A kernel-based PEM estimator for forward models

TL;DR

This paper introduces a kernel-based Prediction Error Method for learning forward model impulse responses, avoiding high-order ARX models and directly estimating MAX models with optimized kernel hyperparameters.

Contribution

It proposes a novel kernel-based framework for forward model identification that directly estimates impulse responses, improving over traditional ARX-based approaches.

Findings

Effective impulse response estimation demonstrated through numerical results.

Kernel hyperparameters optimized via a new marginal likelihood evaluation method.

Method outperforms traditional high-order ARX models in accuracy.

Abstract

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.