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

arXiv: https://arxiv.org/abs/1503.01057 · HTML: https://mlsanity.com/paper/1503.01057/

## Key facts

- Cited by 177 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2015.

## Built on by (most cited first, 30 of 177)

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- [Compute Better Spent: Replacing Dense Layers with Structured Matrices](https://mlsanity.com/paper/2406.06248/) (2024)
- [Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent](https://mlsanity.com/paper/2306.11589/) (2023)
- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Preconditioning for Scalable Gaussian Process Hyperparameter Optimization](https://mlsanity.com/paper/2107.00243/) (2021)
- [Conditioning Sparse Variational Gaussian Processes for Online Decision-making](https://mlsanity.com/paper/2110.15172/) (2021)
- [Integrating Random Effects in Deep Neural Networks](https://mlsanity.com/paper/2206.03314/) (2022)
- [Kernel Interpolation for Scalable Online Gaussian Processes](https://mlsanity.com/paper/2103.01454/) (2021)
- [Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks](https://mlsanity.com/paper/2105.04554/) (2021)
- [Diverse Video Generation using a Gaussian Process Trigger](https://mlsanity.com/paper/2107.04619/) (2021)
- [High-Dimensional Gaussian Process Inference with Derivatives](https://mlsanity.com/paper/2102.07542/) (2021)
- [Scaling Gaussian Processes with Derivative Information Using Variational Inference](https://mlsanity.com/paper/2107.04061/) (2021)
- [Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior](https://mlsanity.com/paper/2305.09017/) (2023)
- [Solving High Frequency and Multi-Scale PDEs with Gaussian Processes](https://mlsanity.com/paper/2311.04465/) (2023)
- [Toward Large Kernel Models](https://mlsanity.com/paper/2302.02605/) (2023)
- [Scalable Gaussian Processes for Data-Driven Design using Big Data with Categorical Factors](https://mlsanity.com/paper/2106.15356/) (2021)
- [The Role of Predictive Uncertainty and Diversity in Embodied AI and Robot Learning](https://mlsanity.com/paper/2405.03164/) (2024)
- [Uncertainty Quantification for Hallucination Detection in Large Language Models: Foundations, Methodology, and Future Directions](https://mlsanity.com/paper/2510.12040/) (2025)
- [Kernel Packet: An Exact and Scalable Algorithm for Gaussian Process Regression with Mat'ern Correlations](https://mlsanity.com/paper/2203.03116/) (2022)
- [Scalable First-Order Bayesian Optimization via Structured Automatic Differentiation](https://mlsanity.com/paper/2206.08366/) (2022)
- [Scaling Gaussian Processes for Learning Curve Prediction via Latent Kronecker Structure](https://mlsanity.com/paper/2410.09239/) (2024)
- [SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes](https://mlsanity.com/paper/2106.06695/) (2021)
- [Exact Gaussian Processes for Massive Datasets via Non-Stationary Sparsity-Discovering Kernels](https://mlsanity.com/paper/2205.09070/) (2022)
- [Kernel Regression with Infinite-Width Neural Networks on Millions of Examples](https://mlsanity.com/paper/2303.05420/) (2023)

## 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.