mlsanityData to 7 Oct 2026

Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices

arXiv 2609.30348 ↗First posted 24 Sep 2026stat.ML cs.AI cs.LGcited by 0

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Abstract (arXiv)

Gaussian processes constitute a cornerstone of probabilistic machine learning, yet scaling them to large datasets typically forces a trade-off between computational efficiency and model fidelity. This work bridges this gap by presenting an adaptive multi-resolution Gaussian process framework that is both scalable and exact. Our key innovation is constructing a naturally data-sparse covariance matrix with adaptive multi-resolution basis functions. These basis functions are directly anchored to samples, eliminating the need for auxiliary points. By shrinking the support domains of multi-resolution basis, the matrix block sizes are limited, guaranteeing sparsity. The inverse of the data-sparse covariance matrix is computed exactly and efficiently via the sparse Cholesky inverse algorithm. To further improve predictive uncertainties, we construct an augmented basis function. Theoretical analysis and numerical experiments demonstrate that our model achieves exact inference with O(n log2 n) training cost and O(logd n) prediction cost, establishing a principled framework for scalable and high-fidelity Gaussian process regression.

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References · 32

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20 more
  1. 2018Product Kernel Interpolation for Scalable Gaussian Processescited by 31
  2. 2023Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processescited by 31
  3. 2016Permutation and Grouping Methods for Sharpening Gaussian Process Approximationscited by 24
  4. 2017Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexitycited by 24
  5. 2022Posterior and Computational Uncertainty in Gaussian Processescited by 23
  6. 2015A multi-resolution approximation for massive spatial datasetscited by 20
  7. 2021Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networkscited by 17
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  9. 2021Bayesian Numerical Methods for Nonlinear Partial Differential Equationscited by 15
  10. 2022Basis-Function Models in Spatial Statisticscited by 9
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  12. 2022Variational Nearest Neighbor Gaussian Processcited by 8
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  14. 2022Gaussian Process Hydrodynamicscited by 4
  15. 2023Actually Sparse Variational Gaussian Processescited by 4
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  17. 2025All Emulators are Wrong, Many are Useful, and Some are More Useful Than Others: A Reproducible Comparison of Computer Model Surrogatescited by 3
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  19. 2023Accurate and Scalable Stochastic Gaussian Process Regression via Learnable Coreset-based Variational Inferencecited by 1
  20. 2025Mind the Jumps: A Scalable Robust Local Gaussian Process for Multidimensional Response Surfaces with Discontinuitiescited by 1

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