22 citations · 50 across the 14 of their papers we have counts for
5 papers · 1 filter
Stochastic Wasserstein Hamiltonian Flows
Jianbo Cui, Shu Liu, Haomin Zhou
In this paper, we study the stochastic Hamiltonian flow in Wasserstein manifold, the probability density space equipped with -Wasserstein metric tensor, via the Wong--Zakai ap…
Neural Monge Map estimation and its applications
Jiaojiao Fan, Shu Liu, Shaojun Ma +2
Monge map refers to the optimal transport map between two probability distributions and provides a principled approach to transform one distribution to another. Neural network base…
Approximating the Optimal Transport Plan via Particle-Evolving Method
Shu Liu, Haodong Sun, Hongyuan Zha
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely us…
Learning High Dimensional Wasserstein Geodesics
Shu Liu, Shaojun Ma, Yongxin Chen +2
We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagran…
What is a stochastic Hamiltonian process on finite graph? An optimal transport answer
Jianbo Cui, Shu liu, Haomin Zhou
We present a definition of stochastic Hamiltonian process on finite graph via its corresponding density dynamics in Wasserstein manifold. We demonstrate the existence of stochastic…