Title: Theoretic and computational guarantee for mean-field variational Bayes methods on community detection
Authors: Anderson Ye Zhang - University of Chicago (United States) [presenting]
Abstract: Mean field variational inference is widely used in statistics and machine learning to approximate posterior distributions. Despite its popularity, there exist remarkably little fundamental theoretical justifications. The success of variational inference mainly lies in its iterative algorithm, which, to the best of our knowledge, has never been investigated for any high-dimensional or complex model. We will describe the statistics/computation interface of the iterative algorithm of mean field variational inference. We will study it from a frequentist perspective, quantifying it by posterior contraction. For community detection problem, we will show that the iterative algorithm has a linear convergence to the optimal statistical accuracy within log n iterations. The technique can be extended to analyzing Expectation- maximization and Gibbs sampler with similar guarantees obtained, which will be briefly described. The considered community detection problem provides a test case and playground, and it is promising to understand mean field under a general class of latent variable models.