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.

翻译：我们提出了一种新颖的拟蒙特卡洛机制来改进基于图的采样，称为排斥随机游走。通过在一个交互系综中引入轨迹间的相关性，同时保持其边际转移概率不变，我们能够更高效地探索图结构，提升统计估计量的集中性并保持其无偏性。该机制具有简单的即插即用实现方式。我们在多种场景中展示了排斥随机游走的有效性，包括图核估计、PageRank向量以及图元浓度估计。我们提供了详细的实验评估和坚实的理论保证。据我们所知，排斥随机游走是首个被严格研究的、在图上游走者间关联方向的拟蒙特卡洛方案，为这一激动人心的新兴领域开辟了新的研究方向。