Learning Structured Weight Uncertainty in Bayesian Neural Networks

Deep neural networks (DNNs) are increasingly popular in modern machine learning. Bayesian learning affords the opportunity to quantify posterior uncertainty on DNN model parameters. Most existing work adopts independent Gaussian priors on the model weights, ignoring possible structural information. In this paper, we consider the matrix variate Gaussian (MVG) distribution to model structured correlations within the weights of a DNN. To make posterior inference feasible, a reparametrization is proposed for the MVG prior, simplifying the complex MVG-based model to an equivalent yet simpler model with independent Gaussian priors on the transformed weights. Consequently, we develop a scalable Bayesian online inference algorithm by adopting the recently proposed probabilistic backpropagation framework. Experiments on several synthetic and real datasets indicate the superiority of our model, achieving competitive performance in terms of model likelihood and predictive root mean square error. Importantly, it also yields faster convergence speed compared to related Bayesian DNN models.