mlsanityData to 7 Oct 2026

Scalable Log Determinants for Gaussian Process Kernel Learning

arXiv 1711.03481 ↗First posted 9 Nov 2017stat.ML cs.AI cs.LGcited by 34

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Abstract (arXiv)

For applications as varied as Bayesian neural networks, determinantal point processes, elliptical graphical models, and kernel learning for Gaussian processes (GPs), one must compute a log determinant of an n × n positive definite matrix, and its derivatives - leading to prohibitive O(n3) computations. We propose novel O(n) approaches to estimating these quantities from only fast matrix vector multiplications (MVMs). These stochastic approximations are based on Chebyshev, Lanczos, and surrogate models, and converge quickly even for kernel matrices that have challenging spectra. We leverage these approximations to develop a scalable Gaussian process approach to kernel learning. We find that Lanczos is generally superior to Chebyshev for kernel learning, and that a surrogate approach can be highly efficient and accurate with popular kernels.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Nov 2017.

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Citing papers per year: 2021: 10; 2022: 6; 2023: 2; 2024: 4; 2025: 9; 2026: 3.

34 papers.

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  1. 2021Practical and Rigorous Uncertainty Bounds for Gaussian Process Regressioncited by 49
  2. 2022Joint Entropy Search for Multi-objective Bayesian Optimizationcited by 45
  3. 2021Preconditioning for Scalable Gaussian Process Hyperparameter Optimizationcited by 22
  4. 2021Bias-Free Scalable Gaussian Processes via Randomized Truncationscited by 15
  5. 2021Implicit Riemannian Concave Potential Mapscited by 10
  6. 2022Uncertainty Estimation for Computed Tomography with a Linearised Deep Image Priorcited by 10
  7. 2022Scalable First-Order Bayesian Optimization via Structured Automatic Differentiationcited by 10
  8. 2021The Fast Kernel Transformcited by 8
  9. 2024Robust Gaussian Processes via Relevance Pursuitcited by 7
  10. 2021Active Learning for Deep Neural Networks on Edge Devicescited by 6
  11. 2023Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Modelscited by 6
  12. 2021Gauss-Legendre Features for Gaussian Process Regressioncited by 5
22 more
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  2. 2022Optimal Query Complexities for Dynamic Trace Estimationcited by 5
  3. 2025Compute-Optimal LLMs Provably Generalize Better With Scalecited by 5
  4. 2021Sensitivity Prewarping for Local Surrogate Modelingcited by 4
  5. 2024Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Datacited by 4
  6. 2025Scalable Gaussian Processes with Latent Kronecker Structurecited by 4
  7. 2025Determinant Estimation under Memory Constraints and Neural Scaling Lawscited by 3
  8. 2022Adaptive Cholesky Gaussian Processescited by 2
  9. 2022Spatially scalable recursive estimation of Gaussian process terrain maps using local basis functionscited by 2
  10. 2023Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Modelscited by 1
  11. 2024Gradients of Functions of Large Matricescited by 1
  12. 2025Derivation of Output Correlation Inferences for Multi-Output (aka Multi-Task) Gaussian Processcited by 1
  13. 2025BOLT: Block-Orthonormal Lanczos for Trace estimation of matrix functionscited by 1
  14. 2025nuGPR: GPU-Accelerated Gaussian Process Regression with Iterative Algorithms and Low-Rank Approximationscited by 1
  15. 2021Surveillance Evasion Through Bayesian Reinforcement Learningcited by 0
  16. 2024Batch Active Learning in Gaussian Process Regression using Derivativescited by 0
  17. 2025Scalable Krylov Subspace Methods for Generalized Mixed-Effects Models with Crossed Random Effectscited by 0
  18. 2025Vecchia-Inducing-Points Full-Scale Approximations for Gaussian Processescited by 0
  19. 2025Stochastic Trace Optimization of Parameter Dependent Matrices Based on Statistical Learning Theorycited by 0
  20. 2026Dynamic estimation of slowly varying sequencescited by 0
  21. 2026Implicit Neural Speckle Denoisingcited by 0
  22. 2026Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matricescited by 0