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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…