Bayesian multi-task learning using finite-dimensional models: A comparative study

Elena Arcari, Anna Scampicchio, Andrea Carron, Melanie N. Zeilinger

Abstract: Simultaneous estimation of related tasks has been widely studied in the statistics and machine learning literature, and its effectiveness has been proven in many contexts such as econometrics and bioinformatics. However, state-of-the-art approaches leveraging Gaussian processes are encumbered by high computational costs that hinder their applicability to model-based and adaptive control design. In this paper, we address this issue by approximating non-parametric multi-task models by means of trigonometric basis functions. We estimate the involved parameters in a Bayesian framework using several deterministic and stochastic approaches, and highlight their advantages within an extensive comparative study. Overall, the proposed setup is able to suitably leverage task relatedness to outperform single-task methods, especially when single datasets are small.