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Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) approachthat exhibits favourable exploration properties in high-dimensional models suchas neural networks. Unfortunately, HMC has limited use in large-data regimesand little work has explored suitable approaches that aim to preserve theentire Hamiltonian. In our work, we introduce a new symmetric integrationscheme for split HMC that does not rely on stochastic gradients. We show thatour new formulation is more efficient than previous approaches and is easy toimplement with a single GPU. As a result, we are able to perform full HMC overcommon deep learning architectures using entire data sets. In addition, when wecompare with stochastic gradient MCMC, we show that our method achieves betterperformance in both accuracy and uncertainty quantification. Our approachdemonstrates HMC as a feasible option when considering inference schemes forlarge-scale machine learning problems.

Scaling Hamiltonian Monte Carlo Inference for Bayesian Neural Networks with Symmetric Splitting