Incorporating Dependencies in Spectral Kernels for Gaussian Processes

• Published in: Machine Learning and Knowledge Discovery in Databases pp. 565 - 581
• Main Authors: Chen, Kai, van Laarhoven, Twan, Chen, Jinsong, Marchiori, Elena
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2020
• Series: Lecture Notes in Computer Science
• Subjects: Convolution; Dependency; Gaussian processes; Spectral mixture; Uncertainty
• ISBN: 3030461467; 9783030461461
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-46147-8_34

Gaussian processes (GPs) are an elegant Bayesian approach to model an unknown function. The choice of the kernel characterizes one’s assumption on how the unknown function autocovaries. It is a core aspect of a GP design, since the posterior distribution can significantly vary for different kernels. The spectral mixture (SM) kernel is derived by modelling a spectral density - the Fourier transform of a kernel - with a linear mixture of Gaussian components. As such, the SM kernel cannot model dependencies between components. In this paper we use cross convolution to model dependencies between components and derive a new kernel called Generalized Convolution Spectral Mixture (GCSM). Experimental analysis of GCSM on synthetic and real-life datasets indicates the benefit of modeling dependencies between components for reducing uncertainty and for improving performance in extrapolation tasks.