212 citations · 625 across the 54 of their papers we have counts for
8 papers · 1 filter
Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances
Jialin Liu, Wotao Yin, Wuchen Li +1
We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with homogeneous of degree one transport cos…
Ricci curvature for parametric statistics via optimal transport
Wuchen Li, Guido Montufar
We elaborate the notion of a Ricci curvature lower bound for parametrized statistical models. Following the seminal ideas of Lott-Strum-Villani, we define this notion based on the…
Constrained dynamical optimal transport and its Lagrangian formulation
Wuchen Li, Stanley Osher
We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution…
Solving Large-Scale Optimization Problems with a Convergence Rate Independent of Grid Size
Matt Jacobs, Flavien Léger, Wuchen Li +1
We present a primal-dual method to solve L1-type non-smooth optimization problems independently of the grid size. We apply these results to two important problems : the Rudin-Osher…
Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula
Yat Tin Chow, Wuchen Li, Stanley Osher +1
We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games. We overcome the curse-of-infinite-dim…
Optimal transport natural gradient for statistical manifolds with continuous sample space
Yifan Chen, Wuchen Li
We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the -Wasserstein metric tensor in the pr…
Natural gradient via optimal transport
Wuchen Li, Guido Montufar
We study a natural Wasserstein gradient flow on manifolds of probability distributions with discrete sample spaces. We derive the Riemannian structure for the probability simplex f…
Transport information geometry I: Riemannian calculus on probability simplex
Wuchen Li
We formulate the Riemannian calculus of the probability set embedded with -Wasserstein metric. This is an initial work of transport information geometry. Our investigation sta…