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Abstract:
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We propose multivariate Graphical Gaussian Processes (GGP) using a novel construction called "stitching" to directly incorporate graphical models into cross-covariance functions ensuring process-level conditional independence among variables. For the Mat\'ern family of functions, stitching yields a multivariate GGP whose univariate components are exactly Mat\'ern GPs over the entire domain, and that conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive gains both in terms of parameter dimensionality and computations. Using simulation experiments we demonstrate the utility of the graphical GP with a Mat\'ern covariance to jointly model spatial data on many variables. We conclude with an application to air-pollution modelling.
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