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In this paper, we employ variational arguments to establish a connectionbetween ensemble methods for Neural Networks and Bayesian inference. Weconsider an ensemble-based scheme where each model/particle corresponds to aperturbation of the data by means of parametric bootstrap and a perturbation ofthe prior. We derive conditions under which any optimization steps of theparticles makes the associated distribution reduce its divergence to theposterior over model parameters. Such conditions do not require any particularform for the approximation and they are purely geometrical, giving insights onthe behavior of the ensemble on a number of interesting models such as NeuralNetworks with ReLU activations. Experiments confirm that ensemble methods canbe a valid alternative to approximate Bayesian inference; the theoreticaldevelopments in the paper seek to explain this behavior.

A Variational View on Bootstrap Ensembles as Bayesian Inference