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Linear Regression With a Sparse Parameter Vector
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2007 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 55, no 2, 451-460 p.Article in journal (Refereed) Published
Abstract [en]

We consider linear regression under a model where the parameter vector is known to be sparse. Using a Bayesian framework, we derive the minimum mean-square error (MMSE) estimate of the parameter vector, and a computationally efficient approximation of it. We also derive an empirical-Bayesian version of the estimator, which does not need any a priori information, nor does it need the selection of any user parameters. As a byproduct, we obtain a powerful model (``basis'') selection tool for sparse models. The performance and robustness of our new estimators are illustrated via numerical examples.

Place, publisher, year, edition, pages
2007. Vol. 55, no 2, 451-460 p.
Keyword [en]
Linear regression, sparse models, Bayesian inference, MMSE estimation, basis selection, model selection, variable selection, model averaging, Lasso
National Category
Engineering and Technology
URN: urn:nbn:se:uu:diva-82080DOI: 10.1109/TSP.2006.887109ISI: 000243952600005OAI: oai:DiVA.org:uu-82080DiVA: diva2:109995
Available from: 2007-02-15 Created: 2007-02-15 Last updated: 2011-02-15Bibliographically approved

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