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Maximum Entropy Kernels for System Identification
University of Liege, Belgium; University of Cambridge, England.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Chinese University of Hong Kong, Peoples R China.ORCID iD: 0000-0001-8655-2655
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
2017 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 3, 1471-1477 p.Article in journal (Refereed) Published
Abstract [en]

Bayesian nonparametric approaches have been recently introduced in system identification scenario where the impulse response is modeled as the realization of a zero-mean Gaussian process whose covariance (kernel) has to be estimated from data. In this scheme, quality of the estimates crucially depends on the parametrization of the covariance of the Gaussian process. A family of kernels that have been shown to be particularly effective in the system identification framework is the family of Diagonal/Correlated (DC) kernels. Maximum entropy properties of a related family of kernels, the Tuned/Correlated (TC) kernels, have been recently pointed out in the literature. In this technical note, we show that maximum entropy properties indeed extend to the whole family of DC kernels. The maximum entropy interpretation can be exploited in conjunction with results on matrix completion problems in the graphical models literature to shed light on the structure of the DC kernel. In particular, we prove that the DC kernel admits a closed-form factorization, inverse, and determinant. These results can be exploited both to improve the numerical stability and to reduce the computational complexity associated with the computation of the DC estimator.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2017. Vol. 62, no 3, 1471-1477 p.
Keyword [en]
Covariance extension; Gaussian process; kernel methods; maximum entropy; system identification
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-136046DOI: 10.1109/TAC.2016.2582642ISI: 000395924300038OAI: oai:DiVA.org:liu-136046DiVA: diva2:1084874
Note

Funding Agencies|Swedish Research Council [2014-5894]; Chinese University of Hong Kong, Shenzhen; ERC - European Research Council; Belgian Fund for Scientific Research (FNRS)

Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2017-03-27

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