4.6 Article

Distributed Wasserstein Barycenters via Displacement Interpolation

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Automation & Control Systems

The multimarginal optimal transport formulation of adversarial multiclass classification

Nicolas Garcia Trillos et al.

Summary: This study examines a family of adversarial multiclass classification problems and provides equivalent reformulations using two different approaches. The results reveal the geometric structure of these problems and extend previous findings in binary classification. Furthermore, computational implications suggest that our solutions can recover optimal classification rules and adversarial strategies for the original problem.

JOURNAL OF MACHINE LEARNING RESEARCH (2023)

Article Automation & Control Systems

NETWORK CONSENSUS IN THE WASSERSTEIN METRIC SPACE OF PROBABILITY MEASURES

Adrian N. Bishop et al.

Summary: This work introduces distributed consensus in the Wasserstein metric space of probability measures on the real line, proving convergence of each agent's measure to a common measure under weak network connectivity conditions. The common measure reached at each agent is obtained by minimizing a weighted sum of its Wasserstein distance to all initial agent measures, known as the Wasserstein barycenter. Special cases involving Gaussian measures, empirical measures, and time-invariant network topologies are considered, with convergence rates and average-consensus results provided. This work has potential applications in computer vision, machine learning, clustering, and estimation.

SIAM JOURNAL ON CONTROL AND OPTIMIZATION (2021)

Article Computer Science, Information Systems

Optimal Transport for Gaussian Mixture Models

Yongxin Chen et al.

IEEE ACCESS (2019)

Article Computer Science, Artificial Intelligence

Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning

Morgan A. Schmitz et al.

SIAM JOURNAL ON IMAGING SCIENCES (2018)

Article Statistics & Probability

Existence and consistency of Wasserstein barycenters

Thibaut Le Gouic et al.

PROBABILITY THEORY AND RELATED FIELDS (2017)

Article Computer Science, Artificial Intelligence

Optimal Transport for Domain Adaptation

Nicolas Courty et al.

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (2017)

Article Computer Science, Software Engineering

Wasserstein Barycentric Coordinates: Histogram Regression Using Optimal Transport

Nicolas Bonneel et al.

ACM TRANSACTIONS ON GRAPHICS (2016)

Article Mathematics, Applied

A fixed-point approach to barycenters in Wasserstein space

Pedro C. Alvarez-Esteban et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2016)

Article Operations Research & Management Science

Discrete Wasserstein barycenters: optimal transport for discrete data

Ethan Anderes et al.

MATHEMATICAL METHODS OF OPERATIONS RESEARCH (2016)

Article Computer Science, Artificial Intelligence

A Smoothed Dual Approach for Variational Wasserstein Problems

Marco Cuturi et al.

SIAM JOURNAL ON IMAGING SCIENCES (2016)

Article Mathematics, Applied

NUMERICAL METHODS FOR MATCHING FOR TEAMS AND WASSERSTEIN BARYCENTERS

Guillaume Carlier et al.

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE (2015)

Article Engineering, Electrical & Electronic

On Wasserstein Barycenters and MMOSPA Estimation

Marcus Baum et al.

IEEE SIGNAL PROCESSING LETTERS (2015)

Article Automation & Control Systems

The Asymptotic Consensus Problem on Convex Metric Spaces

Ion Matei et al.

IEEE TRANSACTIONS ON AUTOMATIC CONTROL (2015)

Article Computer Science, Artificial Intelligence

Sliced and Radon Wasserstein Barycenters of Measures

Nicolas Bonneel et al.

JOURNAL OF MATHEMATICAL IMAGING AND VISION (2015)

Article Biology

Statistical properties of the quantile normalization method for density curve alignment

Santiago Gallon et al.

MATHEMATICAL BIOSCIENCES (2013)

Article Optics

Optimal-transport formulation of electronic density-functional theory

Giuseppe Buttazzo et al.

PHYSICAL REVIEW A (2012)

Review Automation & Control Systems

Consensus on nonlinear spaces

R. Sepulchre

ANNUAL REVIEWS IN CONTROL (2011)

Article Mathematics, Applied

BARYCENTERS IN THE WASSERSTEIN SPACE

Martial Agueh et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2011)

Article Mathematics, Interdisciplinary Applications

Opinion Dynamics and Learning in Social Networks

Daron Acemoglu et al.

DYNAMIC GAMES AND APPLICATIONS (2011)

Article Automation & Control Systems

Consensus Over Ergodic Stationary Graph Processes

Alireza Tahbaz-Salehi et al.

IEEE TRANSACTIONS ON AUTOMATIC CONTROL (2010)

Article Economics

Matching for teams

G. Carlier et al.

ECONOMIC THEORY (2010)

Article Mathematics, Applied

A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem

JD Benamou et al.

NUMERISCHE MATHEMATIK (2000)