Diffeomorphic random sampling using optimal information transport
For researchers needing efficient sampling from low-dimensional nonuniform distributions on manifolds, this method offers a semi-explicit alternative to OMT and MCMC, though no concrete performance numbers are provided.
The authors propose a diffeomorphic random sampling algorithm for nonuniform distributions on Riemannian manifolds using optimal information transport (OIT), which avoids solving the nonlinear Monge-Ampère equation. They claim it is a promising alternative to optimal mass transport and Markov Chain Monte Carlo for low-dimensional distributions requiring many samples.
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.