Streaming Sparse Gaussian Process Approximations

Sparse approximations for Gaussian process models provide a suite of methods that enable these models to be deployed in large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a principled method to handle streaming data in which the posterior distribution over function values and the hyperparameters 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 principled methods for learning hyperparameters and optimising pseudo-input locations. The proposed framework is experimentally validated using synthetic and real-world datasets.