Zu Chongzhi Research Seminar

Date and Time (China standard time): Thursday, Oct 30, 10:00 am – 11:00 am

Location: IB 1011

Zoom: 986 7682 5929, Passcode: dkumath

Title: A generalized discontinuous Hamilton Monte Carlo for transdimensional sampling

Speaker: Lei Li, Shanghai Jiao Tong Unviersity 

Abstract: We propose a discontinuous Hamilton Monte Carlo (DHMC) to sample from dimensional varying distributions, and particularly the grand canonical ensemble. The DHMC was proposed in [Biometrika, 107(2)] for discontinuous potential where the variable has a fixed dimension. When the dimension changes, there is no clear explanation of the volume-preserving property, and the conservation of energy is also not necessary. We use a random sampling for the extra dimensions, which corresponds to a measure transform. We show that when the energy is corrected suitably for the trans-dimensional Hamiltonian dynamics, the detailed balance condition is then satisfied. For the grand canonical ensemble, such a procedure can be explained very naturally to be the extra free energy change brought by the newly added particles, which justifies the rationality of our approach.

Bio: Lei Li is currently an associate professor in the Institute of Natural Sciences and the School of Mathematical Scieces at Shanghai Jiao Tong Unviersity (SJTU). He obtained his B.S. from Tsinghua University in 2010 and Ph.D. from the University of Wisconsin-Madison in 2015. Then, he was an assistant research professor at Duke University, and joined SJTU in 2018. His main research interest is in applied mathematics, especially designing and analyzing numerical methods for stochastic models arising from physics and data sciences. Currently, he is focusing on simulation methods and sampling algorithms for the interacting particle systems and data science.