290 citations · 492 across the 36 of their papers we have counts for
4 papers · 1 filter
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…
Kernel approximation on algebraic varieties
Jason M. Altschuler, Pablo A. Parrilo
Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in p…
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…
Wasserstein barycenters are NP-hard to compute
Jason M. Altschuler, Enric Boix-Adsera
Computing Wasserstein barycenters (a.k.a. Optimal Transport barycenters) is a fundamental problem in geometry which has recently attracted considerable attention due to many applic…