Sparse Orthogonal Variational Inference for Gaussian Processes

TL;DR

This paper presents a new interpretation of sparse variational Gaussian process approximations that improves scalability, tightens lower bounds, and enables more efficient stochastic inference algorithms, achieving state-of-the-art results on CIFAR-10.

Contribution

It introduces a novel decomposition-based interpretation of sparse variational inference for Gaussian processes, leading to tighter bounds and improved algorithms.

Findings

Achieved state-of-the-art results on CIFAR-10 with GP models.

Developed more scalable stochastic variational inference algorithms.

Provided a unified interpretation that recovers existing methods.

Abstract

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 spanned by a finite basis of inducing points and the other capturing the remaining variation. 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 among purely GP-based models.