Distributional barycenter problem through data-driven flows

TL;DR

This paper introduces a novel data-driven method for solving the distributional barycenter problem using flows, improving upon adversarial approaches by reducing parameterization and enabling flexible cost functions.

Contribution

It presents a new approach that simplifies the solution process for distributional barycenters and extends applicability to general cost functions.

Findings

Effective in analyzing MNIST with new cost functions

Reduces complexity compared to adversarial methods

Allows flexible, non-isometric cost functions

Abstract

A new method is proposed for the solution of the data-driven optimal transport barycenter problem and of the more general distributional barycenter problem that the article introduces. The method improves on previous approaches based on adversarial games, by slaving the discriminator to the generator, minimizing the need for parameterizations and by allowing the adoption of general cost functions. It is applied to numerical examples, which include analyzing the MNIST data set with a new cost function that penalizes non-isometric maps.