Time Series Forecasting with Gaussian Processes Needs Priors

• Published in: Machine Learning and Knowledge Discovery in Databases. Applied Data Science Track Vol. 12978; pp. 103 - 117
• Main Authors: Corani, Giorgio, Benavoli, Alessio, Zaffalon, Marco
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 9783030865139; 3030865134
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-86514-6_7

Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. Gaussian Processes (GPs) are a powerful tool for modeling time series, but so far there are no competitive approaches for automatic forecasting based on GPs. We propose practical solutions to two problems: automatic selection of the optimal kernel and reliable estimation of the hyperparameters. We propose a fixed composition of kernels, which contains the components needed to model most time series: linear trend, periodic patterns, and other flexible kernel for modeling the non-linear trend. Not all components are necessary to model each time series; during training the unnecessary components are automatically made irrelevant via automatic relevance determination (ARD). We moreover assign priors to the hyperparameters, in order to keep the inference within a plausible range; we design such priors through an empirical Bayes approach. We present results on many time series of different types; our GP model is more accurate than state-of-the-art time series models. Thanks to the priors, a single restart is enough the estimate the hyperparameters; hence the model is also fast to train.