Orthogonally Decoupled Variational Gaussian Processes

TL;DR

This paper introduces an orthogonal decoupled variational Gaussian process method that improves scalability and convergence speed by leveraging an orthogonal basis for the mean function, extending prior decoupled approaches.

Contribution

It proposes a novel orthogonal decoupled parametrization for variational GPs, enhancing performance and convergence speed over existing decoupled methods.

Findings

Faster convergence demonstrated in multiple experiments

Achieves better performance than previous decoupled approaches

Maintains linear complexity in the number of mean parameters

Abstract

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art sparse variational inference methods trade modeling accuracy against complexity. However, the complexities of these methods still scale superlinearly in the number of basis functions, implying that that sparse GP methods are able to learn from large datasets only when a small model is used. Recently, a decoupled approach was proposed that removes the unnecessary coupling between the complexities of modeling the mean and the covariance functions of a GP. It achieves a linear complexity in the number of mean parameters, so an expressive posterior mean function can be modeled. While promising, this approach suffers from optimization difficulties due to ill-conditioning and non-convexity. In this work, we propose an alternative decoupled parametrization. It adopts an orthogonal basis in the mean function to model the residues that cannot be learned by the standard coupled approach. Therefore, our method extends, rather than replaces, the coupled approach to achieve strictly better performance. This construction admits a straightforward natural gradient update rule, so the structure of the information manifold that is lost during decoupling can be leveraged to speed up learning. Empirically, our algorithm demonstrates significantly faster convergence in multiple experiments.