SILO: Variational inference – reconciling statistical and convergence guarantees

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.  I shall talk about a general theory to show how the choice of variational family is critical to good statistical performance of the algorithmic solution. I shall also present a few case studies, caution against potential pitfalls, and offer remedies.

Bio:

Dr. Debdeep Pati received his Ph.D. in Statistics from Duke University in 2012, prior to being on the faculty at Florida State from 2012-2017, at Texas A&M from 2017-2024 and at UW-Madison from 2024 onwards.  His research focuses on understanding statistical and computational trade-off for probabilistic inference in complex models. His research received the JASA reproducibility award in 2023 and he was the recipient of the Young Researcher Award from the International Indian Statistical Association in 2017 and obtained an honorable mention for Leonard J. Savage award for best Bayesian dissertation in the theory and methods section in 2013.