# A Unifying Framework for Gaussian Process Pseudo-Point Approximations using Power Expectation Propagation

arXiv: https://arxiv.org/abs/1605.07066 · HTML: https://mlsanity.com/paper/1605.07066/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2016.

## Built on by (most cited first, 3 of 3)

- [Correlated Product of Experts for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2112.09519/) (2021)
- [A Latent Restoring Force Approach to Nonlinear System Identification](https://mlsanity.com/paper/2109.10681/) (2021)
- [Reservoir History Matching of the Norne field with generative exotic priors and a coupled Mixture of Experts -- Physics Informed Neural Operator Forward Model](https://mlsanity.com/paper/2406.00889/) (2024)

## Abstract (arXiv)

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.