Conditionally Factorized Variational Bayes with Importance Sampling

Coordinate ascent variational inference (CAVI) is a popular approximate inference method; however, it relies on a mean-field assumption that can lead to large estimation errors for highly correlated variables. In this paper, we propose a conditionally factorized variational family with an adjustable conditional structure and derive the corresponding coordinate ascent algorithm for optimization. The algorithm is termed Conditionally factorized Variational Bayes (CVB) and implemented with importance sampling. We show that by choosing a finer conditional structure, our algorithm can be guaranteed to achieve a better variational lower bound, thus providing a flexible trade-off between computational cost and inference accuracy. The validity of the method is demonstrated in a simple posterior computation task.