On the Convergence of Coordinate Ascent Variational Inference

As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming increasingly popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable efficacy and superior efficiency. Several recent works provide theoretical justifications of VI by proving its statistical optimality for parameter estimation under various settings; meanwhile, formal analysis on the algorithmic convergence aspects of VI is still largely lacking. In this talk, we will discuss some recent advances towards studying convergence of the popular coordinate ascent variational inference algorithm. We will present some specific case studies and proceed to develop a general framework for studying such questions.