mlsanityData to 7 Oct 2026

Kernel Packet: An Exact and Scalable Algorithm for Gaussian Process Regression with Mat'ern Correlations

arXiv 2203.03116 ↗First posted 7 Mar 2022stat.ML cs.LG stat.MEcited by 10

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Abstract (arXiv)

We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat'ern correlations whose smoothness parameter nu is a half-integer. The proposed algorithm only requires O(nu3 n) operations and O(nu n) storage. This leads to a linear-cost solver since nu is chosen to be fixed and usually very small in most applications. The proposed method can be applied to multi-dimensional problems if a full grid or a sparse grid design is used. The proposed method is based on a novel theory for Mat'ern correlation functions. We find that a suitable rearrangement of these correlation functions can produce a compactly supported function, called a "kernel packet". Using a set of kernel packets as basis functions leads to a sparse representation of the covariance matrix that results in the proposed algorithm. Simulation studies show that the proposed algorithm, when applicable, is significantly superior to the existing alternatives in both the computational time and predictive accuracy.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 13 of its 45 references that are in the map. First posted on arXiv 7 Mar 2022.

Builds on

13 of 45 references.

References · 13

  1. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 603
  2. 2015Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)cited by 175
  3. 2015Gaussian Processes for Data-Efficient Learning in Robotics and Controlcited by 97
  4. 2019Rates of Convergence for Sparse Variational Gaussian Process Regressioncited by 62
  5. 2013Local Gaussian process approximation for large computer experimentscited by 59
  6. 2015Probabilistic Numerics and Uncertainty in Computationscited by 59
  7. 2015Optimal Rates for Random Fourier Featurescited by 38
  8. 2015A multi-resolution approximation for massive spatial datasetscited by 20
  9. 2015A theoretical framework for calibration in computer models: parametrization, estimation and convergence propertiescited by 12
  10. 2020Linear-time inference for Gaussian Processes on one dimensioncited by 11
  11. 2014Fast prediction of deterministic functions using sparse grid experimental designscited by 7
  12. 2020Generalization Guarantees for Sparse Kernel Approximation with Entropic Optimal Featurescited by 5
1 more
  1. 2017Linear-Cost Covariance Functions for Gaussian Random Fieldscited by 4

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Cited by year

Citing papers per year: 2023: 3; 2024: 6; 2025: 1.

10 papers.

  1. 2023Random Smoothing Regularization in Kernel Gradient Descent Learningcited by 6
  2. 2024A spectral mixture representation of isotropic kernels with application to random Fourier featurescited by 4
  3. 2023Representing Additive Gaussian Processes by Sparse Matricescited by 0
  4. 2023Privacy-aware Gaussian Process Regressioncited by 0
  5. 2024Beyond State Space Representation: A General Theory for Kernel Packetscited by 0
  6. 2024Kernel Multigrid: Accelerate Back-fitting via Sparse Gaussian Process Regressioncited by 0
  7. 2024Gaussian Processes Sampling with Sparse Grids under Additive Schwarz Preconditionercited by 0
  8. 2024Aggregation Models with Optimal Weights for Distributed Gaussian Processescited by 0
  9. 2024Linear cost and exponentially convergent approximation of Gaussian Mat'ern processes on intervalscited by 0
  10. 2025KP-PINNs: Kernel Packet Accelerated Physics Informed Neural Networkscited by 0