Multi-kernel Gaussian processes

Authors:
Arman Melkumyan;Fabio Ramos
Affiliations:
Australian Centre for Field Robotics, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW, Australia;Australian Centre for Field Robotics, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW, Australia
Venue:
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Year:
2011

Citing 4
Cited 2

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Abstract

Multi-task learning remains a difficult yet important problem in machine learning. In Gaussian processes the main challenge is the definition of valid kernels (covariance functions) able to capture the relationships between different tasks. This paper presents a novel methodology to construct valid multi-task covariance functions (Mercer kernels) for Gaussian processes allowing for a combination of kernels with different forms. The method is based on Fourier analysis and is general for arbitrary stationary covariance functions. Analytical solutions for cross covariance terms between popular forms are provided including Matérn, squared exponential and sparse covariance functions. Experiments are conducted with both artificial and real datasets demonstrating the benefits of the approach.