Adaptive Magnetic Hamiltonian Monte Carlo

Magnetic Hamiltonian Monte Carlo (MHMC) is a Markov Chain Monte Carlo method that expands on Hamiltonian Monte Carlo (HMC) by adding a magnetic field to Hamiltonian dynamics. This magnetic field offers a great deal of flexibility over HMC and encourages more efficient exploration of the target poste...

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Autores principales:	Wilson Tsakane Mongwe, Rendani Mbuvha, Tshilidzi Marwala
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Bayesian logistic regression jump diffusion processes adaptive Magnetic Hamiltonian Monte Carlo Markov Chain Monte Carlo Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/11741b05895b4cef99bef5d3b1f5ec8a
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id	oai:doaj.org-article:11741b05895b4cef99bef5d3b1f5ec8a
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spelling	oai:doaj.org-article:11741b05895b4cef99bef5d3b1f5ec8a2021-11-20T00:03:07ZAdaptive Magnetic Hamiltonian Monte Carlo2169-353610.1109/ACCESS.2021.3127931https://doaj.org/article/11741b05895b4cef99bef5d3b1f5ec8a2021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9614186/https://doaj.org/toc/2169-3536Magnetic Hamiltonian Monte Carlo (MHMC) is a Markov Chain Monte Carlo method that expands on Hamiltonian Monte Carlo (HMC) by adding a magnetic field to Hamiltonian dynamics. This magnetic field offers a great deal of flexibility over HMC and encourages more efficient exploration of the target posterior. This results in faster convergence and lower autocorrelations in the generated samples compared to HMC. However, as with HMC, MHMC is sensitive to the user specified trajectory length and step size. Automatically setting the parameters of MHMC is yet to be considered in the literature. In this work, we present the Adaptive MHMC (A-MHMC) algorithm which extends MHMC in that it automatically sets the parameters of MHMC and thus eliminates the need for the user to manually set a trajectory length and step size. The trajectory length adaptation is based on an extension of the No-U-Turn Sampler (NUTS) methodology to incorporate the magnetic field present in MHMC, while the step size is set via dual averaging during the burn-in period. Empirical results based on experiments performed on jump diffusion processes calibrated to real world financial market data, a simulation study using multivariate Gaussian distributions and real world benchmark datasets modelled using Bayesian Logistic Regression show that A-MHMC outperforms MHMC and NUTS on an effective sample size basis. In addition, A-MHMC provides significant relative speed up (up to 40 times) over MHMC and produces similar time normalised effective samples sizes relative to NUTS.Wilson Tsakane MongweRendani MbuvhaTshilidzi MarwalaIEEEarticleBayesian logistic regressionjump diffusion processesadaptiveMagnetic Hamiltonian Monte CarloMarkov Chain Monte CarloElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 9, Pp 152993-153003 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Bayesian logistic regression jump diffusion processes adaptive Magnetic Hamiltonian Monte Carlo Markov Chain Monte Carlo Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Bayesian logistic regression jump diffusion processes adaptive Magnetic Hamiltonian Monte Carlo Markov Chain Monte Carlo Electrical engineering. Electronics. Nuclear engineering TK1-9971 Wilson Tsakane Mongwe Rendani Mbuvha Tshilidzi Marwala Adaptive Magnetic Hamiltonian Monte Carlo
description	Magnetic Hamiltonian Monte Carlo (MHMC) is a Markov Chain Monte Carlo method that expands on Hamiltonian Monte Carlo (HMC) by adding a magnetic field to Hamiltonian dynamics. This magnetic field offers a great deal of flexibility over HMC and encourages more efficient exploration of the target posterior. This results in faster convergence and lower autocorrelations in the generated samples compared to HMC. However, as with HMC, MHMC is sensitive to the user specified trajectory length and step size. Automatically setting the parameters of MHMC is yet to be considered in the literature. In this work, we present the Adaptive MHMC (A-MHMC) algorithm which extends MHMC in that it automatically sets the parameters of MHMC and thus eliminates the need for the user to manually set a trajectory length and step size. The trajectory length adaptation is based on an extension of the No-U-Turn Sampler (NUTS) methodology to incorporate the magnetic field present in MHMC, while the step size is set via dual averaging during the burn-in period. Empirical results based on experiments performed on jump diffusion processes calibrated to real world financial market data, a simulation study using multivariate Gaussian distributions and real world benchmark datasets modelled using Bayesian Logistic Regression show that A-MHMC outperforms MHMC and NUTS on an effective sample size basis. In addition, A-MHMC provides significant relative speed up (up to 40 times) over MHMC and produces similar time normalised effective samples sizes relative to NUTS.
format	article
author	Wilson Tsakane Mongwe Rendani Mbuvha Tshilidzi Marwala
author_facet	Wilson Tsakane Mongwe Rendani Mbuvha Tshilidzi Marwala
author_sort	Wilson Tsakane Mongwe
title	Adaptive Magnetic Hamiltonian Monte Carlo
title_short	Adaptive Magnetic Hamiltonian Monte Carlo
title_full	Adaptive Magnetic Hamiltonian Monte Carlo
title_fullStr	Adaptive Magnetic Hamiltonian Monte Carlo
title_full_unstemmed	Adaptive Magnetic Hamiltonian Monte Carlo
title_sort	adaptive magnetic hamiltonian monte carlo
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/11741b05895b4cef99bef5d3b1f5ec8a
work_keys_str_mv	AT wilsontsakanemongwe adaptivemagnetichamiltonianmontecarlo AT rendanimbuvha adaptivemagnetichamiltonianmontecarlo AT tshilidzimarwala adaptivemagnetichamiltonianmontecarlo
_version_	1718419819785617408

Adaptive Magnetic Hamiltonian Monte Carlo

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