ARMA Identification of Graphical Models
Consider a Gaussian stationary stochastic vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nod...
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ndltd-UPSALLA1-oai-DiVA.org-kth-390652013-06-28T04:08:04ZARMA Identification of Graphical ModelsengAvventi, EnricoLindquist, AndersWahlberg, BoKTH, Optimeringslära och systemteoriKTH, Optimeringslära och systemteoriKTH, Optimeringslära och systemteori2013Autoregressive moving-average (ARMA) modelingconditional independencegraphical modelssystem identificationMATHEMATICSMATEMATIKConsider a Gaussian stationary stochastic vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. This leads to a sparsity pattern in the inverse of the matrix-valued spectral density. Such graphical models find applications in speech, bioinformatics, image processing, econometrics and many other fields, where the problem to fit an autoregressive (AR) model to such a process has been considered. In this paper we take this problem one step further, namely to fit an autoregressive moving-average (ARMA) model to the same data. We develop a theoretical framework and an optimization procedure which also spreads further light on previous approaches and results. This procedure is then applied to the identification problem of estimating the ARMA parameters as well as the topology of the graph from statistical data. <p>Updated from "Preprint" to "Article" QC 20130627</p>Article in journalinfo:eu-repo/semantics/articletexthttp://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-39065doi:10.1109/TAC.2012.2231551ISI:000318542200006IEEE Transactions on Automatic Control, 0018-9286, 2013, 58:5, s. 1167-1178application/pdfinfo:eu-repo/semantics/openAccess |
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English |
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Others
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Autoregressive moving-average (ARMA) modeling conditional independence graphical models system identification MATHEMATICS MATEMATIK |
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Autoregressive moving-average (ARMA) modeling conditional independence graphical models system identification MATHEMATICS MATEMATIK Avventi, Enrico Lindquist, Anders Wahlberg, Bo ARMA Identification of Graphical Models |
description |
Consider a Gaussian stationary stochastic vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. This leads to a sparsity pattern in the inverse of the matrix-valued spectral density. Such graphical models find applications in speech, bioinformatics, image processing, econometrics and many other fields, where the problem to fit an autoregressive (AR) model to such a process has been considered. In this paper we take this problem one step further, namely to fit an autoregressive moving-average (ARMA) model to the same data. We develop a theoretical framework and an optimization procedure which also spreads further light on previous approaches and results. This procedure is then applied to the identification problem of estimating the ARMA parameters as well as the topology of the graph from statistical data. === <p>Updated from "Preprint" to "Article" QC 20130627</p> |
author |
Avventi, Enrico Lindquist, Anders Wahlberg, Bo |
author_facet |
Avventi, Enrico Lindquist, Anders Wahlberg, Bo |
author_sort |
Avventi, Enrico |
title |
ARMA Identification of Graphical Models |
title_short |
ARMA Identification of Graphical Models |
title_full |
ARMA Identification of Graphical Models |
title_fullStr |
ARMA Identification of Graphical Models |
title_full_unstemmed |
ARMA Identification of Graphical Models |
title_sort |
arma identification of graphical models |
publisher |
KTH, Optimeringslära och systemteori |
publishDate |
2013 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-39065 |
work_keys_str_mv |
AT avventienrico armaidentificationofgraphicalmodels AT lindquistanders armaidentificationofgraphicalmodels AT wahlbergbo armaidentificationofgraphicalmodels |
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1716590283396743168 |