Mean-field Variational Inference via Wasserstein Gradient Flow

Understand

Variational inference, such as the mean-field (MF) approximation, 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.
• In this work, we introduce a general computational framework to implement MF variational inference for Bayesian models, with or without latent variables, using the Wasserstein gradient flow (WGF), a modern mathematical technique for realizing a gradient flow over the space of probability measures.
• Theoretically, we analyze the algorithmic convergence of the proposed approaches, providing an explicit expression for the contraction factor.