mlsanityData to 7 Oct 2026

Spatio-Temporal Variational Gaussian Processes

arXiv 2111.01732 ↗First posted 2 Nov 2021cs.LG stat.MLcited by 32

Not on the map. Why?

Abstract (arXiv)

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with respect to time. Our natural gradient approach enables application of parallel filtering and smoothing, further reducing the temporal span complexity to be logarithmic in the number of time steps. We derive a sparse approximation that constructs a state-space model over a reduced set of spatial inducing points, and show that for separable Markov kernels the full and sparse cases exactly recover the standard variational GP, whilst exhibiting favourable computational properties. To further improve the spatial scaling we propose a mean-field assumption of independence between spatial locations which, when coupled with sparsity and parallelisation, leads to an efficient and accurate method for large spatio-temporal problems.

Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). Builds on 26 of its 55 references that are in the map. First posted on arXiv 2 Nov 2021.

Builds on

26 of 55 references.

References · 26

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Variational Inference: A Review for Statisticianscited by 1,466
  3. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 603
  4. 2013Gaussian Processes for Big Datacited by 377
  5. 2014Scalable Variational Gaussian Process Classificationcited by 226
  6. 2015Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)cited by 175
  7. 2016GPflow: A Gaussian process library using TensorFlowcited by 139
  8. 2019Exact Gaussian Processes on a Million Data Pointscited by 118
  9. 2016Variational Fourier features for Gaussian processescited by 85
  10. 2014Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasetscited by 71
  11. 2016Understanding Probabilistic Sparse Gaussian Process Approximationscited by 68
  12. 2017Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Modelscited by 65
14 more
  1. 2018Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Modelscited by 38
  2. 2019Temporal Parallelization of Bayesian Smootherscited by 31
  3. 2019Scalable Exact Inference in Multi-Output Gaussian Processescited by 25
  4. 2020Fast Variational Learning in State-Space Gaussian Process Modelscited by 20
  5. 2020Doubly Sparse Variational Gaussian Processescited by 14
  6. 2018State Space Gaussian Processes with Non-Gaussian Likelihoodcited by 12
  7. 2019Banded Matrix Operators for Gaussian Markov Models in the Automatic Differentiation Eracited by 11
  8. 2020State Space Expectation Propagation: Efficient Inference Schemes for Temporal Gaussian Processescited by 10
  9. 2021Sparse Algorithms for Markovian Gaussian Processescited by 10
  10. 2021Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processescited by 7
  11. 2016AutoGP: Exploring the Capabilities and Limitations of Gaussian Process Modelscited by 6
  12. 2018Efficient Inference in Multi-task Cox Process Modelscited by 5
  13. 2018Scalable high-resolution forecasting of sparse spatiotemporal events with kernel methods: a winning solution to the NIJ "Real-Time Crime Forecasting Challenge"cited by 4
  14. 2019End-to-End Probabilistic Inference for Nonstationary Audio Analysiscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 9; 2024: 6; 2025: 13; 2026: 3.

32 papers.

Sort:

  1. 2022Markovian Gaussian Process Variational Autoencoderscited by 16
  2. 2024Computation-Aware Kalman Filtering and Smoothingcited by 12
  3. 2024Scalable Spatiotemporal Prediction with Bayesian Neural Fieldscited by 10
  4. 2025Robust and Conjugate Spatio-Temporal Gaussian Processescited by 9
  5. 2025Revisiting Kernel Attention with Correlated Gaussian Process Representationcited by 9
  6. 2024eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modelingcited by 7
  7. 2024Physics-Informed Variational State-Space Gaussian Processescited by 7
  8. 2023Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trainscited by 5
  9. 2023The Rank-Reduced Kalman Filter: Approximate Dynamical-Low-Rank Filtering In High Dimensionscited by 5
  10. 2023Sequential Monte Carlo Learning for Time Series Structure Discoverycited by 5
  11. 2023Actually Sparse Variational Gaussian Processescited by 4
  12. 2025SING: SDE Inference via Natural Gradientscited by 4
20 more
  1. 2023Gaussian Processes for Monitoring Air-Quality in Kampalacited by 3
  2. 2025Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modellingcited by 3
  3. 2024Scalable Multi-Output Gaussian Processes with Stochastic Variational Inferencecited by 2
  4. 2023Short-term Prediction and Filtering of Solar Power Using State-Space Gaussian Processescited by 1
  5. 2023Efficient Sensor Placement from Regression with Sparse Gaussian Processes in Continuous and Discrete Spacescited by 1
  6. 2025STACI: Spatio-Temporal Aleatoric Conformal Inferencecited by 1
  7. 2025BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fieldscited by 1
  8. 2026UrbanFM: Scaling Urban Spatio-Temporal Foundation Modelscited by 1
  9. 2026Spatio-Temporal Gaussian Process for Building Terrain-Incorporating Wind Power Curvescited by 1
  10. 2023Deep Functional Factor Models: Forecasting High-Dimensional Functional Time Series via Bayesian Nonparametric Factorizationcited by 0
  11. 2023Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systemscited by 0
  12. 2024Learning Coupled Subspaces for Multi-Condition Spike Datacited by 0
  13. 2025Diffusion-aware Censored Gaussian Processes for Demand Modellingcited by 0
  14. 2025Effect Decomposition of Functional-Output Computer Experiments via Orthogonal Additive Gaussian Processescited by 0
  15. 2025Spatiodynamic inference using vision-based generative modellingcited by 0
  16. 2025A New Lens on Homelessness: Daily Tent Monitoring with 311 Calls and Street Imagescited by 0
  17. 2025Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantificationcited by 0
  18. 2025Designing an Optimal Sensor Network via Minimizing Information Losscited by 0
  19. 2025Spatially-informed transformers: Injecting geostatistical covariance biases into self-attention for spatio-temporal forecastingcited by 0
  20. 2026A Factor Graph Approach to Scalable Multi-Output Gaussian Process Regressioncited by 0