General Graph Random Features
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Keywords: Graphs, kernels, random walks, Laplacian, adjacency matrix, kernel learning, ordinary differential equation, neural network
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TL;DR: A novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix
Abstract: We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined
general graph random features (g-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 g-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.
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Primary Area: learning on graphs and other geometries & topologies
Submission Number: 2711
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