32 citations · 110 across the 12 of their papers we have counts for
13 papers
Geometry and barycenters in large $\CAT(κ)$ spaces
Yassine Boukhateb, Victor-Emmanuel Brunel, Austin J. Stromme
We study the geometry and resulting properties of Fréchet functions and barycenters in metric spaces with curvature bounded above by a positive constant in the sense of Alexandrov.…
Finite-sample bounds for regularized optimal transport
Alberto González-Sanz, Marcel Nutz, Austin J. Stromme
We study the sample complexity of regularized optimal transport for general convex regularizations including the Kullback--Leibler divergence and penalties. Our main results…
The ballistic limit of the log-Sobolev constant equals the Polyak-Łojasiewicz constant
Sinho Chewi, Austin J. Stromme
The Polyak-Lojasiewicz (PL) constant of a function characterizes the best exponential rate of convergence of gradient flow for , uniformly…
Minimum intrinsic dimension scaling for entropic optimal transport
Austin J. Stromme
Motivated by the manifold hypothesis, which states that data with a high extrinsic dimension may yet have a low intrinsic dimension, we develop refined statistical bounds for entro…
On the sample complexity of entropic optimal transport
Philippe Rigollet, Austin J. Stromme
We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by…
Asymptotics for semi-discrete entropic optimal transport
Jason M. Altschuler, Jonathan Niles-Weed, Austin J. Stromme
We compute exact second-order asymptotics for the cost of an optimal solution to the entropic optimal transport problem in the continuous-to-discrete, or semi-discrete, setting. In…
Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent
Jason M. Altschuler, Sinho Chewi, Patrik Gerber +1
We study first-order optimization algorithms for computing the barycenter of Gaussian distributions with respect to the optimal transport metric. Although the objective is geodesic…
Fast and Smooth Interpolation on Wasserstein Space
Sinho Chewi, Julien Clancy, Thibaut Le Gouic +3
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean sett…
Exponential ergodicity of mirror-Langevin diffusions
Sinho Chewi, Thibaut Le Gouic, Chen Lu +3
Motivated by the problem of sampling from ill-conditioned log-concave distributions, we give a clean non-asymptotic convergence analysis of mirror-Langevin diffusions as introduced…
Gradient descent algorithms for Bures-Wasserstein barycenters
Sinho Chewi, Tyler Maunu, Philippe Rigollet +1
We study first order methods to compute the barycenter of a probability distribution over the space of probability measures with finite second moment. We develop a framework to…
Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space
Thibaut Le Gouic, Quentin Paris, Philippe Rigollet +1
This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically,…
Algebraic Properties of Generalized Graph Laplacians: Resistor Networks, Critical Groups, and Homological Algebra
David Jekel, Avi Levy, Will Dana +2
We propose an algebraic framework for generalized graph Laplacians which unifies the study of resistor networks, the critical group, and the eigenvalues of the Laplacian and adjace…
Frog model wakeup time on the complete graph
Nikki Cartern, Brittany Dygert, Matthew Junge +4
The frog model is a system of random walks where active particles set sleeping particles in motion. On the complete graph with n vertices it is equivalent to a well-understood rumo…