Efficient Updates for Data Association with Mixtures of Gaussian Processes

Gaussian processes (GPs) enable a probabilistic approach to important estimation and classification tasks that arise in robotics applications. Meanwhile, most GP-based methods are often prohibitively slow, thereby posing a substantial barrier to practical applications. Existing "sparse" methods to speed up GPs seek to either make the model more sparse, or find ways to more efficiently manage a large covariance matrix. In this paper, we present an orthogonal approach that memoises (i.e. reuses) previous computations in GP inference. We demonstrate that a substantial speedup can be achieved by incorporating memoisation into applications in which GPs must be updated frequently. Moreover, we derive a novel online update scheme for sparse GPs that can be used in conjunction with our memoisation approach for a synergistic improvement in performance. Across three robotic vision applications, we demonstrate between 40-100% speed-up over the standard method for inference in GP mixtures.