Sparse multiple kernels for impulse response estimation with majorization minimization algorithms

Tianshi Chen, Lennart Ljung, Martin Skovgaard Andersen, A. Chiuso, F. Carli, G. Pillonetto

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


This contribution aims to enrich the recently introduced kernel-based regularization method for linear system identification. Instead of a single kernel, we use multiple kernels, which can be instances of any existing kernels for the impulse response estimation of linear systems. We also introduce a new class of kernels constructed based on output error (OE) model estimates. In this way, a more flexible and richer representation of the kernel is obtained. Due to this representation the associated hyper-parameter estimation problem has two good features. First, it is a difference of convex functions programming (DCP) problem. While it is still nonconvex, it can be transformed into a sequence of convex optimization problems with majorization minimization (MM) algorithms and a local minima can thus be found iteratively. Second, it leads to sparse hyper-parameters and thus sparse multiple kernels. This feature shows the kernel-based regularization method with multiple kernels has the potential to tackle various problems of finding sparse solutions in linear system identification.
Original languageEnglish
Title of host publication2012 IEEE 51st Annual Conference on Decision and Control (CDC)
Publication date2012
ISBN (Print)978-1-4673-2065-8
Publication statusPublished - 2012
Externally publishedYes
Event51st IEEE Conference on Decision and Control - Maui, HI, United States
Duration: 10 Dec 201213 Dec 2012
Conference number: 51


Conference51st IEEE Conference on Decision and Control
CountryUnited States
CityMaui, HI

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