mlsanityData to 14 Oct 2026

Robust and Conjugate Spatio-Temporal Gaussian Processes

arXiv 2502.02450 ↗First posted 4 Feb 2025stat.CO stat.ME stat.MLcited by 9

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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.

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

25 of 65 references.

References · 25

  1. 2013Gaussian Processes for Big Datacited by 383
  2. 2015Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)cited by 177
  3. 2013A General Framework for Updating Belief Distributionscited by 175
  4. 2016Understanding Probabilistic Sparse Gaussian Process Approximationscited by 68
  5. 2019Minimum Stein Discrepancy Estimatorscited by 57
  6. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  7. 2018Constant-Time Predictive Distributions for Gaussian Processescited by 48
  8. 2019Temporal Parallelization of Bayesian Smootherscited by 33
  9. 2021Spatio-Temporal Variational Gaussian Processescited by 32
  10. 2019Stein Point Markov Chain Monte Carlocited by 29
  11. 2020Optimal Thinning of MCMC Outputcited by 26
  12. 2020A comparison of learning rate selection methods in generalized Bayesian inferencecited by 23
13 more
  1. 2024Outlier-robust Kalman Filtering through Generalised Bayescited by 21
  2. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  3. 2023Robust and Scalable Bayesian Online Changepoint Detectioncited by 16
  4. 2022Generalised Bayesian Inference for Discrete Intractable Likelihoodcited by 14
  5. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
  6. 2021Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guaranteescited by 13
  7. 2018State Space Gaussian Processes with Non-Gaussian Likelihoodcited by 12
  8. 2024Robust Gaussian Processes via Relevance Pursuitcited by 8
  9. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  10. 2023Robustifying likelihoods by optimistically re-weighting datacited by 6
  11. 2022Online Time Series Anomaly Detection with State Space Gaussian Processescited by 5
  12. 2022Generalized Score Matching for Regressioncited by 5
  13. 2024A Gaussian Process-based Streaming Algorithm for Prediction of Time Series With Regimes and Outlierscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 8; 2026: 1.

9 papers.

  1. 2025Scalable Gaussian Processes with Latent Kronecker Structurecited by 5
  2. 2025Martingale Posterior Neural Networks for Fast Sequential Decision Makingcited by 4
  3. 2025SMRS: advocating a unified reporting standard for surrogate models in the artificial intelligence eracited by 2
  4. 2025Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Setscited by 2
  5. 2025Robust, Online, and Adaptive Decentralized Gaussian Processescited by 2
  6. 2025Multi-Output Robust and Conjugate Gaussian Processescited by 2
  7. 2025BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fieldscited by 1
  8. 2025Robust Bayesian Optimisation with Unbounded Corruptionscited by 1
  9. 2026Generalised Robust Bayes for Joint Inference of Model and Contaminationcited by 1