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Aggregate data often appear in various fields such as socio-economics andpublic security. The aggregate data are associated not with points but withsupports (e.g., spatial regions in a city). Since the supports may have variousgranularities depending on attributes (e.g., poverty rate and crime rate),modeling such data is not straightforward. This article offers a multi-outputGaussian process (MoGP) model that infers functions for attributes usingmultiple aggregate datasets of respective granularities. In the proposed model,the function for each attribute is assumed to be a dependent GP modeled as alinear mixing of independent latent GPs. We design an observation model with anaggregation process for each attribute; the process is an integral of the GPover the corresponding support. We also introduce a prior distribution of themixing weights, which allows a knowledge transfer across domains (e.g., cities)by sharing the prior. This is advantageous in such a situation where thespatially aggregated dataset in a city is too coarse to interpolate; theproposed model can still make accurate predictions of attributes by utilizingaggregate datasets in other cities. The inference of the proposed model isbased on variational Bayes, which enables one to learn the model parametersusing the aggregate datasets from multiple domains. The experiments demonstratethat the proposed model outperforms in the task of refining coarse-grainedaggregate data on real-world datasets: Time series of air pollutants in Beijingand various kinds of spatial datasets from New York City and Chicago.

Aggregated Multi-output Gaussian Processes with Knowledge Transfer Across Domains