Distribution's template estimate with Wasserstein metrics

TL;DR

This paper introduces a method using Wasserstein barycenters to compare distributions, estimate a mean distribution, and recover a common template when distributions are warped by random operators.

Contribution

It proposes an iterative Wasserstein barycenter approach for distribution comparison and template recovery in warped measure scenarios.

Findings

Effective estimation of mean distributions using Wasserstein barycenters.

Ability to recover distribution templates from warped measures.

Applicability to various random distribution scenarios.

Abstract

In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an estimation of the mean distribution. Moreover, when the distributions are a common measure warped by a centered random operator, then the barycenter enables to recover this distribution template.