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Neural network gradient Hamiltonian Monte Carlo

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Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the algorithm requires repeated gradient calculations, and these computations become increasingly burdensome as data sets scale. We present a method to substantially reduce the computation burden by using a neural network to approximate the gradient. First, we prove that the proposed method still maintains convergence to the true distribution though the approximated gradient no longer comes from a Hamiltonian system. Second, we conduct experiments on synthetic examples and real data to validate the proposed method.

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Babak Shahbaba is supported by NSF Grant DMS1622490 and NIH Grant R01MH115697.

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Correspondence to Lingge Li.

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Li, L., Holbrook, A., Shahbaba, B. et al. Neural network gradient Hamiltonian Monte Carlo. Comput Stat 34, 281–299 (2019).

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