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

Autor:	Kapoor, Sanyam, Finzi, Marc, Wang, Ke Alexander, Wilson, Andrew Gordon
Rok vydání:	2021
Předmět:	Computer Science - Machine Learning Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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. Comment: International Conference on Machine Learning (ICML), 2021
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2106.06695 Zobrazit plný text záznamu View this record from Arxiv