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Neural network gradient Hamiltonian Monte Carlo

Author

Listed:
  • Lingge Li

    (University of California)

  • Andrew Holbrook

    (University of California)

  • Babak Shahbaba

    (University of California)

  • Pierre Baldi

    (University of California)

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 to validate the proposed method.

Suggested Citation

  • Lingge Li & Andrew Holbrook & Babak Shahbaba & Pierre Baldi, 2019. "Neural network gradient Hamiltonian Monte Carlo," Computational Statistics, Springer, vol. 34(1), pages 281-299, March.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:1:d:10.1007_s00180-018-00861-z
    DOI: 10.1007/s00180-018-00861-z
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    Citations

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    Cited by:

    1. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver," CARF F-Series CARF-F-504, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2022.
    2. Han, Xiaohui & Dong, Jianping, 2023. "Applications of fractional gradient descent method with adaptive momentum in BP neural networks," Applied Mathematics and Computation, Elsevier, vol. 448(C).

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