6 papers
A Kernel Formula for Kinetic Fokker-Planck Equations
Fuqun Han, Wuchen Li
We derive an explicit one-step kernel formula for the kinetic Fokker-Planck equation. The construction begins with a reference dynamics admitting an explicit transition kernel and…
Convergence of Noise-Free Sampling Algorithms with Regularized Wasserstein Proximals
Fuqun Han, Stanley Osher, Wuchen Li
In this work, we investigate the convergence properties of the backward regularized Wasserstein proximal (BRWP) method for sampling a target distribution. The BRWP approach can be…
Sparse Transformer Architectures via Regularized Wasserstein Proximal Operator with Prior
Fuqun Han, Stanley Osher, Wuchen Li
In this work, we propose a sparse transformer architecture that incorporates prior information about the underlying data distribution directly into the transformer structure of the…
Splitting Regularized Wasserstein Proximal Algorithms for Nonsmooth Sampling Problems
Fuqun Han, Stanley Osher, Wuchen Li
Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the…
Inexact Proximal Point Algorithms for Zeroth-Order Global Optimization
Minxin Zhang, Fuqun Han, Yat Tin Chow +2
This work concerns the zeroth-order global minimization of continuous nonconvex functions with a unique global minimizer and possibly multiple local minimizers. We formulate a theo…
Tensor train based sampling algorithms for approximating regularized Wasserstein proximal operators
Fuqun Han, Stanley Osher, Wuchen Li
We present a tensor train (TT) based algorithm designed for sampling from a target distribution and employ TT approximation to capture the high-dimensional probability density evol…