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