A0384
Title: Mean-field variational inference via Wasserstein gradient flow
Authors: Rentian Yao - University of Illinois at Urbana Champaign (United States) [presenting]
Abstract: Variational inference, such as the Mean-Field (MF), requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on the variational approximation family. A computational framework is introduced to implement MF variational inference for Bayesian models, with or without latent variables, using the Wasserstein gradient flow (WGF), a modern mathematical technique for performing a gradient flow over the space of probability measures. Theoretically, the algorithmic convergence of the proposed approaches is analyzed, providing an explicit expression for the contraction factor. Existing results on MF variational posterior concentration from a polynomial to an exponential contraction are also strengthened by utilizing the fixed point equation of the time-discretized WGF. Computationally, a new constraint-free function approximation method is proposed using neural networks to numerically realize the algorithm. This method is shown to be more precise and efficient than traditional particle approximation methods based on Langevin dynamics.
