Sparse Gaussian Processes using Pseudo-inputs

We present a new Gaussian process (GP) regression model whose covariance is parameterized by the the locations of M pseudo-input points, which we learn by a gradient based optimization. We take M N, where N is the number of real data points, and hence obtain a sparse regression method which has O(M 2 N) training cost and O(M 2) prediction cost per test case. We also find hyperparameters of the covariance function in the same joint optimization. The method can be viewed as a Bayesian regression model with particular input dependent noise. The method turns out to be closely related to several other sparse GP approaches, and we discuss the relation in detail.