mlsanityData to 7 Oct 2026

Mat'ern Gaussian Processes on Graphs

arXiv 2010.15538 ↗First posted 29 Oct 2020stat.ML cs.LGcited by 65

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Abstract (arXiv)

Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Mat'ern Gaussian processes - a widely-used model class in the Euclidean setting - to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Mat'ern Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.

Key facts. Cited by 65 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Oct 2020.

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Citing papers per year: 2021: 9; 2022: 8; 2023: 14; 2024: 11; 2025: 11; 2026: 12.

65 papers.

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  1. 2024Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similaritiescited by 156
  2. 2021Generative Models as Distributions of Functionscited by 89
  3. 2021Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classificationcited by 79
  4. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  5. 2022Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact casecited by 25
  6. 2021Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernelscited by 24
  7. 2021Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernelscited by 19
  8. 2023Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimizationcited by 18
  9. 2023Hodge-Compositional Edge Gaussian Processescited by 16
  10. 2023Feature Transportation Improves Graph Neural Networkscited by 15
  11. 2023Gaussian Processes on Cellular Complexescited by 15
  12. 2021Adaptive Gaussian Processes on Graphs via Spectral Graph Waveletscited by 11
38 more
  1. 2021Non-separable Spatio-temporal Graph Kernels via SPDEscited by 11
  2. 2024Uncertainty for Active Learning on Graphscited by 11
  3. 2023General Graph Random Featurescited by 10
  4. 2024The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphscited by 10
  5. 2022Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifoldscited by 9
  6. 2024Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equationscited by 8
  7. 2022Isotropic Gaussian Processes on Finite Spaces of Graphscited by 7
  8. 2023Bayesian Optimisation of Functions on Graphscited by 7
  9. 2024Linear Transformer Topological Masking with Graph Random Featurescited by 7
  10. 2023Intrinsic Gaussian Process on Unknown Manifolds with Probabilistic Metricscited by 6
  11. 2023Posterior Contraction Rates for Mat'ern Gaussian Processes on Riemannian Manifoldscited by 6
  12. 2023Implicit Gaussian process representation of vector fields over arbitrary latent manifoldscited by 6
  13. 2022Mario Plays on a Manifold: Generating Functional Content in Latent Space through Differential Geometrycited by 5
  14. 2026Topological Flow Matchingcited by 5
  15. 2022Optimization on Manifolds via Graph Gaussian Processescited by 4
  16. 2023Dimensionality Reduction as Probabilistic Inferencecited by 4
  17. 2023Implicit Manifold Gaussian Process Regressioncited by 4
  18. 2025Graph Random Features for Scalable Gaussian Processescited by 4
  19. 2021Nonnegative spatial factorizationcited by 2
  20. 2021Modeling Advection on Directed Graphs using Mat'ern Gaussian Processes for Traffic Flowcited by 2
  21. 2022Scalable Deep Gaussian Markov Random Fields for General Graphscited by 2
  22. 2023Graph Neural Stochastic Differential Equationscited by 2
  23. 2024Variance-Reducing Couplings for Random Featurescited by 2
  24. 2024Linear Opinion Pooling for Uncertainty Quantification on Graphscited by 2
  25. 2024Residual Deep Gaussian Processes on Manifoldscited by 2
  26. 2025Stochastic Poisson Surface Reconstruction with One Solve using Geometric Gaussian Processescited by 2
  27. 2021Evolving-Graph Gaussian Processescited by 1
  28. 2022Transductive Kernels for Gaussian Processes on Graphscited by 1
  29. 2023Stochastic PDE representation of random fields for large-scale Gaussian process regression and statistical finite element analysiscited by 1
  30. 2024On Probabilistic Pullback Metrics for Latent Hyperbolic Manifoldscited by 1
  31. 2025Discrete Gaussian Vector Fields On Meshescited by 1
  32. 2025Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Latercited by 1
  33. 2025Conformalized Gaussian processes for online uncertainty quantification over graphscited by 1
  34. 2025Omnipresent Yet Overlooked: Heat Kernels in Combinatorial Bayesian Optimizationcited by 1
  35. 2023Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systemscited by 0
  36. 2024Reconstructing Blood Flow in Data-Poor Regimes: A Vasculature Network Kernel for Gaussian Process Regressioncited by 0
  37. 2024Intrinsic Gaussian Process Regression Modeling for Manifold-valued Response Variablecited by 0
  38. 2025Low-rank computation of the posterior mean in Multi-Output Gaussian Processescited by 0

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