SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes
SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes
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发表时间：
2021-06
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通讯作者：
Sanyam Kapoor;Marc Finzi;Ke Alexander Wang;A. Wilson
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作者：
Sanyam Kapoor;Marc Finzi;Ke Alexander Wang;A. Wilson
最先进的可扩展高斯过程方法使用迭代算法，需要快速矩阵向量乘法（MVMs）与协方差核。结构化内核插值（SKI）框架通过在网格上执行高效的mvm并插值回原始空间来加速这些mvm。在这项工作中，我们建立了SKI和用于高维快速双边滤波的多面体晶格之间的联系。使用稀疏的简单网格代替密集的矩形网格，我们可以在维度上比SKI更快地执行GP推理。我们的方法，Simplex-GP，可以将SKI扩展到高维，同时保持强大的预测性能。我们还提供了Simplex-GP的CUDA实现，它可以实现基于MVM的推理的显著GPU加速。
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.