Related papers: Parameterized Wasserstein Hamiltonian Flow
We use Wasserstein distances to characterize and study probabilistic frames. Adapting results from Olkin and Pukelsheim, from Gelbrich and from Cuesta-Albertos, Matran-Bea and Tuero-Diaz to frame operators, we show that the sets of…
We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…
Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Flux Approximation Finite Volume schemes discretizing such…
Policy optimization is a core component of reinforcement learning (RL), and most existing RL methods directly optimize parameters of a policy based on maximizing the expected total reward, or its surrogate. Though often achieving…
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
The acceleration of gradient-based optimization methods is a subject of significant practical and theoretical importance, particularly within machine learning applications. While much attention has been directed towards optimizing within…
In this work, we propose and analyze a new local time-decoupled squared Wasserstein-2 method for reconstructing the distribution of unknown parameters in dynamical systems. Specifically, we show that a stochastic neural network model, which…
We formulate well-posed continuous-time generative flows for learning distributions that are supported on low-dimensional manifolds through Wasserstein proximal regularizations of $f$-divergences. Wasserstein-1 proximal operators regularize…
Optimal transport (OT) and the related Wasserstein metric (W) are powerful and ubiquitous tools for comparing distributions. However, computing pairwise Wasserstein distances rapidly becomes intractable as cohort size grows. An attractive…
Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow for…
Active galactic nuclei, x-ray binaries, pulsars, and gamma-ray bursts are all believed to be powered by compact objects surrounded by relativistic plasma flows driving phenomena such as accretion, winds, and jets. These flows are often…
We present a method to efficiently compute Wasserstein gradient flows. Our approach is based on a generalization of the back-and-forth method (BFM) introduced by Jacobs and L\'eger to solve optimal transport problems. We evolve the gradient…
We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted to particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the…
The Bayesian update step poses significant computational challenges in high-dimensional nonlinear estimation. While log-homotopy particle flow filters offer an alternative to stochastic sampling, existing formulations usually yield stiff…
The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite samples requires solving a variational problem. We study the…
We present a method for estimating parameters in stochastic models of biochemical reaction networks by fitting steady-state distributions using Wasserstein distances. We simulate a reaction network at different parameter settings and train…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated…