ANC Workshop - Kai Xu and James Ritchie

Speaker: Kai Xu

Title: Couplings for Multinomial Hamiltonian Monte Carlo

Abstract:  HMC is a popular MCMC method in Bayesian inference. Recently, Heng & Jacob (2019) studied Metropolis HMC with couplings for unbiased Monte Carlo estimation, establishing a generic parallelizable scheme for HMC. However, in practice a different HMC method, multinomial HMC, is considered as the go-to method, e.g. as part of the no-U-turn sampler. In multinomial HMC, proposed states are not limited to end-points as in Metropolis HMC; instead points along the entire trajectory can be proposed. In this talk, I will introduce unbiased MCMC via couplings, and discuss how to establish couplings for multinomial HMC, based on optimal transport for multinomial sampling in its transition. Compared to Heng & Jacob (2019), coupled multinomial HMC generally attains a smaller meeting time, and is more robust to choices of step sizes and trajectory lengths, which allows re-use of existing adaptation methods for HMC. These improvements together make coupled HMC methods more practical.

The talk is based on the AISTATS paper: http://proceedings.mlr.press/v130/xu21i.html

Speaker: James Ritchie

Title: to follow

Abstract:  to follow