Abstract
Gaussian processes (GPs) are flexible distributions over functions that
enable high-level assumptions about unknown functions to be encoded in a
parsimonious, flexible and general way. Although elegant, the application of
GPs is limited by computational and analytical intractabilities that arise when
data are sufficiently numerous or when employing non-Gaussian models.
Consequently, a wealth of GP approximation schemes have been developed over the
last 15 years to address these key limitations. Many of these schemes employ a
small set of pseudo data points to summarise the actual data. In this paper, we
develop a new pseudo-point approximation framework using Power Expectation
Propagation (Power EP) that unifies a large number of these pseudo-point
approximations. Unlike much of the previous venerable work in this area, the
new framework is built on standard methods for approximate inference
(variational free-energy, EP and Power EP methods) rather than employing
approximations to the probabilistic generative model itself. In this way, all
of approximation is performed at `inference time' rather than at `modelling
time' resolving awkward philosophical and empirical questions that trouble
previous approaches. Crucially, we demonstrate that the new framework includes
new pseudo-point approximation methods that outperform current approaches on
regression and classification tasks.
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