Neural Network Gradient Hamiltonian Monte Carlo

Lingge Li; Andrew Holbrook; Babak Shahbaba; Pierre Baldi

doi:10.1007/s00180-018-00861-z

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arXiv · 1711.05307

Neural Network Gradient Hamiltonian Monte Carlo

Lingge Li·Andrew Holbrook·Babak Shahbaba·Pierre Baldi

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Abstract

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 sets to validate the proposed method.

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BibTeX RIS

Lingge Li, Andrew Holbrook, Babak Shahbaba, Pierre Baldi. 2017-11-14. Neural Network Gradient Hamiltonian Monte Carlo. https://doi.org/10.1007/s00180-018-00861-z

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