Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selection

Understand

Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference.

• The core idea is to trade statistical accuracy for computational efficiency.
• In this work, we study these statistical and computational trade-offs in variational inference via a case study in inferential model selection.
• Focusing on Gaussian inferential models (or variational approximating families) with diagonal plus low-rank precision matrices, we initiate a theoretical study of the trade-offs in two aspects, Bayesian posterior inference error and frequentist uncertainty quantification error.