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Grand Canonical Ensembles of Sparse Networks and Bayesian Inference
Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarch...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2022
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9146839/ https://www.ncbi.nlm.nih.gov/pubmed/35626517 http://dx.doi.org/10.3390/e24050633 |
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author | Bianconi, Ginestra |
author_facet | Bianconi, Ginestra |
author_sort | Bianconi, Ginestra |
collection | PubMed |
description | Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e., with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e., the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction. |
format | Online Article Text |
id | pubmed-9146839 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-91468392022-05-29 Grand Canonical Ensembles of Sparse Networks and Bayesian Inference Bianconi, Ginestra Entropy (Basel) Article Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e., with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e., the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction. MDPI 2022-04-30 /pmc/articles/PMC9146839/ /pubmed/35626517 http://dx.doi.org/10.3390/e24050633 Text en © 2022 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Bianconi, Ginestra Grand Canonical Ensembles of Sparse Networks and Bayesian Inference |
title | Grand Canonical Ensembles of Sparse Networks and Bayesian Inference |
title_full | Grand Canonical Ensembles of Sparse Networks and Bayesian Inference |
title_fullStr | Grand Canonical Ensembles of Sparse Networks and Bayesian Inference |
title_full_unstemmed | Grand Canonical Ensembles of Sparse Networks and Bayesian Inference |
title_short | Grand Canonical Ensembles of Sparse Networks and Bayesian Inference |
title_sort | grand canonical ensembles of sparse networks and bayesian inference |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9146839/ https://www.ncbi.nlm.nih.gov/pubmed/35626517 http://dx.doi.org/10.3390/e24050633 |
work_keys_str_mv | AT bianconiginestra grandcanonicalensemblesofsparsenetworksandbayesianinference |