Regularized System Identification: A Hierarchical Bayesian Approach
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Author / Producer
Date
2020-11
Publication Type
Conference Paper
ETH Bibliography
yes
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Abstract
In this paper, the hierarchical Bayesian method for regularized system identification is introduced. To this end, a hyperprior distribution is considered for the regularization matrix and then, the impulse response and the regularization matrix are jointly estimated based on a maximum a posteriori (MAP) approach. Toward introducing a suitable hyperprior, we decompose the regularization matrix using Cholesky decomposition and reduce the estimation problem to the cone of upper triangular matrices with positive diagonal entries. Following this, the hyperprior is introduced on a designed sub-cone of this set. The method differs from the current trend in regularized system identification from various aspect, e.g., the estimation is performed by solving a single stage problem. The MAP estimation problem reduces to a multi-convex optimization problem and a sequential convex programming algorithm is introduced for solving this problem. Consequently, the proposed method is a computationally efficient strategy specially when the regularization matrix has a large size. The method is numerically verified on benchmark examples. Owing to the employed full Bayesian approach, the estimation method shows a satisfactory bias-variance trade-off.
Permanent link
Publication status
published
External links
Book title
21st IFAC World Congress
Journal / series
Volume
53 (2)
Pages / Article No.
406 - 411
Publisher
Elsevier
Event
1st Virtual IFAC World Congress (IFAC-V 2020)
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
System identification; Hierarchical Bayesian; Sequential convex programming
Organisational unit
08814 - Smith, Roy (Tit.-Prof.) (ehemalig) / Smith, Roy (Tit.-Prof.) (former)
Notes
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)