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.