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

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 no...

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Bibliographic Details
Published inarXiv.org
Main Authors Graßhoff, Jan, Jankowski, Alexandra, Rostalski, Philipp
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.12.2019
Subjects
Approximation
Economic models
Estimating techniques
Gaussian process
Interpolation
Kernels
Signal processing
Stationary processes
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Summary: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 presents 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. Kernel learning is done by optimizing the marginal likelihood, which can be approximated efficiently using stochastic trace estimation methods. Our approach is demonstrated on numerical examples and large biomedical datasets.
ISSN:2331-8422