Vector-Valued Kernel Ridge Regression for the Modeling of High-Speed Links

Abstract

This paper presents a preliminary implementation of a general modeling framework for vector-valued functions based on a multi-output kernel Ridge regression (KRR). The proposed approach is based on a generalized definition of the reproducing kernel Hilbert space (RKHS) to the case of vector-valued functions, thus bridging the gap between multi-output Neural Network (NN) structures and standard scalar kernel-based approaches. The above concept is then used within the KRR to train a multi-output surrogate model able to predict the frequency responses of a high-speed link affected by four parameters with a large variability. The performance of the proposed approach, in terms of parametric and stochastic analysis, is compared with the one provided by two state-of-the-art techniques, such as the combination of the principal components analysis (PCA) and the least-squares support vector machine (LS-SVM) regression and a multi-output feed-forward NN structure.