Reviews: Spatially Aggregated Gaussian Processes with Multivariate Areal Outputs

The authors propose a model, based on Gaussian processes (GPs), that handles data defined as regions of the input space. The model initially follows the standard multivariate GP strategy by defining independent latent GPs, which are then linearly combined to form a multivariate dependent GP. To handle data at different granularities, observations are assumed to be area integrals of the multivariate GP. This allows the model to infer function values on a fine-scale from coarsely sampled data. The model also naturally handles data from different domains by sharing the latent GPs across the domains. The proposed model is evaluated using a total of 13 datasets from two cities, each with varying granularity. A refinement task, estimating small-scale structure from large-scale, is considered in two different set-ups: refining data within a single city and refining data across cities by utilising the transfer learning capabilities of the model. The model shows performance improvements over both baselines and competing models.