Parametric Bootstrap Ensembles as Variational Inference

Dimitrios Milios, Pietro Michiardi, Maurizio Filippone

Keywords: bootstrap, bayesian inference, variational methods

Abstract: In this paper, we employ variational arguments to establish a connection between ensemble methods for Neural Networks and Bayesian inference. We consider an ensemble-based scheme where each model/particle corresponds to a perturbation of the data by means of parametric bootstrap and a perturbation of the prior. Our goal is to characterize the ensemble distribution in terms of the the Bayesian posterior. We derive conditions under which any optimization steps of the particles makes the associated distribution reduce its divergence to the posterior over model parameters.