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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…
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…
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…