Hamiltonian Monte Carlo with Energy Conserving Subsampling

Khue-Dung Dang, Matias Quiroz (), Robert Kohn (), Minh-Ngoc Tran and Mattias Villani
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Khue-Dung Dang: School of Economics, UNSW Business School, University of New South Wales, ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)
Matias Quiroz: School of Economics, UNSW Business School, University of New South Wales, ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), Research Division, Sveriges Riksbank, Postal: Sveriges Riksbank, SE-103 37 Stockholm, Sweden
Minh-Ngoc Tran: ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), Discipline of Business Analytics, University of Sidney

No 372, Working Paper Series from Sveriges Riksbank (Central Bank of Sweden)

Abstract: Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC computationally costly, especially in problems with large datasets, since it is necessary to compute posterior densities and their derivatives with respect to the parameters. Naively computing the Hamiltonian dynamics on a subset of the data causes HMC to lose its key ability to generate distant parameter proposals with high acceptance probability. The key insight in our article is that efficient subsampling HMC for the parameters is possible if both the dynamics and the acceptance probability are computed from the same data subsample in each complete HMC iteration. We show that this is possible to do in a principled way in a HMC-within-Gibbs framework where the subsample is updated using a pseudo marginal MH step and the parameters are then updated using an HMC step, based on the current subsample. We show that our subsampling methods are fast and compare favorably to two popular sampling algorithms that utilize gradient estimates from data subsampling. We also explore the current limitations of subsampling HMC algorithms by varying the quality of the variance reducing control variates used in the estimators of the posterior density and its gradients.

Keywords: Large datasets; Bayesian inference; Stochastic gradient (search for similar items in EconPapers)
JEL-codes: C11 C15 C55 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2019-04-01
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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