Sparse Orthogonal Variational Inference for Gaussian Processes

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of two independent processes: one in the subspace spanned by the inducing basis and the other in the orthogonal complement to this subspace. We show that this formulation recovers existing approximations and at the same time allows to obtain tighter lower bounds on the marginal likelihood and new stochastic variational inference algorithms. We demonstrate the efficiency of these algorithms in several Gaussian process models ranging from standard regression to multi-class classification using (deep) convolutional Gaussian processes and report state-of-the-art results on CIFAR-10 with purely GP-based models.