Open Access
June 2018 On the use of bootstrap with variational inference: Theory, interpretation, and a two-sample test example
Yen-Chi Chen, Y. Samuel Wang, Elena A. Erosheva
Ann. Appl. Stat. 12(2): 846-876 (June 2018). DOI: 10.1214/18-AOAS1169


Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator 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 the study the underlying bootstrap theory in both fixed- and increasing-dimension settings. We then use 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.


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Yen-Chi Chen. Y. Samuel Wang. Elena A. Erosheva. "On the use of bootstrap with variational inference: Theory, interpretation, and a two-sample test example." Ann. Appl. Stat. 12 (2) 846 - 876, June 2018.


Received: 1 November 2017; Revised: 1 April 2018; Published: June 2018
First available in Project Euclid: 28 July 2018

zbMATH: 06980478
MathSciNet: MR3834288
Digital Object Identifier: 10.1214/18-AOAS1169

Keywords: bootstrap , increasing dimension , mixed membership model , two-sample test , variational inference

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.12 • No. 2 • June 2018
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