Low-Complexity Identification by Sparse Hyperparameter Estimation
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Author / Producer
Date
2020-11
Publication Type
Conference Paper
ETH Bibliography
yes
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Abstract
This paper presents a novel kernel-based system identification method, which promotes low complexity of the model in terms of the McMillan degree of the system. The regularization matrix is characterized as a linear combination of pre-selected rank-one matrices with unknown hyperparameter coefficients, and the hyperparameters are derived using a maximum a posteriori estimation approach. Each basis matrix is the optimal regularization matrix for a first-order system. With this basis matrix selection, the McMillan degree of the identified model is upper-bounded by the rank of the regularization matrix, which in turn is equal to the cardinality of the hyperparameters. For this reason, a sparsity-promoting prior is chosen for hyperparameter tuning. The resulting optimization problem has a difference of convex program form which can be efficiently solved. The advantages of the proposed method are that the identified model has a low-complexity structure and that an improved bias-variance trade-off is achieved. Numerical results confirm that the proposed method achieves a better bias-variance trade-off as well as a better fit to the model compared to both the empirical Bayes method and the atomic-norm regularization.
Permanent link
Publication status
published
External links
Book title
21st IFAC World Congress
Journal / series
Volume
53 (2)
Pages / Article No.
412 - 417
Publisher
Elsevier
Event
1st Virtual IFAC World Congress (IFAC-V 2020)
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
System identification; Regularization; Complexity tuning; Hyperparameter estimation
Organisational unit
08814 - Smith, Roy (Tit.-Prof.) (ehemalig) / Smith, Roy (Tit.-Prof.) (former)
Notes
This research project is part of the Swiss Competence Center for Energy Research SCCER FEEB&D of the Swiss Innovation Agency Innosuisse, and supported by the Swiss National Science Foundation under grant no.: 200021 178890.
Due to the Coronavirus (COVID-19) the 21st IFAC World Congress 2020 became the 1st Virtual IFAC World Congress (IFAC-V 2020).
Funding
178890 - Modeling, Identification and Control of Periodic Systems in Energy Applications (SNF)