12 papers
Diffusion Approximations to Schrödinger Bridges and the Convergence of Entropic Potentials
Garrett Mulcahy, Soumik Pal
Consider the Monge-Kantorovich optimal transport problem between two Euclidean densities and and quadratic cost. The -Schrödinger bridge is the solution to the…
Mirror Langevin diffusions: Convergence rates and Markov chain approximations
Benjamin Capdeville, Young-Heon Kim, Soumik Pal
Given a strongly convex function , equip with a Riemannian metric given by the Hessian . This is a so-called Hessian manifold. Given a probability density …
Diffusion Approximations to Schrödinger Bridges on Manifolds
Garrett Mulcahy, Soumik Pal
We present a collection of explicit diffusion approximations to small temperature Schrödinger bridges on manifolds. Our most precise results are when both marginals are the same an…
Finite Markov chains and Monte-Carlo Methods: An Undergraduate Introduction
Soumik Pal, Tim Mesikepp
This is a free textbook suitable for a one-semester course on Markov chains, covering basics of finite-state chains, many classical models, asymptotic behavior and mixing times, Mo…
Langevin Diffusion Approximation to Same Marginal Schrödinger Bridge
Medha Agarwal, Zaid Harchaoui, Garrett Mulcahy +1
We introduce a novel approximation to the same marginal Schrödinger bridge using the Langevin diffusion. As , it is known that the barycentric projection…
On the Wasserstein alignment problem
Soumik Pal, Bodhisattva Sen, Ting-Kam Leonard Wong
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces -- namely the…