Consensus in the Wasserstein Metric Space of Probability Measures

Abstract

Distributed consensus in the Wasserstein metric space of probability measures is introduced in this work. Convergence of each agents measure to a common measure value is proven under a weak network connectivity condition. The common measure reached a teach agent is one minimizing a weighted sum of its Wasserstein distance to all initial agent measures. This measure is known as the Wasserstein bary centre. Special cases involving Gaussian measures, empirical measures, and time-invariant network topologies are considered, where convergence rates and average-consensus results are given. This algorithm has potential applicability in computer vision, machine learning and distributed estimation, etc.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2015
Accession Number
AD1042531

Entities

People

  • Adrain N. Bishop
  • Arnaud Doucet

Organizations

  • University of Technology Sydney

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Consensus Algorithms
  • Convergence
  • Curvature
  • Distribution Functions
  • Eigenvalues
  • Estimators
  • Information Science
  • Lyapunov Functions
  • Mathematical Filters
  • Maximum Likelihood Estimation
  • Network Topology
  • Networks
  • Sensor Networks
  • Standards
  • Topology

Fields of Study

  • Computer science

Readers

  • Agent-Based Social Robotics and Mobile-Assisted Learning in Virtual Environments.
  • Approximation Theory.
  • Regression Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • Space