Identification of forward models: a nonparametric approach
Abstract
In this paper we propose a new kernel-based method for the identification of the impulse responses of forward models. The resulting estimator leads to a nonlinear Tikhonov regularization problem for which we prove the existence of a solution. The latter result makes legitimate to approximate the forward model through a high-order Moving Average with eXogenous input (MAX) model, i.e. the numerical solution found using this model introduces only a negligible bias in the estimate. The optimization of the marginal likelihood to estimate the kernel hyperparameters is also taken into account. Since there does not exist a closed-form expression for the marginal likelihood, we present an evaluation method that relies on the Laplace approximation of the marginal likelihood. Finally, some numerical experiments are discussed to show the effectiveness of the proposed method.
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BibTeX
@misc{fattore2026identification,
title = {{Identification of forward models: a nonparametric approach}},
author = {Giulio Fattore and Marco Peruzzo and Giacomo Sartori and Mattia Zorzi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08440},
eprint = {2609.08440},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08440},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Identification of forward models: a nonparametric approach
AU - Giulio Fattore
AU - Marco Peruzzo
AU - Giacomo Sartori
AU - Mattia Zorzi
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08440
UR - https://arxiv.org/abs/2609.08440
AB - In this paper we propose a new kernel-based method for the identification of the impulse responses of forward models. The resulting estimator leads to a nonlinear Tikhonov regularization problem for which we prove the existence of a solution. The latter result makes legitimate to approximate the forward model through a high-order Moving Average with eXogenous input (MAX) model, i.e. the numerical solution found using this model introduces only a negligible bias in the estimate. The optimization of the marginal likelihood to estimate the kernel hyperparameters is also taken into account. Since there does not exist a closed-form expression for the marginal likelihood, we present an evaluation method that relies on the Laplace approximation of the marginal likelihood. Finally, some numerical experiments are discussed to show the effectiveness of the proposed method.
ER -