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A Model Selection Criterion for High-Dimensional Linear Regression
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-6855-5868
2018 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 13, p. 3436-3446Article in journal (Refereed) Published
Abstract [en]

Statistical model selection is a great challenge when the number of accessible measurements is much smaller than the dimension of the parameter space. We study the problem of model selection in the context of subset selection for high-dimensional linear regressions. Accordingly, we propose a new model selection criterion with the Fisher information that leads to the selection of a parsimonious model from all the combinatorial models up to some maximum level of sparsity. We analyze the performance of our criterion as the number of measurements grows to infinity, as well as when the noise variance tends to zero. In each case, we prove that our proposed criterion gives the true model with a probability approaching one. Additionally, we devise a computationally affordable algorithm to conduct model selection with the proposed criterion in practice. Interestingly, as a side product, our algorithm can provide the ideal regularization parameter for the Lasso estimator such that Lasso selects the true variables. Finally, numerical simulations are included to support our theoretical findings.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2018. Vol. 66, no 13, p. 3436-3446
Keywords [en]
Model selection, high-dimensional inference, subset selection, Bayesian information criterion, Lasso, sparse estimation, regularization
National Category
Control Engineering Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-231694DOI: 10.1109/TSP.2018.2821628ISI: 000435193800003Scopus ID: 2-s2.0-85044784662OAI: oai:DiVA.org:kth-231694DiVA, id: diva2:1241768
Note

QC 20180824

Available from: 2018-08-24 Created: 2018-08-24 Last updated: 2019-08-20Bibliographically approved

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Jansson, Magnus

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