Scalable Gaussian Process Regression for Kernels with a Non-Stationary Phase

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Authors

Jan Graßhoff, Alexandra Jankowski, Philipp Rostalski

Abstract

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel matrix. Previous methods, however, cannot easily deal with non-stationary processes. This paper investigates an efficient GP framework, that extends structured kernel interpolation methods to GPs with a non-stationary phase. We particularly treat mixtures of non-stationary processes, which are commonly used in the context of separation problems e.g. in biomedical signal processing. Our approach employs multiple sets of non-equidistant inducing points to account for the non-stationarity and retrieve Toeplitz and Kronecker structure in the kernel matrix allowing for efficient inference and kernel learning. The approach is demonstrated on numerical examples and large biomedical datasets.