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.
KeywordsBayesian inference MCMC Neural networks
Babak Shahbaba is supported by NSF Grant DMS1622490 and NIH Grant R01MH115697.
- 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 1683–1691Google 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 985–990Google Scholar
- Kingma D, Ba J (2014) Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980
- 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 681–688Google Scholar
- 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