mlsanityData to 14 Oct 2026

Scaling Gaussian Process Regression with Derivatives

arXiv 1810.12283 ↗First posted 29 Oct 2018cs.LG cs.AI stat.MLcited by 27

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Abstract (arXiv)

Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at n points in d dimensions requires linear solves and log determinants with an n(d+1) × n(d+1) positive definite matrix -- leading to prohibitive O(n3d3) computations for standard direct methods. We propose iterative solvers using fast O(nd) matrix-vector multiplications (MVMs), together with pivoted Cholesky preconditioning that cuts the iterations to convergence by several orders of magnitude, allowing for fast kernel learning and prediction. Our approaches, together with dimensionality reduction, enables Bayesian optimization with derivatives to scale to high-dimensional problems and large evaluation budgets.

Key facts. Cited by 27 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 Oct 2018.

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

27 papers.

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  1. 2023Unexpected Improvements to Expected Improvement for Bayesian Optimizationcited by 149
  2. 2023Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processescited by 31
  3. 2024A survey and benchmark of high-dimensional Bayesian optimization of discrete sequencescited by 23
  4. 2021High-Dimensional Gaussian Process Inference with Derivativescited by 16
  5. 2021Scaling Gaussian Processes with Derivative Information Using Variational Inferencecited by 15
  6. 2022Scalable First-Order Bayesian Optimization via Structured Automatic Differentiationcited by 10
  7. 2022Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fieldscited by 7
  8. 2024Physics-Informed Variational State-Space Gaussian Processescited by 7
  9. 2021Global optimization using random embeddingscited by 6
  10. 2021Using Distance Correlation for Efficient Bayesian Optimizationcited by 3
  11. 2022PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equationscited by 3
  12. 2022Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safetycited by 2
15 more
  1. 2024Active search for Bifurcationscited by 2
  2. 2025Towards Scalable Bayesian Optimization via Gradient-Informed Bayesian Neural Networkscited by 2
  3. 2025Two-dimensional RMSD projections for reaction path visualization and validationcited by 2
  4. 2025Scaling Gaussian Process Regression with Full Derivative Observationscited by 1
  5. 2025When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learningcited by 1
  6. 2021CobBO: Coordinate Backoff Bayesian Optimization with Two-Stage Kernelscited by 0
  7. 2021A probabilistic Taylor expansion with Gaussian processescited by 0
  8. 2022Integrated Gradient attribution for Gaussian Processes with non-Gaussian likelihoodscited by 0
  9. 2023Large-scale magnetic field maps using structured kernel interpolation for Gaussian process regressioncited by 0
  10. 2024Batch Active Learning in Gaussian Process Regression using Derivativescited by 0
  11. 2025Fast Gaussian Processes under Monotonicity Constraintscited by 0
  12. 2026Gradient-Enhanced Partitioned Gaussian Processes for Real-Time Quadrotor Dynamics Modelingcited by 0
  13. 2026Gradient-Informed Bayesian and Interior Point Optimization for Efficient Inverse Design in Nanophotonicscited by 0
  14. 2026Uncertainty-quantified Pulse Signal Recovery from Facial Video using Regularized Stochastic Interpolantscited by 0
  15. 2026Scalable Derivative Gaussian Processes via Exact Gradient Reductioncited by 0