A kernel-based PEM estimator for forward models

Fuente: arXiv
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Main Authors: Fattore, Giulio, Peruzzo, Marco, Sartori, Giacomo, Zorzi, Mattia
Format: Preprint
Published: 2024
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author Fattore, Giulio
Peruzzo, Marco
Sartori, Giacomo
Zorzi, Mattia
author_facet Fattore, Giulio
Peruzzo, Marco
Sartori, Giacomo
Zorzi, Mattia
contents This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with a high-order stable ARX model. However, such choice induces a certain undesired prior information in the system that we want to estimate. To overcome this issue, we propose a new kernel-based paradigm which is formulated directly in terms of the impulse responses of the forward model and leading to the identification of a high-order MAX model. The most challenging step is the estimation of the kernel hyperparameters optimizing the marginal likelihood. The latter, indeed, does not admit a closed form expression. We propose a method for evaluating the marginal likelihood which makes possible the hyperparameters estimation. Finally, some numerical results showing the effectiveness of the method are presented.
format Preprint
id arxiv_https___arxiv_org_abs_2409_09679
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A kernel-based PEM estimator for forward models
Fattore, Giulio
Peruzzo, Marco
Sartori, Giacomo
Zorzi, Mattia
Optimization and Control
This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with a high-order stable ARX model. However, such choice induces a certain undesired prior information in the system that we want to estimate. To overcome this issue, we propose a new kernel-based paradigm which is formulated directly in terms of the impulse responses of the forward model and leading to the identification of a high-order MAX model. The most challenging step is the estimation of the kernel hyperparameters optimizing the marginal likelihood. The latter, indeed, does not admit a closed form expression. We propose a method for evaluating the marginal likelihood which makes possible the hyperparameters estimation. Finally, some numerical results showing the effectiveness of the method are presented.
title A kernel-based PEM estimator for forward models
topic Optimization and Control
url https://arxiv.org/abs/2409.09679