Repelling Random Walks

Published: 16 Jan 2024, Last Modified: 02 Apr 2024ICLR 2024 posterEveryoneRevisionsBibTeX
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Keywords: Graphs, random walkers, quasi-Monte Carlo, kernel, PageRank, graphlets, scalable, mixing
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TL;DR: A novel mechanism to correlate the trajectories of random walkers on graphs, improving the concentration properties of estimators whilst leaving them unbiased
Abstract: We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities are unmodified, we are able to explore the graph more efficiently, improving the concentration of statistical estimators whilst leaving them unbiased. The mechanism has a trivial drop-in implementation. We showcase the effectiveness of repelling random walks in a range of settings including estimation of graph kernels, the PageRank vector and graphlet concentrations. We provide detailed experimental evaluation and robust theoretical guarantees. To our knowledge, repelling random walks constitute the first rigorously studied quasi-Monte Carlo scheme correlating the directions of walkers on a graph, inviting new research in this exciting nascent domain.
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Primary Area: learning on graphs and other geometries & topologies
Submission Number: 2704