SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes
This enables scalable Gaussian process inference for high-dimensional data, addressing a key bottleneck in machine learning applications.
The paper tackles the problem of scaling Gaussian processes to high dimensions by introducing Simplex-GP, which uses a sparse simplicial grid based on the permutohedral lattice to accelerate matrix-vector multiplies, achieving exponential speed-ups in dimension while maintaining strong predictive performance.
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.