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Neural network gradient Hamiltonian Monte Carlo

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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 to validate the proposed method.

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References

  • Baldi P, Sadowski P (2016) A theory of local learning, the learning channel, and the optimality of backpropagation. Neural Netw 83:51–74

    Article  Google Scholar 

  • Betancourt M (2015) The fundamental incompatibility of Hamiltonian Monte Carlo and data subsampling. arXiv preprint arXiv:1502.01510

  • Chen T, Fox E, Guestrin C (2014) Stochastic gradient Hamiltonian Monte Carlo. In: International conference on machine learning, pp 1683–1691

  • Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst (MCSS) 2(4):303–314

    Article  MathSciNet  MATH  Google Scholar 

  • Huang GB, Zhu QY, Siew CK (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: Proceedings of IEEE international joint conference on neural networks, IEEE, vol 2, pp 985–990

  • Kingma D, Ba J (2014) Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980

  • Lan S, Bui-Thanh T, Christie M, Girolami M (2016) Emulation of higher-order tensors in manifold monte carlo methods for bayesian inverse problems. J Comput Phys 308:81–101

    Article  MathSciNet  MATH  Google Scholar 

  • Leimkuhler B, Reich S (2004) Simulating Hamiltonian dynamics, vol 14. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Neal RM (2012) Bayesian learning for neural networks, vol 118. Springer, New York

    MATH  Google Scholar 

  • Neal RM et al (2011) Mcmc using Hamiltonian dynamics. Handbook Markov Chain Monte Carlo 2:113–162

    MathSciNet  MATH  Google Scholar 

  • Rasmussen CE, Bernardo J, Bayarri M, Berger J, Dawid A, Heckerman D, Smith A, West M (2003) Gaussian processes to speed up hybrid monte carlo for expensive bayesian integrals. Bayesian Stat 7:651–659

    MathSciNet  Google Scholar 

  • Welling M, Teh YW (2011) Bayesian learning via stochastic gradient langevin dynamics. In: Proceedings of the 28th international conference on machine learning (ICML-11), pp 681–688

  • Zhang C, Shahbaba B, Zhao H (2017) Hamiltonian monte carlo acceleration using surrogate functions with random bases. Stat Comput 27:1473. https://doi.org/10.1007/s11222-016-9699-1

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Acknowledgements

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

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Authors and Affiliations

  1. Donald Bren School of Information and Computer Sciences, University of California, Irvine, USA

    Lingge Li, Babak Shahbaba & Pierre Baldi

  2. Department of Human Genetics, David Geffen School of Medicine, University of California, Los Angeles, USA

    Andrew Holbrook

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  1. Lingge Li
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  2. Andrew Holbrook
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  3. Babak Shahbaba
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  4. Pierre Baldi
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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). https://doi.org/10.1007/s00180-018-00861-z

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  • DOI: https://doi.org/10.1007/s00180-018-00861-z

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