  The advance of modern sensor technologies enables collection of multi-stream
longitudinal data where multiple signals from different units are collected in
real-time. In this article, we present a non-parametric approach to predict the
evolution of multi-stream longitudinal data for an in-service unit through
borrowing strength from other historical units. Our approach first decomposes
each stream into a linear combination of eigenfunctions and their corresponding
functional principal component (FPC) scores. A Gaussian process prior for the
FPC scores is then established based on a functional semi-metric that measures
similarities between streams of historical units and the in-service unit.
Finally, an empirical Bayesian updating strategy is derived to update the
established prior using real-time stream data obtained from the in-service
unit. Experiments on synthetic and real world data show that the proposed
framework outperforms state-of-the-art approaches and can effectively account
for heterogeneity as well as achieve high predictive accuracy.
