We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can only utilize the sufficiently fine-grained auxiliary data sets on the same domain (e.g., a city). With the proposed model, the functions for respective areal data sets are assumed to be a multivariate dependent Gaussian process (GP) that is modeled as a linear mixing of independent latent GPs. Sharing of latent GPs across multiple areal data sets allows us to effectively estimate the spatial correlation for each areal data set; moreover it can easily be extended to transfer learning across multiple domains. To handle the multivariate areal data, we design an observation model with a spatial aggregation process for each areal data set, which is an integral of the mixed GP over the corresponding region. By deriving the posterior GP, we can predict the data value at any location point by considering the spatial correlations and the dependences between areal data sets, simultaneously. Our experiments on real-world data sets demonstrate that our model can 1) accurately refine coarse-grained areal data, and 2) offer performance improvements by using the areal data sets from multiple domains.

Existing regression-based models can only utilize the sufficiently fine-grained auxiliary data sets on the same domain (e.g., a city).

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.

We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can only utilize the sufficiently fine-grained auxiliary data sets on the same domain (e.g., a city). With the proposed model, the functions for respective areal data sets are assumed to be a multivariate dependent Gaussian process (GP) that is modeled as a linear mixing of independent latent GPs. Sharing of latent GPs across multiple areal data sets allows us to effectively estimate the spatial correlation for each areal data set; moreover it can easily be extended to transfer learning across multiple domains.

We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can only utilize the sufficiently fine-grained auxiliary data sets on the same domain (e.g., a city). With the proposed model, the functions for respective areal data sets are assumed to be a multivariate dependent Gaussian process (GP) that is modeled as a linear mixing of independent latent GPs. Sharing of latent GPs across multiple areal data sets allows us to effectively estimate the spatial correlation for each areal data set; moreover it can easily be extended to transfer learning across multiple domains.

We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models require the fine-grained auxiliary data sets on the same domain. With the proposed model, the functions for respective areal data sets are assumed to be a multivariate dependent Gaussian process (GP) that is modeled as a linear mixing of independent latent GPs. Sharing of latent GPs across multiple areal data sets allows us to effectively estimate spatial correlation for each areal data set; moreover it can easily be extended to transfer learning across multiple domains. To handle the multivariate areal data, we design its observation model with a spatial aggregation process for each areal data set, which is an integral of the mixed GP over the corresponding region. By deriving the posterior GP, we can predict the data value at any location point by considering the spatial correlations and the dependences between areal data sets simultaneously. Our experiments on real-world data sets demonstrate that our model can 1) accurately refine the coarse-grained areal data, and 2) offer performance improvements by using the areal data sets from multiple domains.