The Minecraft Kernel: Modelling correlated Gaussian Processes in the Fourier domain

• URL: http://arxiv.org/abs/2103.06950v1
• Date: Thu, 11 Mar 2021 20:54:51 GMT
• Title: The Minecraft Kernel: Modelling correlated Gaussian Processes in the Fourier domain
• Authors: Fergus Simpson, Alexis Boukouvalas, Vaclav Cadek, Elvijs Sarkans, Nicolas Durrande
• Abstract summary: We present a family of kernel that can approximate any stationary multi-output kernel to arbitrary precision. The proposed family of kernel represents the first multi-output generalisation of the spectral mixture kernel.
• Score: 3.6526103325150383
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the univariate setting, using the kernel spectral representation is an appealing approach for generating stationary covariance functions. However, performing the same task for multiple-output Gaussian processes is substantially more challenging. We demonstrate that current approaches to modelling cross-covariances with a spectral mixture kernel possess a critical blind spot. For a given pair of processes, the cross-covariance is not reproducible across the full range of permitted correlations, aside from the special case where their spectral densities are of identical shape. We present a solution to this issue by replacing the conventional Gaussian components of a spectral mixture with block components of finite bandwidth (i.e. rectangular step functions). The proposed family of kernel represents the first multi-output generalisation of the spectral mixture kernel that can approximate any stationary multi-output kernel to arbitrary precision.

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