Global ETD Search
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Showing 1 to 6 of 6 for “"Wasserstein Barycenters"”.
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An optimization perspective on log-concave sampling and beyond
… the main tools in this work—diffusions and Wasserstein gradient flows—through applications to functional inequalities, the entropic barrier, Wasserstein barycenters, variational inference, and diffusion models.
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Optimal transportation and barycenter problems via convex functions
… transportation problems and the associatedWasserstein distances in increasing levels of specificity. The first chapter introduces optimal transport problems and known properties characterizing optimal transport plans. The second chapter develops the Wasserstein distances, arising from …
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Transport and Beyond: Efficient Optimization over Probability Distributions
… attention to the popular MOT application of Wasserstein barycenters--resolving the complexity of this problem and uncovering the subtle dependence of the dimension on the answer.
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Geometric methods in computational optimal transport and high-dimensional inference
… algorithms. Second, a framework for regularised Wasserstein estimators incorporating new entropic penalties is developed. For measures supported on finite sets, a dual formulation is derived that enables stochastic updates with O(1) complexity per iteration, independent of support size. Under …
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Efficient algorithms for distributed learning, optimization and belief systems over networks
… to the problem of distributed computation of Wasserstein barycenters of finite distributions. Finally, we discuss some future directions of research for the design and analysis of distributed algorithms, both from theoretical and applied perspectives.
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Optimal transport: theory, algorithms and applications
… 3.1, we consider the problem of computing Wasserstein barycenters of discrete measures, which is NP-hard in general. Here, we analyze a well-known simple framework for approximating Wasserstein-p barycenters, where we mainly consider the most common case p=2 and p=1, which is not as well …