MAGMA: inference and prediction using multi-task Gaussian processes with common mean

• Published in: Machine learning Vol. 111; no. 5; pp. 1821 - 1849
• Main Authors: Leroy, Arthur, Latouche, Pierre, Guedj, Benjamin, Gey, Servane
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2022; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Artificial Intelligence; Computation; Computer Science; Control; Data analysis; Datasets; Gaussian process; Information sharing; Machine Learning; Magma; Mechatronics; Methodology; Natural Language Processing (NLP); Optimization; Performance prediction; Robotics; Simulation and Modeling; Statistics; Time series; Multi-task learning; EM algorithm; Common mean process; Functional data analysis; Gaussian processes; Gaussian process
• ISSN: 0885-6125; 1573-0565; 1573-0565
• DOI: 10.1007/s10994-022-06172-1

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.