Scalable Stochastic Gradient Riemannian Langevin Dynamics in Non-Diagonal Metrics

Bayesian neural network inference is often carried out using stochastic gradient sampling methods. For best performance the methods should use a Riemannian metric that improves posterior exploration by accounting for the local curvature, but the existing methods resort to simple diagonal metrics to remain computationally efficient. This loses some of the gains. We propose two non-diagonal metrics that can be used in stochastic samplers to improve convergence and exploration but that have only a minor computational overhead over diagonal metrics. We show that for neural networks with complex posteriors, caused e.g. by use of sparsity-inducing priors, using these metrics provides clear improvements. For some other choices the posterior is sufficiently easy also for the simpler metrics.