Quantum-Inspired Magnetic Hamiltonian Monte Carlo

Wilson Tsakane Mongwe, Rendani Mbuvha, Tshilidzi Marwala
<span title="2021-10-05">2021</span> <i title="Public Library of Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s3gm7274mfe6fcs7e3jterqlri" style="color: black;">PLoS ONE</a> </i> &nbsp;
Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo algorithm that is able to generate distant proposals via the use of Hamiltonian dynamics, which are able to incorporate first-order gradient information about the target posterior. This has driven its rise in popularity in the machine learning community in recent times. It has been shown that making use of the energy-time uncertainty relation from quantum mechanics, one can devise an extension to HMC by allowing the mass matrix to be
more &raquo; ... ndom with a probability distribution instead of a fixed mass. Furthermore, Magnetic Hamiltonian Monte Carlo (MHMC) has been recently proposed as an extension to HMC and adds a magnetic field to HMC which results in non-canonical dynamics associated with the movement of a particle under a magnetic field. In this work, we utilise the non-canonical dynamics of MHMC while allowing the mass matrix to be random to create the Quantum-Inspired Magnetic Hamiltonian Monte Carlo (QIMHMC) algorithm, which is shown to converge to the correct steady state distribution. Empirical results on a broad class of target posterior distributions show that the proposed method produces better sampling performance than HMC, MHMC and HMC with a random mass matrix.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pone.0258277">doi:10.1371/journal.pone.0258277</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/34610053">pmid:34610053</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC8491946/">pmcid:PMC8491946</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iatt2xwovnfnfnltoczx7ulwgm">fatcat:iatt2xwovnfnfnltoczx7ulwgm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211011103342/https://storage.googleapis.com/plos-corpus-prod/10.1371/journal.pone.0258277/1/pone.0258277.pdf?X-Goog-Algorithm=GOOG4-RSA-SHA256&amp;X-Goog-Credential=wombat-sa%40plos-prod.iam.gserviceaccount.com%2F20211011%2Fauto%2Fstorage%2Fgoog4_request&amp;X-Goog-Date=20211011T103341Z&amp;X-Goog-Expires=86400&amp;X-Goog-SignedHeaders=host&amp;X-Goog-Signature=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" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6b/20/6b204a2a8cc4ee8e5836301afa237f50aa02551c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pone.0258277"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> plos.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8491946" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>