Magnetic Hamiltonian Monte Carlo With Partial Momentum Refreshment
Magnetic Hamiltonian Monte Carlo (MHMC) has been shown to provide more efficient sampling of the target posterior compared to Hamiltonian Monte Carlo (HMC). It achieves this by utilising a user specified magnetic field and the resultant non-canonical Hamiltonian dynamics. This is important for multi...
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doaj-f066d6777b0745d698d867ae938d2b402021-08-06T23:00:36ZengIEEEIEEE Access2169-35362021-01-01910800910801610.1109/ACCESS.2021.31018109503422Magnetic Hamiltonian Monte Carlo With Partial Momentum RefreshmentWilson Tsakane Mongwe0https://orcid.org/0000-0003-2832-3584Rendani Mbuvha1https://orcid.org/0000-0002-7337-9176Tshilidzi Marwala2School of Electrical Engineering, University of Johannesburg, Auckland Park, South AfricaSchool of Statistics and Actuarial Science, University of Witwatersrand, Johannesburg, South AfricaSchool of Electrical Engineering, University of Johannesburg, Auckland Park, South AfricaMagnetic Hamiltonian Monte Carlo (MHMC) has been shown to provide more efficient sampling of the target posterior compared to Hamiltonian Monte Carlo (HMC). It achieves this by utilising a user specified magnetic field and the resultant non-canonical Hamiltonian dynamics. This is important for multi-modal distributions which are common in machine learning. In generating each sample in MHMC and HMC, the auxiliary momentum variable is fully regenerated from a Gaussian distribution. Partially updating the momentum has previously been employed in HMC to improve sampling behaviour. It has also been used in the context of sampling using integrator dependent shadow Hamiltonian Monte Carlo methods. In this work, we combine the sampling benefits of non-canonical Hamiltonian dynamics offered by MHMC with partial momentum refreshment to create the Magnetic Hamiltonian Monte Carlo with Partial Momentum Refreshment (PMHMC) algorithm. Numerical experiments across various target posterior distributions show that the proposed method outperforms HMC, MHMC and HMC with partial momentum refreshment across all the metrics considered.https://ieeexplore.ieee.org/document/9503422/Hamiltonian Monte Carlopartial momentum refreshmentMagnetic Hamiltonian Monte CarloMarkov Chain Monte Carlo |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Wilson Tsakane Mongwe Rendani Mbuvha Tshilidzi Marwala |
spellingShingle |
Wilson Tsakane Mongwe Rendani Mbuvha Tshilidzi Marwala Magnetic Hamiltonian Monte Carlo With Partial Momentum Refreshment IEEE Access Hamiltonian Monte Carlo partial momentum refreshment Magnetic Hamiltonian Monte Carlo Markov Chain Monte Carlo |
author_facet |
Wilson Tsakane Mongwe Rendani Mbuvha Tshilidzi Marwala |
author_sort |
Wilson Tsakane Mongwe |
title |
Magnetic Hamiltonian Monte Carlo With Partial Momentum Refreshment |
title_short |
Magnetic Hamiltonian Monte Carlo With Partial Momentum Refreshment |
title_full |
Magnetic Hamiltonian Monte Carlo With Partial Momentum Refreshment |
title_fullStr |
Magnetic Hamiltonian Monte Carlo With Partial Momentum Refreshment |
title_full_unstemmed |
Magnetic Hamiltonian Monte Carlo With Partial Momentum Refreshment |
title_sort |
magnetic hamiltonian monte carlo with partial momentum refreshment |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2021-01-01 |
description |
Magnetic Hamiltonian Monte Carlo (MHMC) has been shown to provide more efficient sampling of the target posterior compared to Hamiltonian Monte Carlo (HMC). It achieves this by utilising a user specified magnetic field and the resultant non-canonical Hamiltonian dynamics. This is important for multi-modal distributions which are common in machine learning. In generating each sample in MHMC and HMC, the auxiliary momentum variable is fully regenerated from a Gaussian distribution. Partially updating the momentum has previously been employed in HMC to improve sampling behaviour. It has also been used in the context of sampling using integrator dependent shadow Hamiltonian Monte Carlo methods. In this work, we combine the sampling benefits of non-canonical Hamiltonian dynamics offered by MHMC with partial momentum refreshment to create the Magnetic Hamiltonian Monte Carlo with Partial Momentum Refreshment (PMHMC) algorithm. Numerical experiments across various target posterior distributions show that the proposed method outperforms HMC, MHMC and HMC with partial momentum refreshment across all the metrics considered. |
topic |
Hamiltonian Monte Carlo partial momentum refreshment Magnetic Hamiltonian Monte Carlo Markov Chain Monte Carlo |
url |
https://ieeexplore.ieee.org/document/9503422/ |
work_keys_str_mv |
AT wilsontsakanemongwe magnetichamiltonianmontecarlowithpartialmomentumrefreshment AT rendanimbuvha magnetichamiltonianmontecarlowithpartialmomentumrefreshment AT tshilidzimarwala magnetichamiltonianmontecarlowithpartialmomentumrefreshment |
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1721217216003702784 |