NDLI: Split Hamiltonian Monte Carlo

Content Provider	Springer Nature Link
Author	Shahbaba, Babak Lan, Shiwei Johnson, Wesley O. Neal, Radford M.
Copyright Year	2013
Abstract	We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by “splitting” the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is possible is when the log density of the distribution of interest (the potential energy function) can be written as the log of a Gaussian density, which is a quadratic function, plus a slowly-varying function. Hamiltonian dynamics for quadratic energy functions can be analytically solved. With the splitting technique, only the slowly-varying part of the energy needs to be handled numerically, and this can be done with a larger stepsize (and hence fewer steps) than would be necessary with a direct simulation of the dynamics. Another context where splitting helps is when the most important terms of the potential energy function and its gradient can be evaluated quickly, with only a slowly-varying part requiring costly computations. With splitting, the quick portion can be handled with a small stepsize, while the costly portion uses a larger stepsize. We show that both of these splitting approaches can reduce the computational cost of sampling from the posterior distribution for a logistic regression model, using either a Gaussian approximation centered on the posterior mode, or a Hamiltonian split into a term that depends on only a small number of critical cases, and another term that involves the larger number of cases whose influence on the posterior distribution is small.
Starting Page	339
Ending Page	349
Page Count	11
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	24
Issue Number	3
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2013-01-24
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Markov chain Monte Carlo Hamiltonian dynamics Bayesian analysis Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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