Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines

Abstract We propose an efficient algorithm to solve inverse problems in the presence of binary clustered datasets. We consider the paradigmatic Hopfield model in a teacher student scenario, where this situation is found in the retrieval phase. This problem has been widely analyzed through various me...

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Autores principales:	Aurelien Decelle, Sungmin Hwang, Jacopo Rocchi, Daniele Tantari
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/89bc6fdcef6349f9af24896d9e340420
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spelling	oai:doaj.org-article:89bc6fdcef6349f9af24896d9e3404202021-12-02T18:01:48ZInverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines10.1038/s41598-021-99353-22045-2322https://doaj.org/article/89bc6fdcef6349f9af24896d9e3404202021-10-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-99353-2https://doaj.org/toc/2045-2322Abstract We propose an efficient algorithm to solve inverse problems in the presence of binary clustered datasets. We consider the paradigmatic Hopfield model in a teacher student scenario, where this situation is found in the retrieval phase. This problem has been widely analyzed through various methods such as mean-field approaches or the pseudo-likelihood optimization. Our approach is based on the estimation of the posterior using the Thouless–Anderson–Palmer (TAP) equations in a parallel updating scheme. Unlike other methods, it allows to retrieve the original patterns of the teacher dataset and thanks to the parallel update it can be applied to large system sizes. We tackle the same problem using a restricted Boltzmann machine (RBM) and discuss analogies and differences between our algorithm and RBM learning.Aurelien DecelleSungmin HwangJacopo RocchiDaniele TantariNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-13 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Aurelien Decelle Sungmin Hwang Jacopo Rocchi Daniele Tantari Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines
description	Abstract We propose an efficient algorithm to solve inverse problems in the presence of binary clustered datasets. We consider the paradigmatic Hopfield model in a teacher student scenario, where this situation is found in the retrieval phase. This problem has been widely analyzed through various methods such as mean-field approaches or the pseudo-likelihood optimization. Our approach is based on the estimation of the posterior using the Thouless–Anderson–Palmer (TAP) equations in a parallel updating scheme. Unlike other methods, it allows to retrieve the original patterns of the teacher dataset and thanks to the parallel update it can be applied to large system sizes. We tackle the same problem using a restricted Boltzmann machine (RBM) and discuss analogies and differences between our algorithm and RBM learning.
format	article
author	Aurelien Decelle Sungmin Hwang Jacopo Rocchi Daniele Tantari
author_facet	Aurelien Decelle Sungmin Hwang Jacopo Rocchi Daniele Tantari
author_sort	Aurelien Decelle
title	Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines
title_short	Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines
title_full	Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines
title_fullStr	Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines
title_full_unstemmed	Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines
title_sort	inverse problems for structured datasets using parallel tap equations and restricted boltzmann machines
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/89bc6fdcef6349f9af24896d9e340420
work_keys_str_mv	AT aureliendecelle inverseproblemsforstructureddatasetsusingparalleltapequationsandrestrictedboltzmannmachines AT sungminhwang inverseproblemsforstructureddatasetsusingparalleltapequationsandrestrictedboltzmannmachines AT jacoporocchi inverseproblemsforstructureddatasetsusingparalleltapequationsandrestrictedboltzmannmachines AT danieletantari inverseproblemsforstructureddatasetsusingparalleltapequationsandrestrictedboltzmannmachines
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Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines

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