# Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processes

@inproceedings{Tebbutt2021CombiningPA, title={Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processes}, author={Will Tebbutt and A. Solin and Richard E. Turner}, booktitle={UAI}, year={2021} }

Gaussian processes (GPs) are important probab-ilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support large numbers of off-the-grid spatial data-points and long time-series which is a hallmark of many applications. Pseudo-point approximations, one of the gold-standard methods for scaling GPs to large data sets, are well suited for handling off-the-grid…

## 3 Citations

Sparse Algorithms for Markovian Gaussian Processes

- Computer ScienceAISTATS
- 2021

This work derives a general site-based approach to approximate inference, whereby the non-Gaussian likelihood is approximate with local Gaussian terms, called sites, and results in a suite of novel sparse extensions to algorithms from both the machine learning and signal processing literature, including variational inference, expectation propagation, and the classical nonlinear Kalman smoothers.

Spatio-Temporal Variational Gaussian Processes

- Computer ScienceNeurIPS
- 2021

A sparse approximation is derived that constructs a state-space model over a reduced set of spatial inducing points, and it is shown that for separable Markov kernels the full and sparse cases exactly recover the standard variational GP, whilst exhibiting favourable computational properties.

Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guarantees

- Computer ScienceArXiv
- 2021

This work forms natural gradient variational inference, expectation propagation, and posterior linearisation as extensions of Newton’s method for optimising the parameters of a Bayesian posterior distribution under the framework of numerical optimisation, and provides new insights into the connections between various inference schemes.

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