Utilising Partial Momentum Refreshment in Separable Shadow Hamiltonian Hybrid Monte Carlo

Sampling using integrator-dependent shadow Hamiltonian’s has been shown to produce improved sampling properties relative to Hamiltonian Monte Carlo. The shadow Hamiltonian’s are typically non-separable, requiring the expensive generation of momenta, with the recent trend being...

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Autores principales:	Wilson Tsakane Mongwe, Rendani Mbuvha, Tshilidzi Marwala
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Bayesian neural networks Bayesian logistic regression Hamiltonian Monte Carlo partial momentum refreshment shadow Hamiltonian Monte Carlo Markov Chain Monte Carlo Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/84772ccb6be84cceb01509d3e9f1f426
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id	oai:doaj.org-article:84772ccb6be84cceb01509d3e9f1f426
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spelling	oai:doaj.org-article:84772ccb6be84cceb01509d3e9f1f4262021-11-17T00:00:33ZUtilising Partial Momentum Refreshment in Separable Shadow Hamiltonian Hybrid Monte Carlo2169-353610.1109/ACCESS.2021.3126812https://doaj.org/article/84772ccb6be84cceb01509d3e9f1f4262021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9610024/https://doaj.org/toc/2169-3536Sampling using integrator-dependent shadow Hamiltonian’s has been shown to produce improved sampling properties relative to Hamiltonian Monte Carlo. The shadow Hamiltonian’s are typically non-separable, requiring the expensive generation of momenta, with the recent trend being to utilise partial momentum refreshment. Separable Shadow Hamiltonian Hybrid Monte Carlo (S2HMC) employs a canonical transformation which results in the Hamiltonian being separable and makes use of a processed leapfrog integrator. In this work, we combine the benefit of sampling using S2HMC with partial momentum refreshment to create the Separable Shadow Hamiltonian Hybrid Monte Carlo with Partial Momentum Refreshment (PS2HMC) algorithm which leaves the target distribution invariant. Numerical experiments across various targets show that the proposed algorithm outperforms S2HMC and Shadow Hamiltonian Monte Carlo with partial momentum refreshment. Comprehensive analysis is performed on the Banana shaped distribution, multivariate Gaussian distributions of various dimensions, Bayesian logistic regression and Bayesian neural networks.Wilson Tsakane MongweRendani MbuvhaTshilidzi MarwalaIEEEarticleBayesian neural networksBayesian logistic regressionHamiltonian Monte Carlopartial momentum refreshmentshadow Hamiltonian Monte CarloMarkov Chain Monte CarloElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 9, Pp 151235-151244 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Bayesian neural networks Bayesian logistic regression Hamiltonian Monte Carlo partial momentum refreshment shadow Hamiltonian Monte Carlo Markov Chain Monte Carlo Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Bayesian neural networks Bayesian logistic regression Hamiltonian Monte Carlo partial momentum refreshment shadow Hamiltonian Monte Carlo Markov Chain Monte Carlo Electrical engineering. Electronics. Nuclear engineering TK1-9971 Wilson Tsakane Mongwe Rendani Mbuvha Tshilidzi Marwala Utilising Partial Momentum Refreshment in Separable Shadow Hamiltonian Hybrid Monte Carlo
description	Sampling using integrator-dependent shadow Hamiltonian’s has been shown to produce improved sampling properties relative to Hamiltonian Monte Carlo. The shadow Hamiltonian’s are typically non-separable, requiring the expensive generation of momenta, with the recent trend being to utilise partial momentum refreshment. Separable Shadow Hamiltonian Hybrid Monte Carlo (S2HMC) employs a canonical transformation which results in the Hamiltonian being separable and makes use of a processed leapfrog integrator. In this work, we combine the benefit of sampling using S2HMC with partial momentum refreshment to create the Separable Shadow Hamiltonian Hybrid Monte Carlo with Partial Momentum Refreshment (PS2HMC) algorithm which leaves the target distribution invariant. Numerical experiments across various targets show that the proposed algorithm outperforms S2HMC and Shadow Hamiltonian Monte Carlo with partial momentum refreshment. Comprehensive analysis is performed on the Banana shaped distribution, multivariate Gaussian distributions of various dimensions, Bayesian logistic regression and Bayesian neural networks.
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	Utilising Partial Momentum Refreshment in Separable Shadow Hamiltonian Hybrid Monte Carlo
title_short	Utilising Partial Momentum Refreshment in Separable Shadow Hamiltonian Hybrid Monte Carlo
title_full	Utilising Partial Momentum Refreshment in Separable Shadow Hamiltonian Hybrid Monte Carlo
title_fullStr	Utilising Partial Momentum Refreshment in Separable Shadow Hamiltonian Hybrid Monte Carlo
title_full_unstemmed	Utilising Partial Momentum Refreshment in Separable Shadow Hamiltonian Hybrid Monte Carlo
title_sort	utilising partial momentum refreshment in separable shadow hamiltonian hybrid monte carlo
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/84772ccb6be84cceb01509d3e9f1f426
work_keys_str_mv	AT wilsontsakanemongwe utilisingpartialmomentumrefreshmentinseparableshadowhamiltonianhybridmontecarlo AT rendanimbuvha utilisingpartialmomentumrefreshmentinseparableshadowhamiltonianhybridmontecarlo AT tshilidzimarwala utilisingpartialmomentumrefreshmentinseparableshadowhamiltonianhybridmontecarlo
_version_	1718426060192743424

Utilising Partial Momentum Refreshment in Separable Shadow Hamiltonian Hybrid Monte Carlo

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