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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
5 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : 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.
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Contributor : Benjamin Guedj <>
Submitted on : Wednesday, July 22, 2020 - 10:57:19 AM
Last modification on : Saturday, June 26, 2021 - 3:35:26 AM


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  • HAL Id : hal-02904446, version 1
  • ARXIV : 2007.10731


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



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