Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis

A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti’s Theorem. In its original form, it applies to infinite 0–1 valued sequences with the special property that the distribution is invariant to permutations (called an exchangeable...

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Autor principal:	András Faragó
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	de Finetti’s Theorem exchangeable sequence decomposition theorem random network analysis Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/ea701aea7e484df3abc9d7bbb866dae1
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spelling	oai:doaj.org-article:ea701aea7e484df3abc9d7bbb866dae12021-11-25T16:13:21ZDecomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis10.3390/a141103361999-4893https://doaj.org/article/ea701aea7e484df3abc9d7bbb866dae12021-11-01T00:00:00Zhttps://www.mdpi.com/1999-4893/14/11/336https://doaj.org/toc/1999-4893A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti’s Theorem. In its original form, it applies to infinite 0–1 valued sequences with the special property that the distribution is invariant to permutations (called an exchangeable sequence). Later it was extended and generalized in numerous directions. After reviewing this line of development, we present our new decomposition theorem, covering cases that have not been previously considered. We also introduce a novel way of applying these types of results in the analysis of random networks. For self-containment, we provide the introductory exposition in more detail than usual, with the intent of making it also accessible to readers who may not be closely familiar with the subject.András FaragóMDPI AGarticlede Finetti’s Theoremexchangeable sequencedecomposition theoremrandom network analysisIndustrial engineering. Management engineeringT55.4-60.8Electronic computers. Computer scienceQA75.5-76.95ENAlgorithms, Vol 14, Iss 336, p 336 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	de Finetti’s Theorem exchangeable sequence decomposition theorem random network analysis Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
spellingShingle	de Finetti’s Theorem exchangeable sequence decomposition theorem random network analysis Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95 András Faragó Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis
description	A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti’s Theorem. In its original form, it applies to infinite 0–1 valued sequences with the special property that the distribution is invariant to permutations (called an exchangeable sequence). Later it was extended and generalized in numerous directions. After reviewing this line of development, we present our new decomposition theorem, covering cases that have not been previously considered. We also introduce a novel way of applying these types of results in the analysis of random networks. For self-containment, we provide the introductory exposition in more detail than usual, with the intent of making it also accessible to readers who may not be closely familiar with the subject.
format	article
author	András Faragó
author_facet	András Faragó
author_sort	András Faragó
title	Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis
title_short	Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis
title_full	Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis
title_fullStr	Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis
title_full_unstemmed	Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis
title_sort	decomposition of random sequences into mixtures of simpler ones and its application in network analysis
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ea701aea7e484df3abc9d7bbb866dae1
work_keys_str_mv	AT andrasfarago decompositionofrandomsequencesintomixturesofsimpleronesanditsapplicationinnetworkanalysis
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Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis

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