5 papers
Gromov-Wasserstein Barycenters: The Analysis Problem
RocÃo DÃaz MartÃn, Ivan V. Medri, James M. Murphy
This paper considers the problem of estimating a matrix that encodes pairwise distances in a finite metric space (or, more generally, the edge weight matrix of a network) under the…
Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphs
David Gentile, James M. Murphy
The optimal transportation problem defines a geometry of probability measures which leads to a definition for weighted averages (barycenters) of measures, finding application in th…
Wasserstein-based identification of metastable states in time series data via change point detection and segment clustering
David Gentile, Joshua Huang, James M. Murphy
Change point detection for time series analysis is a difficult and important problem in applied statistics, for which a variety of approaches have been developed in the past severa…
Linearized Wasserstein Barycenters: Synthesis, Analysis, Representational Capacity, and Applications
Matthew Werenski, Brendan Mallery, Shuchin Aeron +1
We propose the linear barycentric coding model (LBCM) which utilizes the linear optimal transport (LOT) metric for analysis and synthesis of probability measures. We provide a clos…
Synthesis and Analysis of Data as Probability Measures with Entropy-Regularized Optimal Transport
Brendan Mallery, James M. Murphy, Shuchin Aeron
We consider synthesis and analysis of probability measures using the entropy-regularized Wasserstein-2 cost and its unbiased version, the Sinkhorn divergence. The synthesis problem…