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。通过在相互作用的集合轨迹之间引入相关性，同时保持其边缘转移概率不变，我们能够更有效地探索图，提高统计估计量的集中度，同时保持其无偏性。该机制具有简单的即插即用实现。我们展示了排斥随机游走在多种场景下的有效性，包括图核估计、PageRank向量和图元浓度估计。我们提供了详细的实验评估和稳健的理论保证。据我们所知，排斥随机游走构成了首个经过严格研究的、在图上游走方向之间建立相关性的拟蒙特卡洛方案，为这一新兴领域的研究开辟了新的方向。