Diffeomorphic random sampling using optimal information transport
Paper i proceeding, 2017

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.

Fisher–Rao metric

Information geometry

Density matching

Random sampling

Diffeomorphism groups

Image registration

Optimal transport

Författare

M. Bauer

Florida State University

S. Joshi

University of Utah

Klas Modin

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Lecture Notes in Computer Science

0302-9743 (ISSN)

Vol. 10589 135-142

Ämneskategorier

Matematik

DOI

10.1007/978-3-319-68445-1_16

ISBN

978-3-319-68444-4