Work

Complex Gaussian Processes for Regression and Their Connection to WLMMSE

Year: 2024

Type: article

Abstract: The Gaussian process (GP) is a well-established Bayesian nonparametric tool for inference in nonlinear estimation problems. When GPs are used for regression, the goal is to estimate a target signal${y}$from an input vector$\mathbf {x}$without assuming that they are linearly related, but with a probabilistic model$p({y}|\mathbf {x})$that is Gaussian distributed. Therefore, GPs can be understood as a natural nonlinear extension to MMSE estimation. For real-valued GPs, this has been analyzed in the existing literature, and it is concluded that they are the natural nonlinear Bayesian extension to the linear minimum mean-squared error (LMMSE) estimation. In this letter, we show that, consequently, complex-valued GP regression (GPR) models are the natural nonlinear Bayesian extension of the widely linear minimum mean squared-error (WLMMSE) estimation. As in the real-valued case, complex-valued GPs are able to better model many regression problems by making use of the information that the complementary kernel or pseudo-kernel provides.

Source: IEEE Signal Processing Letters

DOI: 10.1109/lsp.2024.3515818

Authors: Rafael Boloix-Tortosa, Juan José Murillo-Fuentes

Institution: Universidad de Sevilla

Language: English

Topic: Gaussian Processes and Bayesian Inference

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,495

Funder: Agencia Estatal de Investigación