General Graph Random Features

TL;DR

This paper introduces a scalable, random walk-based algorithm for estimating graph functions efficiently, enabling large-scale graph kernel learning with theoretical guarantees and diverse applications.

Contribution

The paper presents a novel, scalable algorithm for unbiased graph function estimation using random walks, with neural network modulation for improved accuracy and efficiency.

Findings

Subquadratic time complexity for graph kernel estimation

Neural network modulation improves kernel quality

Effective in large-scale graph learning tasks

Abstract

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.