Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …

Abstract Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI)
has emerged as a central computational approach to large-scale Bayesian inference …

Variational inference (VI) seeks to approximate a target distribution $\pi $ by an element of a
tractable family of distributions. Of key interest in statistics and machine learning is Gaussian …

Optimal transport maps between two probability distributions $\mu $ and $\nu $ on $\R^ d $
have found extensive applications in both machine learning and statistics. In practice, these …

Statistical Optimal Transport arxiv:2407.18163v2 [math.ST] 7 Nov 2024 Page 1 Statistical
Optimal Transport Sinho Chewi Yale Jonathan Niles-Weed NYU Philippe Rigollet MIT …

Learning Gaussian mixtures using the Wasserstein-Fisher-Rao gradient flow Page 1 The
Annals of Statistics 2024, Vol. 52, No. 4, 1774–1795 https://doi.org/10.1214/24-AOS2416 © …

The static optimal transport $(\mathrm {OT}) $ problem between Gaussians seeks to recover
an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been …

Abstract Stein Variational Gradient Descent (SVGD), a popular sampling algorithm, is often
described as the kernelized gradient flow for the Kullback-Leibler divergence in the …

We study first-order optimization algorithms for computing the barycenter of Gaussian
distributions with respect to the optimal transport metric. Although the objective is …

Computing Wasserstein barycenters (aka optimal transport barycenters) is a fundamental
problem in geometry which has recently attracted considerable attention due to many …