Diffeomorphic random sampling using optimal information transport
  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.
