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arXiv · 1404.0145

Network Consensus in the Wasserstein Metric Space of Probability Measures

Adrian N. Bishop·Arnaud Doucet
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Abstract

Distributed consensus in the Wasserstein metric space of probability measures on the real line is introduced in this work. Convergence of each agent's measure to a common measure is proven under a weak network connectivity condition. The common measure reached at each agent is one minimizing a weighted sum of its Wasserstein distance to all initial agent measures. This measure is known as the Wasserstein barycenter. Special cases involving Gaussian measures, empirical measures, and time-invariant network topologies are considered, where convergence rates and average-consensus results are given. This work has possible applicability in computer vision, machine learning, clustering, and estimation.

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Adrian N. Bishop, Arnaud Doucet. 2014-04-01. Network Consensus in the Wasserstein Metric Space of Probability Measures. https://doi.org/10.1137/19m1268252

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