mlsanityData to 14 Oct 2026

SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes

arXiv 2106.06695 ↗First posted 12 Jun 2021cs.LG stat.MLcited by 9

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Abstract (arXiv)

State-of-the-art methods for scalable Gaussian processes use iterative algorithms, requiring fast matrix vector multiplies (MVMs) with the covariance kernel. The Structured Kernel Interpolation (SKI) framework accelerates these MVMs by performing efficient MVMs on a grid and interpolating back to the original space. In this work, we develop a connection between SKI and the permutohedral lattice used for high-dimensional fast bilateral filtering. Using a sparse simplicial grid instead of a dense rectangular one, we can perform GP inference exponentially faster in the dimension than SKI. Our approach, Simplex-GP, enables scaling SKI to high dimensions, while maintaining strong predictive performance. We additionally provide a CUDA implementation of Simplex-GP, which enables significant GPU acceleration of MVM based inference.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 21 of its 44 references that are in the map. First posted on arXiv 12 Jun 2021.

Builds on

21 of 44 references.

References · 21

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9 more
  1. 2020Kernel Operations on the GPU, with Autodiff, without Memory Overflowscited by 104
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  9. 2014Permutohedral Lattice CNNscited by 4

Built on by

Cited by year

Citing papers per year: 2021: 1; 2022: 2; 2023: 3; 2024: 1; 2025: 2.

9 papers.

  1. 2021When are Iterative Gaussian Processes Reliably Accurate?cited by 12
  2. 2023CoLA: Exploiting Compositional Structure for Automatic and Efficient Numerical Linear Algebracited by 7
  3. 2025Scalable Gaussian Processes with Latent Kronecker Structurecited by 5
  4. 2022Log-Linear-Time Gaussian Processes Using Binary Tree Kernelscited by 4
  5. 2023Actually Sparse Variational Gaussian Processescited by 4
  6. 2022B'ezier Gaussian Processes for Tall and Wide Datacited by 2
  7. 2023Kernel Interpolation with Sparse Gridscited by 2
  8. 2024High-Dimensional Gaussian Process Regression with Soft Kernel Interpolationcited by 1
  9. 2025Scaling Gaussian Process Regression with Full Derivative Observationscited by 1