Gaussian Process Online Learning With a Sparse Data Stream

Abstract

Gaussian processes (GPs) have been exploited for various applications even including online learning. To learn time-varying hyperparameters from an information-limited sparse data stream, we consider the infinite-horizon Gaussian process (IHGP) with a low computational complexity. For example, the IHGP framework could provide efficient GP online learning with a sparse data stream in mobile devices. However, we show that the originally proposed IHGP has difficulty in learning time-varying hyperparameters online from the sparse data stream due to the numerically approximated gradient of the marginal likelihood function. In this paper, we show how to extend the IHGP in order to learn time-varying hyperparameters using a sparse and non-stationary data stream. In particular, our solution approach offers the exact gradient as the solution of a Lyapunov equation. Therefore, our approach achieves better performance with a sparse data stream while still keeping the computational complexity low. Finally, we present the comparison results to demonstrate that our approach outperforms the originally proposed IHGP on practical applications with sparse data streams. To demonstrate the effectiveness of our approach, we consider a multi-rate sensor fusion or an interpolation problem where slow vision systems need to be combined with other fast sensory units for feedback control in the field of autonomous driving. In particular, we apply our approach to vehicle lateral position error estimation together with a deep learning model for autonomous driving using non-stationary lateral position error signals in a model-free and data-driven fashion.