Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) approach
that exhibits favourable exploration properties in high-dimensional models such
as neural networks. Unfortunately, HMC has limited use in large-data regimes
and little work has explored suitable approaches that aim to preserve the
entire Hamiltonian. In our work, we introduce a new symmetric integration
scheme for split HMC that does not rely on stochastic gradients. We show that
our new formulation is more efficient than previous approaches and is easy to
implement with a single GPU. As a result, we are able to perform full HMC over
common deep learning architectures using entire data sets. In addition, when we
compare with stochastic gradient MCMC, we show that our method achieves better
performance in both accuracy and uncertainty quantification. Our approach
demonstrates HMC as a feasible option when considering inference schemes for
large-scale machine learning problems.

本文研究了 Hamiltonian Monte Carlo 算法在大数据情况下应用的问题，提出了不依赖随机梯度的新对称积分方案，实现了全数据集的 HMC，并与随机梯度 MCMC 进行了比较。结果表明，该方法在准确性和不确定性量化方面均优于 SG-MCMC，且可应用于大规模机器学习问题的推断方案。