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Diffeomorphic random sampling using optimal information transport

Conference paper
Authors Martin Bauer
Sarang Joshi
Klas Modin
Published in International Conference on Geometric Science of Information. GSI 2017: Geometric Science of Information. Lecture Notes in Computer Science.
ISSN 0302-9743
Publisher Springer
Publication year 2017
Published at Department of Mathematical Sciences
Language en
Links https://doi.org/10.1007/978-3-319-6...
Keywords Density matching, Diffeomorphism groups, Fisher–Rao metric, Image registration, Information geometry, Optimal transport, Random sampling
Subject categories Mathematics, Geometry

Abstract

© 2017, Springer International Publishing AG. In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)—an analogue of optimal mass transport (OMT). Our framework uses the deep geometric connections between the Fisher-Rao metric on the space of probability densities and the right-invariant information metric on the group of diffeomorphisms. The resulting sampling algorithm is a promising alternative to OMT, in particular as our formulation is semi-explicit, free of the nonlinear Monge–Ampere equation. Compared to Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when a large number of samples from a low dimensional nonuniform distribution is needed.

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