  Learning probability distributions on the weights of neural networks (NNs)
has recently proven beneficial in many applications. Bayesian methods, such as
Stein variational gradient descent (SVGD), offer an elegant framework to reason
about NN model uncertainty. However, by assuming independent Gaussian priors
for the individual NN weights (as often applied), SVGD does not impose prior
knowledge that there is often structural information (dependence) among
weights. We propose efficient posterior learning of structural weight
uncertainty, within an SVGD framework, by employing matrix variate Gaussian
priors on NN parameters. We further investigate the learned structural
uncertainty in sequential decision-making problems, including contextual
bandits and reinforcement learning. Experiments on several synthetic and real
datasets indicate the superiority of our model, compared with state-of-the-art
methods.
