Bayesian posterior approximation with stochastic ensembles

We introduce ensembles of stochastic neural networks to approximate the Bayesian posterior, combining stochastic methods such as dropout with deep ensembles. The stochastic ensembles are formulated as families of distributions and trained to approximate the Bayesian posterior with variational inference. We implement stochastic ensembles based on Monte Carlo dropout, DropConnect and a novel non-parametric version of dropout and evaluate them on a toy problem and CIFAR image classification. For CIFAR, the stochastic ensembles are quantitatively compared to published Hamiltonian Monte Carlo results for a ResNet-20 architecture. We also test the quality of the posteriors directly against Hamiltonian Monte Carlo simulations in a simplified toy model. Our results show that in a number of settings, stochastic ensembles provide more accurate posterior estimates than regular deep ensembles.