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We propose a probabilistic model for inferring the multivariate function frommultiple areal data sets with various granularities. Here, the areal data areobserved not at location points but at regions. Existing regression-basedmodels can only utilize the sufficiently fine-grained auxiliary data sets onthe same domain (e.g., a city). With the proposed model, the functions forrespective areal data sets are assumed to be a multivariate dependent Gaussianprocess (GP) that is modeled as a linear mixing of independent latent GPs.Sharing of latent GPs across multiple areal data sets allows us to effectivelyestimate the spatial correlation for each areal data set; moreover it caneasily be extended to transfer learning across multiple domains. To handle themultivariate areal data, we design an observation model with a spatialaggregation process for each areal data set, which is an integral of the mixedGP over the corresponding region. By deriving the posterior GP, we can predictthe data value at any location point by considering the spatial correlationsand the dependences between areal data sets, simultaneously. Our experiments onreal-world data sets demonstrate that our model can 1) accurately refinecoarse-grained areal data, and 2) offer performance improvements by using theareal data sets from multiple domains.

Spatially Aggregated Gaussian Processes with Multivariate Areal Outputs