mlsanityData to 7 Oct 2026

Non-Stationary Spectral Kernels

arXiv 1705.08736 ↗First posted 24 May 2017stat.ML cs.LGcited by 38

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Abstract (arXiv)

We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-stationary and non-monotonic kernels that can learn input-dependent and potentially long-range, non-monotonic covariances between inputs. We derive efficient inference using model whitening and marginalized posterior, and show with case studies that these kernels are necessary when modelling even rather simple time series, image or geospatial data with non-stationary characteristics.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 May 2017.

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Citing papers per year: 2021: 14; 2022: 6; 2023: 3; 2024: 4; 2025: 5; 2026: 6.

38 papers.

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  1. 2023Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorialcited by 27
  2. 2021On Learning the Transformer Kernelcited by 14
  3. 2021Neural Spectral Marked Point Processescited by 10
  4. 2024Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learningcited by 10
  5. 2022Exact Gaussian Processes for Massive Datasets via Non-Stationary Sparsity-Discovering Kernelscited by 9
  6. 2021Adaptive Inducing Points Selection For Gaussian Processescited by 8
  7. 2022Nonstationary multi-output Gaussian processes via harmonizable spectral mixturescited by 8
  8. 2021A Robust Asymmetric Kernel Function for Bayesian Optimization, with Application to Image Defect Detection in Manufacturing Systemscited by 6
  9. 2021Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Surveycited by 5
  10. 2021Mixed Variable Bayesian Optimization with Frequency Modulated Kernelscited by 4
  11. 2021Marginalising over Stationary Kernels with Bayesian Quadraturecited by 4
  12. 2022Online Estimation of the Koopman Operator Using Fourier Featurescited by 4
26 more
  1. 2023Hierarchical-Hyperplane Kernels for Actively Learning Gaussian Process Models of Nonstationary Systemscited by 4
  2. 2021The Minecraft Kernel: Modelling correlated Gaussian Processes in the Fourier domaincited by 3
  3. 2021A Temporal Kernel Approach for Deep Learning with Continuous-time Informationcited by 3
  4. 2021Learning High-Dimensional Distributions with Latent Neural Fokker-Planck Kernelscited by 2
  5. 2021Accurate Remaining Useful Life Prediction with Uncertainty Quantification: a Deep Learning and Nonstationary Gaussian Process Approachcited by 2
  6. 2022Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Datacited by 2
  7. 2022Uncertainty Disentanglement with Non-stationary Heteroscedastic Gaussian Processes for Active Learningcited by 2
  8. 2022Bayesian Convolutional Deep Sets with Task-Dependent Stationary Priorcited by 2
  9. 2023On the Identifiability and Interpretability of Gaussian Process Modelscited by 2
  10. 2024Nonstationary Sparse Spectral Permanental Processcited by 2
  11. 2025Probabilistic Wind Power Modelling via Heteroscedastic Non-Stationary Gaussian Processescited by 1
  12. 2025STACI: Spatio-Temporal Aleatoric Conformal Inferencecited by 1
  13. 2026Scalable Random Wavelet Features: Efficient Non-Stationary Kernel Approximation with Convergence Guaranteescited by 1
  14. 2021Stochastic Collapsed Variational Inference for Structured Gaussian Process Regression Networkcited by 0
  15. 2021Wasserstein-Splitting Gaussian Process Regression for Heterogeneous Online Bayesian Inferencecited by 0
  16. 2021Remaining useful life prediction with uncertainty quantification: development of a highly accurate model for rotating machinerycited by 0
  17. 2024A New Reliable & Parsimonious Learning Strategy Comprising Two Layers of Gaussian Processes, to Address Inhomogeneous Empirical Correlation Structurescited by 0
  18. 2024Stein Random Feature Regressioncited by 0
  19. 2025Multi-View Oriented GPLVM: Expressiveness and Efficiencycited by 0
  20. 2025Scalable Deep Basis Kernel Gaussian Processescited by 0
  21. 2025Bayesian Optimization over Bounded Domains with the Beta Product Kernelcited by 0
  22. 2026Regular Fourier Features for Nonstationary Gaussian Processescited by 0
  23. 2026Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomizationcited by 0
  24. 2026Hierarchical Bayesian Quadraturecited by 0
  25. 2026ALAS: Additive Learnable Alpha-Stable Kernels for Flexible Bayesian Optimizationcited by 0
  26. 2026Why not to use the Gaussian kernelcited by 0