Gaussian Process Kernels for Pattern Discovery and Extrapolation

TL;DR

This paper introduces new Gaussian process kernels based on Gaussian mixture spectral densities, enabling pattern discovery and long-range extrapolation while maintaining analytic simplicity, demonstrated on synthetic and real data.

Contribution

The paper presents a novel class of closed-form kernels derived from Gaussian mixture spectral densities for improved pattern discovery and extrapolation in Gaussian processes.

Findings

Effective pattern discovery demonstrated on synthetic data.

Successful long-range extrapolation on atmospheric CO2 and airline data.

Reconstruction of standard covariances within the proposed framework.

Abstract

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral density -- the Fourier transform of a kernel -- with a Gaussian mixture. The proposed kernels support a broad class of stationary covariances, but Gaussian process inference remains simple and analytic. We demonstrate the proposed kernels by discovering patterns and performing long range extrapolation on synthetic examples, as well as atmospheric CO2 trends and airline passenger data. We also show that we can reconstruct standard covariances within our framework.