Bridging the Gap Between Artificial Neural Networks and Kernel Regressions for Vector-Valued Problems in Microwave Applications

Abstract

Thanks to their convex formulation, kernel regressions have shown an improved accuracy with respect to artificial neural network (ANN) structures in regression problems where a reduced set of training samples are available. However, despite the above interesting features, kernel regressions are inherently less flexible than ANN structures since their implementations are usually limited to scalar-output regression problems. This article presents a vector-valued (multioutput) formulation of the kernel ridge regression (KRR) aimed at bridging the gap between multioutput ANN structures and scalar kernel-based approaches. The proposed vector-valued KRR relies on a generalized definition of the reproducing kernel Hilbert space (RKHS) and on a new multioutput kernel structure. The mathematical background of the proposed vector-valued formulation is extensively discussed together with different matrix kernel functions and training schemes. Moreover, a compression strategy based on the Nystrom approximation is presented to reduce the computational complexity of the model training. The effectiveness and the performance of the proposed vector-valued KRR are discussed on an illustrative example consisting of a high-speed link and on the optimization of a Doherty amplifier.

Stochastic Time-Domain Mapping for Comprehensive Uncertainty Assessment in Eye Diagrams

“…An alternative modeling approach consists of applying a vector-valued formulation of the KRR, which allows to directly account for the vector-valued nature of the regression problem at hand [6], [7], [17]. Specifically, the vector-valued KRR can be directly adopted to train a single vector-valued surrogate model M KRR : X → Y, which according to the represented theorem for vector-valued regression problems presented in [44], writes…”

“…Many of the first successful approaches were based on polynomial chaos expansion (for an overview of this family of algorithms see [3]). These were followed by other machine learning inspired solutions falling mainly into the category of kernel machine regression (e.g., [4], [5], [6], [7], [8], [9]) and artificial neural networks (ANNs) (e.g., [10], [11], [12], [13], [14]). This article focuses on kernel machine regression techniques, such as: the support vector machine (SVM) regression [15], the least-squares support vector machine (LS-SVM) [16] regression, and the more recent vector-valued kernel ridge regression (KRR) [6], [7], [17], which have been proven particularly effective for various microelectronics and radio-frequency applications [4], [5], [8].…”

“…These were followed by other machine learning inspired solutions falling mainly into the category of kernel machine regression (e.g., [4], [5], [6], [7], [8], [9]) and artificial neural networks (ANNs) (e.g., [10], [11], [12], [13], [14]). This article focuses on kernel machine regression techniques, such as: the support vector machine (SVM) regression [15], the least-squares support vector machine (LS-SVM) [16] regression, and the more recent vector-valued kernel ridge regression (KRR) [6], [7], [17], which have been proven particularly effective for various microelectronics and radio-frequency applications [4], [5], [8]. Indeed, kernel machine regressions provide an interesting alternative to the otherwise more flexible ANNs, especially well-suited for problems in which a "relatively small" set of training data is available [15], [16], [18].…”

Analysis of Doherty Power Amplifier Matching Assisted by Physics-Based Device Modelling

“…A slow AUX turn-on often leads to a significant gain drop in both back-off and the Doherty region [6,18,21]. In conclusion, the DPA design is affected by several competing constrains calling for advanced optimization methods, most recently including neural networks [22][23][24] and digital control [25,26].…”