Product Kernel Interpolation for Scalable Gaussian Processes

TL;DR

This paper introduces a new scalable method for Gaussian process inference that leverages product kernel structure to achieve linear runtime in dimension, improving efficiency for high-dimensional problems.

Contribution

It develops a novel MVM-based learning technique exploiting product kernel structure, significantly enhancing scalability of SKI and multi-task Gaussian processes.

Findings

Achieves linear runtime with respect to dimension for SKI

Provides state-of-the-art asymptotic complexity for multi-task GPs

Demonstrates broad applicability of the proposed technique

Abstract

Recent work shows that inference for Gaussian processes can be performed efficiently using iterative methods that rely only on matrix-vector multiplications (MVMs). Structured Kernel Interpolation (SKI) exploits these techniques by deriving approximate kernels with very fast MVMs. Unfortunately, such strategies suffer badly from the curse of dimensionality. We develop a new technique for MVM based learning that exploits product kernel structure. We demonstrate that this technique is broadly applicable, resulting in linear rather than exponential runtime with dimension for SKI, as well as state-of-the-art asymptotic complexity for multi-task GPs.