Repelling Random Walks
This addresses the problem of slow or inaccurate graph-based sampling for researchers and practitioners in network analysis, offering a drop-in solution with theoretical guarantees, though it appears incremental as a novel method for a known bottleneck.
The paper tackles the problem of inefficient graph exploration in sampling by introducing repelling random walks, a quasi-Monte Carlo mechanism that correlates walker trajectories to improve efficiency while maintaining unbiased estimators, resulting in enhanced concentration in tasks like graph kernel estimation and PageRank computation.
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.