A Jensen-Shannon Divergence Based Loss Function for Bayesian Neural Networks

Kullback-Leibler (KL) divergence is widely used for variational inference of Bayesian Neural Networks (BNNs). However, the KL divergence has limitations such as unboundedness and asymmetry. We examine the Jensen-Shannon (JS) divergence that is more general, bounded, and symmetric. We formulate a novel loss function for BNNs based on the geometric JS divergence and show that the conventional KL divergence-based loss function is its special case. We evaluate the divergence part of the proposed loss function in a closed form for a Gaussian prior. For any other general prior, Monte Carlo approximations can be used. We provide algorithms for implementing both of these cases. We demonstrate that the proposed loss function offers an additional parameter that can be tuned to control the degree of regularisation. We derive the conditions under which the proposed loss function regularises better than the KL divergence-based loss function for Gaussian priors and posteriors. We demonstrate performance improvements over the state-of-the-art KL divergence-based BNN on the classification of a noisy CIFAR data set and a biased histopathology data set.Comment: To be submitted for peer review in IEE