Abstract

Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions. For example, Langevin dynamics (LD) extracts asymptotically exact samples from a diffusion process because the time evolution of its marginal distributions constitutes a curve that minimizes the KL-divergence via steepest descent in the Wasserstein space. Parallel to LD, Stein variational gradient descent (SVGD) similarly minimizes the KL, albeit endowed with a novel Stein-Wasserstein distance, by deterministically transporting a set of particle samples, thus de-randomizes the stochastic diffusion process. We propose de-randomized kernel-based particle samplers to all diffusion-based samplers known as MCMC dynamics. Following previous work in interpreting MCMC dynamics, we equip the Stein-Wasserstein space with a fiber-Riemannian Poisson structure, with the capacity of characterizing a fiber-gradient Hamiltonian flow that simulates MCMC dynamics. Such dynamics discretizes into generalized SVGD (GSVGD), a Stein-type deterministic particle sampler, with particle updates coinciding with applying the diffusion Stein operator to a kernel function. We demonstrate empirically that GSVGD can de-randomize complex MCMC dynamics, which combine the advantages of auxiliary momentum variables and Riemannian structure, while maintaining the high sample quality from an interacting particle system.
Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)
Number of pages11
Publication statusPublished - 2021
MoE publication typeA4 Article in a conference publication
EventConference on Neural Information Processing Systems - Virtual, Online
Duration: 6 Dec 202114 Dec 2021
Conference number: 35
https://neurips.cc

Publication series

NameAdvances in Neural Information Processing Systems
PublisherMorgan Kaufmann Publishers
ISSN (Print)1049-5258

Conference

ConferenceConference on Neural Information Processing Systems
Abbreviated titleNeurIPS
CityVirtual, Online
Period06/12/202114/12/2021
Internet address

Fingerprint

Dive into the research topics of 'De-randomizing MCMC dynamics with the diffusion Stein operator'. Together they form a unique fingerprint.

Cite this