# Scalable Grouped Gaussian Processes via Direct Cholesky Functional Representations

## TL;DR

This paper introduces a scalable multi-task Gaussian process model using sparse Cholesky parameterizations that exploit kernel separability, enabling efficient inference and improved accuracy in large datasets.

## Contribution

It proposes a novel sparse Cholesky factorization approach for grouped Gaussian processes, leveraging kernel separability to enhance scalability and inference efficiency.

## Key findings

- Outperforms existing multi-task GP baselines in solar forecasting.
- Achieves comparable or better accuracy with sparse models.
- Enhances scalability through variational inference with sparse structures.

## Abstract

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 (GP) priors that allow nonzero covariance between grouped latent functions. We show that when these grouped functions are conditionally independent given a group-dependent pivot, it is possible to parameterize the prior through sparse Cholesky factors directly, hence avoiding their computation during inference. Furthermore, we establish that kernels that are multiplicatively separable over input points give rise to such sparse parameterizations naturally without any additional assumptions. Finally, we extend the use of these sparse structures to approximate posteriors within variational inference, further improving scalability on the number of functions. We test our approach on multi-task datasets concerning distributed solar forecasting and show that it outperforms several multi-task GP baselines and that our sparse specifications achieve the same or better accuracy than non-sparse counterparts.