Sparse Grouped Gaussian Processes for Solar Power Forecasting

We consider multi-task regression models where observations are assumed to be a linear combination of several latent node and weight functions, all drawn from Gaussian process priors that allow nonzero covariance between grouped latent functions. Motivated by the problem of developing scalable methods for distributed solar forecasting, we exploit sparse covariance structures where latent functions are assumed to be conditionally independent given a group-pivot latent function. We exploit properties of multivariate Gaussians to construct sparse Cholesky factors directly, rather than obtaining them through iterative routines, and by doing so achieve significantly improved time and memory complexity including prediction complexity that is linear in the number of grouped functions. We test our approach on large multi-task datasets and find that sparse specifications achieve the same or better accuracy than non-sparse counterparts in less time, and improve on benchmark model accuracy.