Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable
solutions by hedging against data perturbations in Wasserstein distance. Despite its recent …

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical
problem arising, eg, in sparse spikes deconvolution or two-layer neural networks training …

Abstract Information geometry and optimal transport are two distinct geometric frameworks
for modeling families of probability measures. During the recent years, there has been a …

Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian
inference literature, for their capacity to yield flexible and accurate approximations. We …

Statistical inference can be performed by minimizing, over the parameter space, the
Wasserstein distance between model distributions and the empirical distribution of the data …

We design and compute first-order implicit-in-time variational schemes with high-order
spatial discretization for initial value gradient flows in generalized optimal transport metric …

We propose efficient numerical schemes for implementing the natural gradient descent
(NGD) for a broad range of metric spaces with applications to PDE-based optimization …

Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-
smooth Riesz kernels show a rich structure as singular measures can become absolutely …

While likelihood-based inference and its variants provide a statistically efficient and widely
applicable approach to parametric inference, their application to models involving …

We consider the maximum mean discrepancy MMD GAN problem and propose a parametric
kernelized gradient flow that mimics the min-max game in gradient regularized MMD GAN …