  Deep neural networks (DNNs) are known for their high prediction performance,
especially in perceptual tasks such as object recognition or autonomous
driving. Still, DNNs are prone to yield unreliable predictions when
encountering completely new situations without indicating their uncertainty.
Bayesian variants of DNNs (BDNNs), such as MC dropout BDNNs, do provide
uncertainty measures. However, BDNNs are slow during test time because they
rely on a sampling approach. Here we present a single shot MC dropout
approximation that preserves the advantages of BDNNs without being slower than
a DNN. Our approach is to analytically approximate for each layer in a fully
connected network the expected value and the variance of the MC dropout signal.
We evaluate our approach on different benchmark datasets and a simulated toy
example. We demonstrate that our single shot MC dropout approximation resembles
the point estimate and the uncertainty estimate of the predictive distribution
that is achieved with an MC approach, while being fast enough for real-time
deployments of BDNNs.
