We consider multi-task regression models where the observations are assumed to be a linear combination of several latent node functions and weight functions, which are both drawn from Gaussian process priors. Driven by the problem of developing scalable methods for forecasting distributed solar and other renewable power generation, we propose coupled priors over groups of (node or weight) processes to exploit spatial dependence between functions. We estimate forecast models for solar power at multiple distributed sites and ground wind speed at multiple proximate weather stations. Our results show that our approach maintains or improves point-prediction accuracy relative to competing solar benchmarks and improves over wind forecast benchmark models on all measures. At the same time our approach provides better quantification of predictive uncertainties.
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