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Full-Text Articles in Physical Sciences and Mathematics
Convexity Of Regularized Optimal Transport Dissimilarity Measures For Signed Signals, Christian P. Fowler
Convexity Of Regularized Optimal Transport Dissimilarity Measures For Signed Signals, Christian P. Fowler
Mathematics & Statistics ETDs
Debiased Sinkhorn divergence (DS divergence) is a distance function of
regularized optimal transport that measures the dissimilarity between two
probability measures of optimal transport. This thesis analyzes the advantages of
using DS divergence when compared to the more computationally expensive
Wasserstein distance as well as the classical Euclidean norm. Specifically, theory
and numerical experiments are used to show that Debiased Sinkhorn divergence
has geometrically desirable properties such as maintained convexity after data
normalization. Data normalization is often needed to calculate Sinkhorn
divergence as well as Wasserstein distance, as these formulas only accept
probability distributions as inputs and do not directly …
A Brief On Optimal Transport, Austin G. Vandegriffe
A Brief On Optimal Transport, Austin G. Vandegriffe
Graduate Student Research & Creative Works
Optimal transport is an interesting and exciting application of measure theory to optimization and analysis. In the following, I will bring you through a detailed treatment of random variable couplings, transport plans, basic properties of transport plans, and finishing with the Wasserstein distance on spaces of probability measures with compact support. No detail is left out in this presentation, but some results have further generality and more intricate consequences when tools like measure disintegration are used. But this is left for future work.