mlsanityData to 7 Oct 2026

Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo

arXiv 1508.04319 ↗First posted 18 Aug 2015stat.MLcited by 29

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Abstract (arXiv)

We present a novel approach for fully non-stationary Gaussian process regression (GPR), where all three key parameters -- noise variance, signal variance and lengthscale -- can be simultaneously input-dependent. We develop gradient-based inference methods to learn the unknown function and the non-stationary model parameters, without requiring any model approximations. We propose to infer full parameter posterior with Hamiltonian Monte Carlo (HMC), which conveniently extends the analytical gradient-based GPR learning by guiding the sampling with model gradients. We also learn the MAP solution from the posterior by gradient ascent. In experiments on several synthetic datasets and in modelling of temporal gene expression, the nonstationary GPR is shown to be necessary for modeling realistic input-dependent dynamics, while it performs comparably to conventional stationary or previous non-stationary GPR models otherwise.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Aug 2015.

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Citing papers per year: 2021: 3; 2022: 8; 2023: 3; 2024: 7; 2025: 5; 2026: 3.

29 papers.

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  1. 2023Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorialcited by 27
  2. 2021Partitioned Active Learning for Heterogeneous Systemscited by 10
  3. 2024Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learningcited by 10
  4. 2022Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classificationcited by 7
  5. 2022Active learning-assisted neutron spectroscopy with log-Gaussian processescited by 4
  6. 2023Hierarchical-Hyperplane Kernels for Actively Learning Gaussian Process Models of Nonstationary Systemscited by 4
  7. 2022Mixtures of Gaussian Process Experts with SMC2cited by 3
  8. 2022Kernel Learning for Explainable Climate Sciencecited by 3
  9. 2022The Normalized Cross Density Functional: A Framework to Quantify Statistical Dependence for Random Processescited by 3
  10. 2023Thin and Deep Gaussian Processescited by 3
  11. 2021Accurate Remaining Useful Life Prediction with Uncertainty Quantification: a Deep Learning and Nonstationary Gaussian Process Approachcited by 2
  12. 2022Bayesian Optimization with Informative Covariancecited by 2
17 more
  1. 2022Uncertainty Disentanglement with Non-stationary Heteroscedastic Gaussian Processes for Active Learningcited by 2
  2. 2024Nonstationary Sparse Spectral Permanental Processcited by 2
  3. 2021Hierarchical Non-Stationary Temporal Gaussian Processes With L1-Regularizationcited by 1
  4. 2022Learning non-stationary and discontinuous functions using clustering, classification and Gaussian process modellingcited by 1
  5. 2024Polynomial Chaos Expanded Gaussian Processcited by 1
  6. 2024Non-stationary and Sparsely-correlated Multi-output Gaussian Process with Spike-and-Slab Priorcited by 1
  7. 2025Deep Jump Gaussian Processes for Surrogate Modeling of High-Dimensional Piecewise Continuous Functionscited by 1
  8. 2025Mind the Jumps: A Scalable Robust Local Gaussian Process for Multidimensional Response Surfaces with Discontinuitiescited by 1
  9. 2024A New Reliable & Parsimonious Learning Strategy Comprising Two Layers of Gaussian Processes, to Address Inhomogeneous Empirical Correlation Structurescited by 0
  10. 2024Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributionscited by 0
  11. 2024Scalable Batch Bayesian Optimization Via Subspace Acquisition Functionscited by 0
  12. 2025SEEK: Self-adaptive Explainable Kernel For Nonstationary Gaussian Processescited by 0
  13. 2025Improving Random Forests by Smoothingcited by 0
  14. 2025A Framework for Nonstationary Gaussian Processes with Neural Network Parameterscited by 0
  15. 2026Correcting Boundary Bias and Observation Independence in Bayesian Experimental Designcited by 0
  16. 2026Predicting Covariate-Driven Spatial Deformation for Nonstationary Gaussian Processescited by 0
  17. 2026Covariance-Boosted Gaussian Processes for Spatiotemporal Irregularitiescited by 0