A0393
Title: Variational bagging: A robust and scalable approach for Bayesian uncertainty quantification
Authors: Ilsang Ohn - Inha University (Korea, South) [presenting]
Abstract: A variational bagging approach that integrates a bagging procedure with variational Bayes is introduced, resulting in a bagged variational posterior, the average of variational posteriors obtained with multiple bootstrap samples, for improved inference. Strong theoretical guarantees for the method are established. First, a Bernstein-von Mises (BvM) theorem is derived for the bagged variational posterior, which ensures valid uncertainty quantification. The BvM theorem reveals that the bagged variational posterior provides reliable uncertainty quantification under model misspecification, while the standard posterior distribution may provide too optimistic uncertainty estimation. Another interesting implication of the BvM theorem is that even when using a mean-field variational family, the limiting behavior of the bagged variational posterior is quite similar to the standard posterior, as it can recover off-diagonal elements of the limiting covariance structure. That is, variational bagging provides a more accurate approximation of the posterior than usual variational Bayes. Posterior contraction rates are also established for general models, which implies that variational bagging conducts an optimal first-order inference. The advantages of the variational bagging approach are illustrated in several numerical examples.
