A0336
Title: Graphical Gaussian processes for high-dimensional multivariate spatial data
Authors: Abhi Datta - Johns Hopkins Bloomberg School of Public Health (United States) [presenting]
Abstract: For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is undesirable, especially for highly multivariate settings, where popular cross-covariance functions such as the multivariate Matern suffer from a "curse of dimensionality" as the number of parameters and floating point operations scale up in quadratic and cubic order, respectively, in the number of variables. A class of multivariate "Graphical Gaussian Processes" is proposed using a general construction called "stitching" that crafts cross-covariance functions from graphs and ensures process-level conditional independence among variables. For the Matern family of functions, stitching yields a multivariate GP whose univariate components are Matern GPs and conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. The utility of the graphical Matern GP is demonstrated to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling.
