Network Inference and Maximum Entropy Estimation on Information Diagrams

Abstract Maximum entropy estimation is of broad interest for inferring properties of systems across many disciplines. Using a recently introduced technique for estimating the maximum entropy of a set of random discrete variables when conditioning on bivariate mutual informations and univariate entro...

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Autores principales:	Elliot A. Martin, Jaroslav Hlinka, Alexander Meinke, Filip Děchtěrenko, Jaroslav Tintěra, Isaura Oliver, Jörn Davidsen
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/6a45a029cd324b9fa75c45f640084384
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spelling	oai:doaj.org-article:6a45a029cd324b9fa75c45f6400843842021-12-02T11:53:08ZNetwork Inference and Maximum Entropy Estimation on Information Diagrams10.1038/s41598-017-06208-w2045-2322https://doaj.org/article/6a45a029cd324b9fa75c45f6400843842017-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-06208-whttps://doaj.org/toc/2045-2322Abstract Maximum entropy estimation is of broad interest for inferring properties of systems across many disciplines. Using a recently introduced technique for estimating the maximum entropy of a set of random discrete variables when conditioning on bivariate mutual informations and univariate entropies, we show how this can be used to estimate the direct network connectivity between interacting units from observed activity. As a generic example, we consider phase oscillators and show that our approach is typically superior to simply using the mutual information. In addition, we propose a nonparametric formulation of connected informations, used to test the explanatory power of a network description in general. We give an illustrative example showing how this agrees with the existing parametric formulation, and demonstrate its applicability and advantages for resting-state human brain networks, for which we also discuss its direct effective connectivity. Finally, we generalize to continuous random variables and vastly expand the types of information-theoretic quantities one can condition on. This allows us to establish significant advantages of this approach over existing ones. Not only does our method perform favorably in the undersampled regime, where existing methods fail, but it also can be dramatically less computationally expensive as the cardinality of the variables increases.Elliot A. MartinJaroslav HlinkaAlexander MeinkeFilip DěchtěrenkoJaroslav TintěraIsaura OliverJörn DavidsenNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-15 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Elliot A. Martin Jaroslav Hlinka Alexander Meinke Filip Děchtěrenko Jaroslav Tintěra Isaura Oliver Jörn Davidsen Network Inference and Maximum Entropy Estimation on Information Diagrams
description	Abstract Maximum entropy estimation is of broad interest for inferring properties of systems across many disciplines. Using a recently introduced technique for estimating the maximum entropy of a set of random discrete variables when conditioning on bivariate mutual informations and univariate entropies, we show how this can be used to estimate the direct network connectivity between interacting units from observed activity. As a generic example, we consider phase oscillators and show that our approach is typically superior to simply using the mutual information. In addition, we propose a nonparametric formulation of connected informations, used to test the explanatory power of a network description in general. We give an illustrative example showing how this agrees with the existing parametric formulation, and demonstrate its applicability and advantages for resting-state human brain networks, for which we also discuss its direct effective connectivity. Finally, we generalize to continuous random variables and vastly expand the types of information-theoretic quantities one can condition on. This allows us to establish significant advantages of this approach over existing ones. Not only does our method perform favorably in the undersampled regime, where existing methods fail, but it also can be dramatically less computationally expensive as the cardinality of the variables increases.
format	article
author	Elliot A. Martin Jaroslav Hlinka Alexander Meinke Filip Děchtěrenko Jaroslav Tintěra Isaura Oliver Jörn Davidsen
author_facet	Elliot A. Martin Jaroslav Hlinka Alexander Meinke Filip Děchtěrenko Jaroslav Tintěra Isaura Oliver Jörn Davidsen
author_sort	Elliot A. Martin
title	Network Inference and Maximum Entropy Estimation on Information Diagrams
title_short	Network Inference and Maximum Entropy Estimation on Information Diagrams
title_full	Network Inference and Maximum Entropy Estimation on Information Diagrams
title_fullStr	Network Inference and Maximum Entropy Estimation on Information Diagrams
title_full_unstemmed	Network Inference and Maximum Entropy Estimation on Information Diagrams
title_sort	network inference and maximum entropy estimation on information diagrams
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/6a45a029cd324b9fa75c45f640084384
work_keys_str_mv	AT elliotamartin networkinferenceandmaximumentropyestimationoninformationdiagrams AT jaroslavhlinka networkinferenceandmaximumentropyestimationoninformationdiagrams AT alexandermeinke networkinferenceandmaximumentropyestimationoninformationdiagrams AT filipdechterenko networkinferenceandmaximumentropyestimationoninformationdiagrams AT jaroslavtintera networkinferenceandmaximumentropyestimationoninformationdiagrams AT isauraoliver networkinferenceandmaximumentropyestimationoninformationdiagrams AT jorndavidsen networkinferenceandmaximumentropyestimationoninformationdiagrams
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Network Inference and Maximum Entropy Estimation on Information Diagrams

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