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We present a novel approach for training deep neural networks in a Bayesianway. Classical, i.e. non-Bayesian, deep learning has two major drawbacks bothoriginating from the fact that network parameters are considered to bedeterministic. First, model uncertainty cannot be measured thus limiting theuse of deep learning in many fields of application and second, training of deepneural networks is often hampered by overfitting. The proposed approach usesvariational inference to approximate the intractable a posteriori distributionon basis of a normal prior. The variational density is designed in such a waythat the a posteriori uncertainty of the network parameters is represented pernetwork layer and depending on the estimated parameter expectation values. Thisway, only a few additional parameters need to be optimized compared to anon-Bayesian network. We apply this Bayesian approach to train and test theLeNet architecture on the MNIST dataset. Compared to classical deep learning,the test error is reduced by 15%. In addition, the trained model containsinformation about the parameter uncertainty in each layer. We show that thisinformation can be used to calculate credible intervals for the prediction andto optimize the network architecture for a given training data set.

Variational Inference to Measure Model Uncertainty in Deep Neural Networks