2 citations · 2 across the 3 of their papers we have counts for
5 papers
Wasserstein Hamiltonian flow with common noise on graph
Jianbo Cui, Shu Liu, Haomin Zhou
We study the Wasserstein Hamiltonian flow with a common noise on the density manifold of a finite graph. Under the framework of stochastic variational principle, we first develop t…
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…
Parametric Fokker-Planck equation
Wuchen Li, Shu Liu, Hongyuan Zha +1
We derive the Fokker-Planck equation on the parametric space. It is the Wasserstein gradient flow of relative entropy on the statistical manifold. We pull back the PDE to a finite…