On the Use of Bootstrap with Variational Inference

• Activity Number: 223 - Annals of Applied Statistics (AOAS) Lecture
• Type: Invited
• Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Elena A Erosheva* and Yen-Chi Chen and Y. Samuel Wang
• Companies: University of Washington and University of Washington and University of Washington

Abstract

Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models. It has been applied to approximate maximum likelihood estimators and to carry out Bayesian inference, however, quantification of uncertainty with variational inference remains challenging from both theoretical and practical perspectives. This paper is concerned with developing uncertainty measures for variational inference by using bootstrap procedures. We first develop two general bootstrap approaches for assessing the uncertainty of a variational estimate and study the underlying bootstrap theory. We then illustrate the bootstrap approach and our theoretical results in the context of mixed membership modeling with multivariate binary data on functional disability from the National Long-Term Care Survey. We carry out a two-sample approach to test for changes in the repeated measures of functional disability for the subset of individuals present in 1989 and 1994 waves.