Multi-task learning models for functional data and application to the prediction of sports performances
Abstract
The present work is dedicated to the analysis of functional data and the definition of multi-task Gaussian processes (GP) models for simultaneously dealing with regression and clustering. The algorithm Magma, from a previous work, enables modelling multiple asynchronous time series, assumed to share information, offering a remarkable improvement in performances compared to standard GP regression, along with a thorough quantification of uncertainty. An extension of this work is proposed from the definition of a multi-task GPs mixture, which enriches the previous approach with a clustering aspect. Learning the hyper-parameters in such model lies on the definition of variational distributions, since likelihood is not available directly, allowing us to maintain explicit posterior distributions. In addition, analytical formulas are derived for prediction of unobserved timestamps. The resulting algorithm, MagmaClust, offers a group-structure identification within a set of curves as well as enhanced predictions compared to Magma. This approach has been implemented and tested on several simulated datasets, exhibiting noticeable performances both on clustering and prediction tasks. A real data application, focusing on the study and forecast of future performance curves for young french swimmers, is proposed as well.
