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The Fundamental Incompatibility of Hamiltonian Monte Carlo and Data Subsampling

Leveraging the coherent exploration of Hamiltonian flow, Hamiltonian Monte Carlo produces computationally efficient Monte Carlo estimators, even with respect to complex and high-dimensional target distributions. When confronted with data-intensive applications, however, the algorithm may be too expensive to implement, leaving us to consider the utility of approximations such as data subsampling. In this paper I demonstrate how data subsampling fundamentally compromises the efficient exploration of Hamiltonian flow and hence the scalable performance of Hamiltonian Monte Carlo itself.