GP kernels for cross-spectrum analysis

Kyle Ulrich, David E. Carlson, Kafui Dzirasa, Lawrence Carin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations

Abstract

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, Wilson and Adams (2013) proposed the spectral mixture (SM) kernel to model the spectral density of a single task in a Gaussian process framework.In this paper, we develop a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. We demonstrate the expressive capabilities of the CSM kernel through implementation of a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel. Results are presented for measured multi-region electrophysiological data.
Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems
PublisherNeural information processing systems foundation
Pages1999-2007
Number of pages9
StatePublished - Jan 1 2015
Externally publishedYes

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