# Robust and Conjugate Spatio-Temporal Gaussian Processes

arXiv: https://arxiv.org/abs/2502.02450 · HTML: https://mlsanity.com/paper/2502.02450/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 65 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 25 of 25)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Constant-Time Predictive Distributions for Gaussian Processes](https://mlsanity.com/paper/1803.06058/) (2018)
- [Temporal Parallelization of Bayesian Smoothers](https://mlsanity.com/paper/1905.13002/) (2019)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Stein Point Markov Chain Monte Carlo](https://mlsanity.com/paper/1905.03673/) (2019)
- [Optimal Thinning of MCMC Output](https://mlsanity.com/paper/2005.03952/) (2020)
- [A comparison of learning rate selection methods in generalized Bayesian inference](https://mlsanity.com/paper/2012.11349/) (2020)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Composite Goodness-of-fit Tests with Kernels](https://mlsanity.com/paper/2111.10275/) (2021)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Generalised Bayesian Inference for Discrete Intractable Likelihood](https://mlsanity.com/paper/2206.08420/) (2022)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guarantees](https://mlsanity.com/paper/2111.01721/) (2021)
- [State Space Gaussian Processes with Non-Gaussian Likelihood](https://mlsanity.com/paper/1802.04846/) (2018)
- [Robust Gaussian Processes via Relevance Pursuit](https://mlsanity.com/paper/2410.24222/) (2024)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Robustifying likelihoods by optimistically re-weighting data](https://mlsanity.com/paper/2303.10525/) (2023)
- [Online Time Series Anomaly Detection with State Space Gaussian Processes](https://mlsanity.com/paper/2201.06763/) (2022)
- [Generalized Score Matching for Regression](https://mlsanity.com/paper/2203.09864/) (2022)
- [A Gaussian Process-based Streaming Algorithm for Prediction of Time Series With Regimes and Outliers](https://mlsanity.com/paper/2406.00570/) (2024)

## Built on by (most cited first, 9 of 9)

- [Scalable Gaussian Processes with Latent Kronecker Structure](https://mlsanity.com/paper/2506.06895/) (2025)
- [Martingale Posterior Neural Networks for Fast Sequential Decision Making](https://mlsanity.com/paper/2506.11898/) (2025)
- [SMRS: advocating a unified reporting standard for surrogate models in the artificial intelligence era](https://mlsanity.com/paper/2502.06753/) (2025)
- [Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets](https://mlsanity.com/paper/2505.03585/) (2025)
- [Robust, Online, and Adaptive Decentralized Gaussian Processes](https://mlsanity.com/paper/2509.18011/) (2025)
- [Multi-Output Robust and Conjugate Gaussian Processes](https://mlsanity.com/paper/2510.26401/) (2025)
- [BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fields](https://mlsanity.com/paper/2509.26005/) (2025)
- [Robust Bayesian Optimisation with Unbounded Corruptions](https://mlsanity.com/paper/2511.15315/) (2025)
- [Generalised Robust Bayes for Joint Inference of Model and Contamination](https://mlsanity.com/paper/2607.25665/) (2026)

## Abstract (arXiv)

State-space formulations allow for Gaussian process (GP) regression with linear-in-time computational cost in spatio-temporal settings, but performance typically suffers in the presence of outliers. In this paper, we adapt and specialise the robust and conjugate GP (RCGP) framework of Altamirano et al. (2024) to the spatio-temporal setting. In doing so, we obtain an outlier-robust spatio-temporal GP with a computational cost comparable to classical spatio-temporal GPs. We also overcome the three main drawbacks of RCGPs: their unreliable performance when the prior mean is chosen poorly, their lack of reliable uncertainty quantification, and the need to carefully select a hyperparameter by hand. We study our method extensively in finance and weather forecasting applications, demonstrating that it provides a reliable approach to spatio-temporal modelling in the presence of outliers.