ExponentialFamilyManifolds.jl: Representing exponential families as Riemannian manifolds

Abstract

ExponentialFamilyManifolds.jl implements exponential family natural parameter spaces as Riemannian manifolds, enabling geometric optimization over probability distributions. The package automatically manages parameter constraints, such as ensuring the positive definiteness of precision matrices for normal distributions. By representing exponential family distributions as manifolds that conform to the ManifoldsBase.jl interface, it allows users to leverage optimization techniques from Manopt.jl for these manifolds. Applications in maximum likelihood estimation and variational inference highlight the package’s practical utility.