  Learning in deep models using Bayesian methods has generated significant
attention recently. This is largely because of the feasibility of modern
Bayesian methods to yield scalable learning and inference, while maintaining a
measure of uncertainty in the model parameters. Stochastic gradient MCMC
algorithms (SG-MCMC) are a family of diffusion-based sampling methods for
large-scale Bayesian learning. In SG-MCMC, multivariate stochastic gradient
thermostats (mSGNHT) augment each parameter of interest, with a momentum and a
thermostat variable to maintain stationary distributions as target posterior
distributions. As the number of variables in a continuous-time diffusion
increases, its numerical approximation error becomes a practical bottleneck, so
better use of a numerical integrator is desirable. To this end, we propose use
of an efficient symmetric splitting integrator in mSGNHT, instead of the
traditional Euler integrator. We demonstrate that the proposed scheme is more
accurate, robust, and converges faster. These properties are demonstrated to be
desirable in Bayesian deep learning. Extensive experiments on two canonical
models and their deep extensions demonstrate that the proposed scheme improves
general Bayesian posterior sampling, particularly for deep models.
