209 citations · 1.4k across the 114 of their papers we have counts for
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Geometric ergodicity of SGLD via reflection coupling
Lei Li, Jian-Guo Liu, Yuliang Wang
We consider the geometric ergodicity of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm under nonconvexity settings. Via the technique of reflection coupling, we prove t…
Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective
Jian-Guo Liu, Ziheng Wang, Yantong Xie +2
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once th…
Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective
Jian-Guo Liu, Ziheng Wang, Yantong Xie +2
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once th…
On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function
Anning Liu, Jian-Guo Liu, Yulong Lu
We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establi…
Semi-groups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
Yuanyuan Feng, Lei Li, Jian-Guo Liu
We study the Markov semigroups for two important algorithms from machine learning: stochastic gradient descent (SGD) and online principal component analysis (PCA). We investigate t…
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
Lei Li, Jian-Guo Liu, Jianfeng Lu
We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of…
Convergence of Stochastic Interacting Particle Systems in Probability under a Sobolev Norm
Jian-Guo Liu, Yuan Zhang
In this paper, we consider particle systems with interaction and Brownian motion. We prove that when the initial data is from the sampling of Chorin's method, i.e., the initial ver…