Repelling Random Walks
Isaac Reid, Eli Berger, Krzysztof Choromanski, Adrian Weller
TL;DR
This paper introduces repelling random walks, a novel quasi-Monte Carlo method that enhances graph sampling efficiency by correlating walker trajectories without bias, demonstrated through various graph analysis tasks.
Contribution
It presents the first rigorous quasi-Monte Carlo scheme for correlated graph-based sampling, improving estimator concentration while maintaining unbiasedness.
Findings
Enhanced estimation accuracy for graph kernels.
Improved PageRank vector approximation.
More efficient graphlet concentration estimation.
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.
Peer Reviews
Decision·ICLR 2024 poster
S1. A novel quasi-Monte Carlo algorithm called repelling random walks is given. S2. Results on typical examples are given to illustrate the new algorithm.
W1. Theoretical results only show that the new variance of estimator is less than classical method, but the author can give a more explicit quantitative analysis of how small it can be. W2. As to the efficiency in sampling, only numerical results are given, which weaken the solidity of the improvement brought by the new algorithm.
S1. The paper introduces a novel quasi-Monte Carlo mechanism, repelling random walks, aimed at enhancing graph-based sampling. This approach could potentially inspire further research in this field. S2. The marginal transition probabilities of repelling random walks remain unchanged, while the variance of these walks is reduced.
W1. The advantage of using repelling random walks over standard random walks appears to be marginal. For instance, the reduction in approximation errors when estimating PageRank using both standard and repelling random walks as shown in Table 2 is relatively minor. W2. The validity of certain arguments is heavily dependent on specific assumptions. Take Theorem 4.2, for example: its accuracy hinges on the assumption that the count of random walks is less than the minimum node degree in the prov
S1. A more vivid random walk mechanism with considering graph topological property S2. experiments on three graph tasks to show the advantage of the proposed S3. Solid theoretical analyses
W1. concern on the audience interest W2. more interesting downstream applications are expected
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Taxonomy
TopicsComplex Network Analysis Techniques · Theoretical and Computational Physics · Stochastic processes and statistical mechanics