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Variational inference is a general approach for approximating complex densityfunctions, such as those arising in latent variable models, popular in machinelearning. It has been applied to approximate the maximum likelihood estimatorand to carry out Bayesian inference, however, quantification of uncertaintywith variational inference remains challenging from both theoretical andpractical perspectives. This paper is concerned with developing uncertaintymeasures for variational inference by using bootstrap procedures. We firstdevelop two general bootstrap approaches for assessing the uncertainty of avariational estimate and the study the underlying bootstrap theory in bothfixed- and increasing-dimension settings. We then use the bootstrap approachand our theoretical results in the context of mixed membership modeling withmultivariate binary data on functional disability from the National Long TermCare Survey. We carry out a two-sample approach to test for changes in therepeated measures of functional disability for the subset of individualspresent in 1989 and 1994 waves.

On the use of bootstrap with variational inference: Theory, interpretation, and a two-sample test example