Representing Model Uncertainty of Neural Networks in Sparse Information Form

This paper addresses the problem of representing a system's belief using multi-variate normal distributions (MND) where the underlying model is based on a deep neural network (DNN). The major challenge with DNNs is the computational complexity that is needed to obtain model uncertainty using MNDs. To achieve a scalable method, we propose a novel approach that expresses the parameter posterior in sparse information form. Our inference algorithm is based on a novel Laplace Approximation scheme, which involves a diagonal correction of the Kronecker-factored eigenbasis. As this makes the inversion of the information matrix intractable - an operation that is required for full Bayesian analysis, we devise a low-rank approximation of this eigenbasis and a memory-efficient sampling scheme. We provide both a theoretical analysis and an empirical evaluation on various benchmark data sets, showing the superiority of our approach over existing methods.