MAGMA: Inference and Prediction with Multi-Task Gaussian Processes

TL;DR

This paper introduces MAGMA, a multi-task Gaussian process framework that shares information across tasks via a common mean process, improving multi-step time series forecasting accuracy and computational efficiency.

Contribution

The paper presents a novel multi-task GP model with a tractable hyper-posterior, fully accounting for uncertainty and handling irregular data grids, which outperforms existing methods.

Findings

Enhanced predictive accuracy in time series forecasting.

Reduced computational complexity compared to traditional models.

Effective handling of irregular observation grids.

Abstract

A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve multiple-step-ahead predictions. The common mean process is defined as a GP for which the hyper-posterior distribution is tractable. Therefore an EM algorithm is derived for handling both hyper-parameters optimisation and hyper-posterior computation. Unlike previous approaches in the literature, the model fully accounts for uncertainty and can handle irregular grids of observations while maintaining explicit formulations, by modelling the mean process in a unified GP framework. Predictive analytical equations are provided, integrating information shared across tasks through a relevant prior mean. This approach greatly improves the predictive performances, even far from observations, and may reduce significantly the computational complexity compared to traditional multi-task GP models. Our overall algorithm is called \textsc{Magma} (standing for Multi tAsk Gaussian processes with common MeAn). The quality of the mean process estimation, predictive performances, and comparisons to alternatives are assessed in various simulated scenarios and on real datasets.