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Toward Tractable Global Solutions to Bayesian Point Estimation Problems via Sparse Sum-of-Squares Relaxations
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).ORCID iD: 0000-0001-7823-2993
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). (System Identification)ORCID iD: 0000-0001-5474-7060
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). (System Identification)ORCID iD: 0000-0002-9368-3079
2020 (English)In: The 2020 American Control Conference, 2020Conference paper, Published paper (Refereed)
Abstract [en]

Bayesian point estimation is commonly used for system identification owing to its good properties for small sample sizes. Although this type of estimator is usually non-parametric, Bayes estimates can also be obtained for rational parametric models, which is often of interest. However, as in maximum-likelihood methods, the Bayes estimate is typically computed via local numerical optimization that requires good initialization and cannot guarantee global optimality. In this contribution, we propose a computationally tractable method that computes the Bayesian parameter estimates with posterior certification of global optimality via sum-of-squares polynomials and sparse semidefinite relaxations. It is shown that the method is applicable to certain discrete-time linear models, which takes advantage of the rational structure of these models and the sparsity in the Bayesian parameter estimation problem. The method is illustrated on a simulation model of a resonant system that is difficult to handle when the sample size is small.

Place, publisher, year, edition, pages
2020.
Keywords [en]
Bayesian Identification; Regularization; LMIs; non-convex; relaxation; sum-of-squares; SOS; sparse
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-266754OAI: oai:DiVA.org:kth-266754DiVA, id: diva2:1386565
Conference
Conference 2020 American Control Conference (ACC), 1-3 July 2020, Sheraton Denver Downtown Hotel, Denver, CO, USA
Funder
Vinnova, 2016-05181Swedish Research Council, 2015-05285Swedish Research Council, 2016-06079
Note

QC 20200120

Available from: 2020-01-17 Created: 2020-01-17 Last updated: 2020-02-03Bibliographically approved

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Authority records BETA

Rodrigues, DiogoAbdalmoaty, MohamedHjalmarsson, Håkan

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