MAGMA: Inference and Prediction with Multi-Task Gaussian Processes

Arthur Leroy (1) , Pierre Latouche (1) , Benjamin Guedj (2, 3, 4, 5, 6) , Servane Gey (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 UCL - University College of London [London]
3 UCL-CS - Department of Computer science [University College of London]
4 Inria-CWI - Inria-CWI
5 MODAL - MOdel for Data Analysis and Learning
6 Inria-London - The Inria London Programme

We investigate the problem of multiple time series forecasting, with the objective to improve multiple-step-ahead predictions. We propose a multi-task Gaussian process framework to simultaneously model batches of individuals with a common mean function and a specific covariance structure. This common mean is defined as a Gaussian process for which the hyper-posterior distribution is tractable. Therefore an EM algorithm can be derived for simultaneous hyper-parameters optimisation and hyper-posterior computation. Unlike previous approaches in the literature, we account for uncertainty and handle uncommon grids of observations while maintaining explicit formulations, by modelling the mean process in a non-parametric probabilistic framework. We also provide predictive formulas integrating this common mean process. This approach greatly improves the predictive performance far from observations, where information shared across individuals provides a relevant prior mean. Our overall algorithm is called MAGMA (standing for Multi tAsk Gaussian processes with common MeAn), and publicly available as a R package. The quality of the mean process estimation, predictive performances, and comparisons to alternatives are assessed in various simulated scenarios and on real datasets.

Mots clés: Multi-task learning; Gaussian process; EM algorithm; Common mean process; Functional data analysis

Domaines: Calcul [stat.CO]; Machine Learning [stat.ML]; Méthodologie [stat.ME]; Apprentissage [cs.LG]

Arthur Leroy, Pierre Latouche, Benjamin Guedj, Servane Gey. MAGMA: Inference and Prediction with Multi-Task Gaussian Processes. 2020. ⟨hal-02904446v1⟩