Understanding Probabilistic Sparse Gaussian Process Approximations

Part of Advances in Neural Information Processing Systems 29 (NIPS 2016)

Authors

Matthias Bauer, Mark van der Wilk, Carl Edward Rasmussen

Abstract

Good sparse approximations are essential for practical inference in Gaussian Processes as the computational cost of exact methods is prohibitive for large datasets. The Fully Independent Training Conditional (FITC) and the Variational Free Energy (VFE) approximations are two recent popular methods. Despite superficial similarities, these approximations have surprisingly different theoretical properties and behave differently in practice. We thoroughly investigate the two methods for regression both analytically and through illustrative examples, and draw conclusions to guide practical application.