  Sparse pseudo-point approximations for Gaussian process (GP) models provide a
suite of methods that support deployment of GPs in the large data regime and
enable analytic intractabilities to be sidestepped. However, the field lacks a
principled method to handle streaming data in which both the posterior
distribution over function values and the hyperparameter estimates are updated
in an online fashion. The small number of existing approaches either use
suboptimal hand-crafted heuristics for hyperparameter learning, or suffer from
catastrophic forgetting or slow updating when new data arrive. This paper
develops a new principled framework for deploying Gaussian process
probabilistic models in the streaming setting, providing methods for learning
hyperparameters and optimising pseudo-input locations. The proposed framework
is assessed using synthetic and real-world datasets.
