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Model Selection and Sparse Modeling
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2007 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

Parametric signal models are used in a multitude of signal processing applications. This thesis deals with signals for which there are many candidate models, and it is not a priori known which model is the most appropriate one. The first part of the thesis treats cases for which the set of models is relatively small, so that it is possible to evaluate each model in the set separately. The second part deals with sparse models, i.e., models sharing the same parameter vector, but for which any combination of zero valued and non-zero valued parameters is possible. Sparse models appear in a variety of applications, such as statistical data analysis, communications, and active sensing, such as radar and non-destructive testing.

An important problem considered in the two parts of the thesis is that of model selection, i.e., how to select the most appropriate model (according to some criterion) from the set of candidates. To this end, both the classical information criterion (IC) approaches, such as AIC, BIC and GIC, as well as maximum a posteriori probability based methods derived in the Bayesian framework are used.

Finally, the task of symbol detection for applications in communications is considered. The maximum a posteriori probability symbol detector is derived for a few different channel models.

Place, publisher, year, edition, pages
Uppsala: Institutionen för informationsteknologi , 2007. , 243 p.
Keyword [en]
model selection, model order selection, model averaging, nested models, sparse models, Bayesian inference, MMSE estimation, MAP estimation, ML estimation, AIC, BIC, GIC, RAKE receivers, pulse compression, radar, linear models, linear regression models
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:uu:diva-8202ISBN: 978-91-506-1955-3 (print)OAI: oai:DiVA.org:uu-8202DiVA: diva2:170683
Public defence
2007-10-12, Room 2446, Building 2, Lägerhyddsvägen 2, Uppsala, 13:15
Opponent
Supervisors
Available from: 2007-09-20 Created: 2007-09-20 Last updated: 2011-02-16Bibliographically approved

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Output format
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