A Variational View on Bootstrap Ensembles as Bayesian Inference

TL;DR

This paper uses variational principles to connect ensemble methods for neural networks with Bayesian inference, providing theoretical insights and experimental validation for ensemble approaches as approximate Bayesian methods.

Contribution

It introduces a variational framework linking ensemble methods to Bayesian inference, with geometric conditions that explain ensemble behavior without specific distribution assumptions.

Findings

Ensemble methods can approximate Bayesian inference effectively.

Theoretical conditions for ensemble convergence to the posterior.

Experimental results support the validity of ensemble as Bayesian approximation.

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. We derive conditions under which any optimization steps of the particles makes the associated distribution reduce its divergence to the posterior over model parameters. Such conditions do not require any particular form for the approximation and they are purely geometrical, giving insights on the behavior of the ensemble on a number of interesting models such as Neural Networks with ReLU activations. Experiments confirm that ensemble methods can be a valid alternative to approximate Bayesian inference; the theoretical developments in the paper seek to explain this behavior.