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We consider multi-task regression models where observations are assumed to bea linear combination of several latent node and weight functions, all drawnfrom Gaussian process (GP) priors that allow nonzero covariance between groupedlatent functions. We show that when these grouped functions are conditionallyindependent given a group-dependent pivot, it is possible to parameterize theprior through sparse Cholesky factors directly, hence avoiding theircomputation during inference. Furthermore, we establish that kernels that aremultiplicatively separable over input points give rise to such sparseparameterizations naturally without any additional assumptions. Finally, weextend the use of these sparse structures to approximate posteriors withinvariational inference, further improving scalability on the number offunctions. We test our approach on multi-task datasets concerning distributedsolar forecasting and show that it outperforms several multi-task GP baselinesand that our sparse specifications achieve the same or better accuracy thannon-sparse counterparts.

Scalable Grouped Gaussian Processes via Direct Cholesky Functional Representations