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SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes
Sanyam Kapoor · Marc Finzi · Ke Alexander Wang · Andrew Wilson

Thu Jul 22 07:20 PM -- 07:40 PM (PDT) @

State-of-the-art methods for scalable Gaussian processes use iterative algorithms, requiring fast matrix vector multiplies (MVMs) with the co-variance 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.

Author Information

Sanyam Kapoor (New York University)
Marc Finzi (New York University)
Ke Alexander Wang (Stanford University)
Andrew Wilson (New York University)
Andrew Wilson

Andrew Gordon Wilson is faculty in the Courant Institute and Center for Data Science at NYU. His interests include probabilistic modelling, Gaussian processes, Bayesian statistics, physics inspired machine learning, and loss surfaces and generalization in deep learning. His webpage is https://cims.nyu.edu/~andrewgw.

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