A0350
Title: Particle variational Bayes
Authors: Minh-Ngoc Tran - University of Sydney (Australia) [presenting]
Paco Tseng - University of Sydney (Australia)
Robert Kohn - University of New South Wales (Australia)
Abstract: Variational Bayes (VB) is widely recognised as a highly efficient and scalable technique for Bayesian inference. However, classical VB often imposes restrictions on the space of variational distributions, typically restricting it to a specific set of parametric distributions or factorised distributions. Ways to relax these restrictions by traversing a set of particles are explored to approximate the target distribution. The theoretical basis of this Particle VB method can be established using the Optimal Transport theory, which allows us to make the space of probability measures into a differential manifold. The focus is particularly on the novel Particle Mean Field Variational Bayes (PMFVB) approach, which extends the classical MFVB method without requiring conjugate priors or analytical calculations. The theoretical basis of the new method by leveraging the connection between Wasserstein gradient flows and Langevin diffusion dynamics is established. The effectiveness of this approach is demonstrated using Bayesian logistic regression, stochastic volatility, and deep neural networks.
