mlsanityData to 7 Oct 2026

Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)

arXiv 1503.01057 ↗First posted 3 Mar 2015cs.LG stat.MLcited by 175

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Abstract (arXiv)

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic kernel interpolation, we introduce KISS-GP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for kernel matrix approximation, kernel learning, and natural sound modelling.

Key facts. Cited by 175 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Mar 2015.

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Citing papers per year: 2020: 1; 2021: 36; 2022: 33; 2023: 32; 2024: 30; 2025: 19; 2026: 24.

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  1. 2021The Promises and Pitfalls of Deep Kernel Learningcited by 81
  2. 2023A Survey on Uncertainty Quantification Methods for Deep Learningcited by 78
  3. 2021Causal Inference for Time series Analysis: Problems, Methods and Evaluationcited by 42
  4. 2021Spatio-Temporal Variational Gaussian Processescited by 32
  5. 2023Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processescited by 31
  6. 2023GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencodercited by 29
  7. 2021Valid prediction intervals for regression problemscited by 28
  8. 2023Sampling from Gaussian Process Posteriors using Stochastic Gradient Descentcited by 27
  9. 2024Compute Better Spent: Replacing Dense Layers with Structured Matricescited by 24
  10. 2021Conditioning Sparse Variational Gaussian Processes for Online Decision-makingcited by 23
  11. 2022Posterior and Computational Uncertainty in Gaussian Processescited by 23
  12. 2021Preconditioning for Scalable Gaussian Process Hyperparameter Optimizationcited by 22
38 more
  1. 2022Integrating Random Effects in Deep Neural Networkscited by 22
  2. 2021Kernel Interpolation for Scalable Online Gaussian Processescited by 18
  3. 2021Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networkscited by 17
  4. 2021Diverse Video Generation using a Gaussian Process Triggercited by 17
  5. 2021High-Dimensional Gaussian Process Inference with Derivativescited by 16
  6. 2021Scaling Gaussian Processes with Derivative Information Using Variational Inferencecited by 15
  7. 2023Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Priorcited by 15
  8. 2023Solving High Frequency and Multi-Scale PDEs with Gaussian Processescited by 14
  9. 2023Toward Large Kernel Modelscited by 12
  10. 2021Scalable Gaussian Processes for Data-Driven Design using Big Data with Categorical Factorscited by 11
  11. 2024The Role of Predictive Uncertainty and Diversity in Embodied AI and Robot Learningcited by 11
  12. 2022Kernel Packet: An Exact and Scalable Algorithm for Gaussian Process Regression with Mat'ern Correlationscited by 10
  13. 2022Scalable First-Order Bayesian Optimization via Structured Automatic Differentiationcited by 10
  14. 2025Uncertainty Quantification for Hallucination Detection in Large Language Models: Foundations, Methodology, and Future Directionscited by 10
  15. 2021SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processescited by 9
  16. 2022Exact Gaussian Processes for Massive Datasets via Non-Stationary Sparsity-Discovering Kernelscited by 9
  17. 2023Kernel Regression with Infinite-Width Neural Networks on Millions of Examplescited by 9
  18. 2024Scaling Gaussian Processes for Learning Curve Prediction via Latent Kronecker Structurecited by 9
  19. 2025Robust and Conjugate Spatio-Temporal Gaussian Processescited by 9
  20. 2021The Fast Kernel Transformcited by 8
  21. 2021Scalable Variational Gaussian Processes via Harmonic Kernel Decompositioncited by 8
  22. 2022Variational Nearest Neighbor Gaussian Processcited by 8
  23. 2022Scalable Gaussian-process regression and variable selection using Vecchia approximationscited by 8
  24. 2023Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimationcited by 8
  25. 2024Scalable Bayesian Optimization via Focalized Sparse Gaussian Processescited by 8
  26. 2021Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processescited by 7
  27. 2023Free-Form Variational Inference for Gaussian Process State-Space Modelscited by 7
  28. 2023CoLA: Exploiting Compositional Structure for Automatic and Efficient Numerical Linear Algebracited by 7
  29. 2024A prediction rigidity formalism for low-cost uncertainties in trained neural networkscited by 7
  30. 2024DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networkscited by 7
  31. 2024Toward Efficient Kernel-Based Solvers for Nonlinear PDEscited by 7
  32. 2021Hierarchical Inducing Point Gaussian Process for Inter-domain Observationscited by 6
  33. 2022Semi-Parametric Inducing Point Networks and Neural Processescited by 6
  34. 2023Random Smoothing Regularization in Kernel Gradient Descent Learningcited by 6
  35. 2023Quantized Fourier and Polynomial Features for more Expressive Tensor Network Modelscited by 6
  36. 2021Gauss-Legendre Features for Gaussian Process Regressioncited by 5
  37. 2021Faster Kernel Interpolation for Gaussian Processescited by 5
  38. 2021Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Surveycited by 5

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