On asymptotic properties of hyperparameter estimators for kernel-based regularization methods

DOI10.1016/j.automatica.2018.04.035zbMath1401.93197arXiv1707.00407OpenAlexW2963774371WikidataQ129741719 ScholiaQ129741719MaRDI QIDQ1797138

Lennart Ljung, Tianshi Chen, Bi-Qiang Mu

Publication date: 17 October 2018

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.00407

zbMATH Keywords

asymptotic analysiskernel-based regularizationempirical Bayes estimationStein's unbiased risk estimator

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Estimation and detection in stochastic control theory (93E10) Least squares and related methods for stochastic control systems (93E24) Identification in stochastic control theory (93E12) Control/observation systems in abstract spaces (93C25)

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Uses Software

• Matlab
• System Identification Toolbox

Cites Work

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• Maximum entropy properties of discrete-time first-order stable spline kernel
• Regularized linear system identification using atomic, nuclear and kernel-based norms: the role of the stability constraint
• Kernel methods in system identification, machine learning and function estimation: a survey
• Prediction error identification of linear systems: a nonparametric Gaussian regression approach
• Tuning complexity in regularized kernel-based regression and linear system identification: the robustness of the marginal likelihood estimator
• A new kernel-based approach for linear system identification
• On the stability of reproducing kernel Hilbert spaces of discrete-time impulse responses
• On kernel design for regularized LTI system identification
• On the robustness of the Bayes and Wiener estimators under model uncertainty
• The harmonic analysis of kernel functions
• On the estimation of transfer functions, regularizations and Gaussian processes-revisited
• System Identification Via Sparse Multiple Kernel-Based Regularization Using Sequential Convex Optimization Techniques
• Kernels for Linear Time Invariant System Identification
• Continuous-Time DC Kernel—A Stable Generalized First-Order Spline Kernel
• Maximum Entropy Kernels for System Identification
• Ridge Regression: Biased Estimation for Nonorthogonal Problems