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ARMA Identification of Graphical Models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-2681-8383
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-1927-1690
2013 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 5, 1167-1178 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2013. Vol. 58, no 5, 1167-1178 p.
Keyword [en]
Autoregressive moving-average (ARMA) modeling, conditional independence, graphical models, system identification
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-39065DOI: 10.1109/TAC.2012.2231551ISI: 000318542200006Scopus ID: 2-s2.0-84886418860OAI: oai:DiVA.org:kth-39065DiVA: diva2:439404
Funder
Swedish Research Council
Note

Updated from "Preprint" to "Article" QC 20130627

Available from: 2011-09-08 Created: 2011-09-07 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Spectral Moment Problems: Generalizations, Implementation and Tuning
Open this publication in new window or tab >>Spectral Moment Problems: Generalizations, Implementation and Tuning
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Spectral moment interpolation find application in a wide array of use cases: robust control, system identification, model reduction to name the most notable ones. This thesis aims to expand the theory of such methods in three different directions. The first main contribution concerns the practical applicability. From this point of view various solving algorithm and their properties are considered. This study lead to identify a globally convergent method with excellent numerical properties. The second main contribution is the introduction of an extended interpolation problem that allows to model ARMA spectra without any explicit information of zero’s positions. To this end it was necessary for practical reasons to consider an approximated interpolation insted. Finally, the third main contribution is the application to some problems such as graphical model identification and ARMA spectral approximation.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. xii, 10 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 11:06
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-39026 (URN)978-91-7501-087-8 (ISBN)
Public defence
2011-09-16, Sal F2, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20110906Available from: 2011-09-06 Created: 2011-09-06 Last updated: 2011-09-08Bibliographically approved

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Lindquist, AndersWahlberg, Bo

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