1 citations · 1 across the 5 of their papers we have counts for
8 papers
Sparse Dictionary Learning for Measure-Valued Data via Linearized Optimal Transport: Efficient Algorithms and Sample Complexity
Brendan Mallery, Shuchin Aeron, James Murphy
We study dictionary learning for probability measure-valued data by embedding measures into Hilbert spaces using features derived from optimal transport geometry. We learn data-ada…
Sliced Wasserstein Barycenters: The Analysis Approach within the Barycentric Coding Model in the Wasserstein Space
Rocío Díaz Martín, James M. Murphy
We study sliced Wasserstein barycenters from a variational perspective in Wasserstein space, with emphasis on the analysis problem in the barycentric coding model: given a query me…
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…
Gromov-Wasserstein Barycenters: The Analysis Problem
Rocío Díaz Martín, 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…
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…
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…
Measuring Segregation via Analysis on Graphs
Moon Duchin, James M. Murphy, Thomas Weighill
In this paper, we use analysis on graphs to study quantitative measures of segregation. We focus on a classical statistic from the geography and urban sociology literature known as…