Dropout as a Bayesian Approximation: Representing Model Uncertainty in\n Deep Learning

Deep learning tools have gained tremendous attention in applied machine\nlearning. However such tools for regression and classification do not capture\nmodel uncertainty. In comparison, Bayesian models offer a mathematically\ngrounded framework to reason about model uncertainty, but usually come with a\nprohibitive computational cost. In this paper we develop a new theoretical\nframework casting dropout training in deep neural networks (NNs) as approximate\nBayesian inference in deep Gaussian processes. A direct result of this theory\ngives us tools to model uncertainty with dropout NNs -- extracting information\nfrom existing models that has been thrown away so far. This mitigates the\nproblem of representing uncertainty in deep learning without sacrificing either\ncomputational complexity or test accuracy. We perform an extensive study of the\nproperties of dropout's uncertainty. Various network architectures and\nnon-linearities are assessed on tasks of regression and classification, using\nMNIST as an example. We show a considerable improvement in predictive\nlog-likelihood and RMSE compared to existing state-of-the-art methods, and\nfinish by using dropout's uncertainty in deep reinforcement learning.\n