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MAGMA: Inference and Prediction using Multi-Task Gaussian Processes with Common Mean

Arthur Leroy 1 Pierre Latouche 2 Benjamin Guedj 3, 4, 5, 6 Servane Gey 2 
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 : 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 MAGMA (standing for Multi tAsk GPs 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.
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https://hal.inria.fr/hal-02904446
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Submitted on : Tuesday, May 24, 2022 - 4:50:18 PM
Last modification on : Thursday, September 1, 2022 - 4:00:34 AM

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Arthur Leroy, Pierre Latouche, Benjamin Guedj, Servane Gey. MAGMA: Inference and Prediction using Multi-Task Gaussian Processes with Common Mean. Machine Learning, Springer Verlag, 2022, ⟨10.1007/s10994-022-06172-1⟩. ⟨hal-02904446v2⟩

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