# Product Kernel Interpolation for Scalable Gaussian Processes

arXiv: https://arxiv.org/abs/1802.08903 · HTML: https://mlsanity.com/paper/1802.08903/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2018.

## Built on by (most cited first, 30 of 31)

- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (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)
- [Toward Large Kernel Models](https://mlsanity.com/paper/2302.02605/) (2023)
- [Scalable First-Order Bayesian Optimization via Structured Automatic Differentiation](https://mlsanity.com/paper/2206.08366/) (2022)
- [SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes](https://mlsanity.com/paper/2106.06695/) (2021)
- [Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processes](https://mlsanity.com/paper/2106.10210/) (2021)
- [CoLA: Exploiting Compositional Structure for Automatic and Efficient Numerical Linear Algebra](https://mlsanity.com/paper/2309.03060/) (2023)
- [DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.21176/) (2024)
- [Faster Kernel Interpolation for Gaussian Processes](https://mlsanity.com/paper/2101.11751/) (2021)
- [Input Dependent Sparse Gaussian Processes](https://mlsanity.com/paper/2107.07281/) (2021)
- [Leveraging Locality and Robustness to Achieve Massively Scalable Gaussian Process Regression](https://mlsanity.com/paper/2306.14731/) (2023)
- [Amortized Linear-time Exact Shapley Value for Product-Kernel Methods](https://mlsanity.com/paper/2505.16516/) (2025)
- [Scalable Gaussian Processes with Latent Kronecker Structure](https://mlsanity.com/paper/2506.06895/) (2025)
- [GP-ConvCNP: Better Generalization for Convolutional Conditional Neural Processes on Time Series Data](https://mlsanity.com/paper/2106.04967/) (2021)
- [Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes](https://mlsanity.com/paper/2308.14142/) (2023)
- [Fast training of large kernel models with delayed projections](https://mlsanity.com/paper/2411.16658/) (2024)
- [B'ezier Gaussian Processes for Tall and Wide Data](https://mlsanity.com/paper/2209.00343/) (2022)
- [Kernel Interpolation with Sparse Grids](https://mlsanity.com/paper/2305.14451/) (2023)
- [New Bounds for Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2502.08730/) (2025)
- [High-Dimensional Gaussian Process Regression with Soft Kernel Interpolation](https://mlsanity.com/paper/2410.21419/) (2024)
- [Scaling Gaussian Process Regression with Full Derivative Observations](https://mlsanity.com/paper/2505.09134/) (2025)
- [nuGPR: GPU-Accelerated Gaussian Process Regression with Iterative Algorithms and Low-Rank Approximations](https://mlsanity.com/paper/2510.12128/) (2025)
- [Time-Varying Transition Matrices with Multi-task Gaussian Processes](https://mlsanity.com/paper/2306.11772/) (2023)
- [A Kronecker product accelerated efficient sparse Gaussian Process (E-SGP) for flow emulation](https://mlsanity.com/paper/2312.10023/) (2023)
- [Kernel Multigrid: Accelerate Back-fitting via Sparse Gaussian Process Regression](https://mlsanity.com/paper/2403.13300/) (2024)
- [Safe Bayesian Optimization for Complex Control Systems via Additive Gaussian Processes](https://mlsanity.com/paper/2408.16307/) (2024)
- [Vecchia-Inducing-Points Full-Scale Approximations for Gaussian Processes](https://mlsanity.com/paper/2507.05064/) (2025)
- [Fast Gaussian process inference by exact Mat'ern kernel decomposition](https://mlsanity.com/paper/2508.01864/) (2025)
- [Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification](https://mlsanity.com/paper/2603.16621/) (2026)

## Abstract (arXiv)

Recent work shows that inference for Gaussian processes can be performed efficiently using iterative methods that rely only on matrix-vector multiplications (MVMs). Structured Kernel Interpolation (SKI) exploits these techniques by deriving approximate kernels with very fast MVMs. Unfortunately, such strategies suffer badly from the curse of dimensionality. We develop a new technique for MVM based learning that exploits product kernel structure. We demonstrate that this technique is broadly applicable, resulting in linear rather than exponential runtime with dimension for SKI, as well as state-of-the-art asymptotic complexity for multi-task GPs.