2021/10/07 by Zheyang Shen, Markus Heinonen, Shen, Zheyang +3
Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2110.03768
openalex publication_date 2021/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.