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Leveraging the coherent exploration of Hamiltonian flow, Hamiltonian MonteCarlo produces computationally efficient Monte Carlo estimators, even withrespect to complex and high-dimensional target distributions. When confrontedwith data-intensive applications, however, the algorithm may be too expensiveto implement, leaving us to consider the utility of approximations such as datasubsampling. In this paper I demonstrate how data subsampling fundamentallycompromises the efficient exploration of Hamiltonian flow and hence thescalable performance of Hamiltonian Monte Carlo itself.

The Fundamental Incompatibility of Hamiltonian Monte Carlo and Data Subsampling