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Diffeomorphic random sampling using optimal information transport

M. Bauer ; S. Joshi ; Klas Modin (Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik)
Lecture Notes in Computer Science: 3rd International Conference on Geometric Science of Information, GSI 2017; Paris; France; 7 November 2017 through 9 November 2017 (0302-9743). Vol. 10589 (2017), p. 135-142.
[Konferensbidrag, refereegranskat]

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.

Nyckelord: Density matching , Diffeomorphism groups , Fisher–Rao metric , Image registration , Information geometry , Optimal transport , Random sampling



Denna post skapades 2017-12-14. Senast ändrad 2017-12-15.
CPL Pubid: 253777

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Tillämpad matematik och statistikInstitutionen för matematiska vetenskaper, Tillämpad matematik och statistik (GU)

Ämnesområden

Matematik

Chalmers infrastruktur