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EM-based hyperparameter optimization for regularized volterra kernel estimation
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0002-9368-3079
2017 (English)In: IEEE Control Systems Letters, ISSN 2475-1456, Vol. 1, no 2, p. 388-393Article in journal (Refereed) Published
Abstract [en]

In nonlinear system identification, Volterra kernel estimation based on regularized least squares can be performed by taking a Bayesian approach. In this framework, covariance structures which describe the Gaussian kernels are represented by a set of hyperparameters. The hyperparameters are traditionally tuned through a global optimization which maximizes their marginal likelihood with respect to the measured data. The global optimization is computationally intensive for high-order estimates, as the number of hyperparameters increases quadratically with the Volterra series order. In this letter, we propose a new method of hyperparameter tuning based on expectation-maximization (EM). The technique allows the global optimization to be split into smaller components such that the search space of any given optimization problem is not prohibitively large. The main advantage of the proposed EM method is improved computation time scaling with respect to Volterra series order. The computation time benefits of the EM-based method are demonstrated through a numerical example for the case where the maximum nonlinear order is known.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2017. Vol. 1, no 2, p. 388-393
Keywords [en]
Nonlinear systems identification, Optimization, Bayesian networks, Global optimization, Maximum principle, Nonlinear systems, Numerical methods, Bayesian approaches, Covariance structures, Expectation Maximization, Hyper-parameter optimizations, Marginal likelihood, Optimization problems, Regularized least squares, Maximum likelihood estimation
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-246204DOI: 10.1109/LCSYS.2017.2719766Scopus ID: 2-s2.0-85051842937OAI: oai:DiVA.org:kth-246204DiVA, id: diva2:1296568
Note

QC 20190315

Available from: 2019-03-15 Created: 2019-03-15 Last updated: 2019-03-18Bibliographically approved

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Hjalmarsson, Håkan

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