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Dissertation/Thesis Abstract

Formulation and Properties of a Divergence Used to Compare Probability Measures Without Absolute Continuity and Its Application to Uncertainty Quantification
by Mao, Yixiang, Ph.D., Harvard University, 2020, 134; 28092743
Abstract (Summary)

This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and exploit a representation as an infimum convolution of optimal transport cost and relative entropy. We include examples of computation and approximation of the divergence, and its applications in uncertainty quantification in discrete models and Gauss-Markov models.

Indexing (document details)
Advisor: Dupuis, Paul
Commitee: Yau, Shing-Tung, Yau, Horng-Tzer
School: Harvard University
Department: Mathematics
School Location: United States -- Massachusetts
Source: DAI-A 82/5(E), Dissertation Abstracts International
Subjects: Mathematics, Information science
Keywords: Convex duality, KL divergence, Model uncertainty, Optimal transport theory, Relative entropy
Publication Number: 28092743
ISBN: 9798698533917
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