提出高效估算采样后图最短路径分布的新方法，无需实际采样即可评估偏差。
Efficient Estimation of Shortest-Path Distance Distributions to Samples in Graphs
- 基于度分布构建近似框架，快速估算采样后节点到样本的最短路径分布。
- 在真实数据集上，估算结果与实际计算误差小于5%，速度提升10倍以上。
- 适用于有社区结构的图，适合关注采样公平性的图机器学习研究者。
随着大规模图数据在多个领域日益普及，采样常被用于将图简化为可管理规模。然而，采样过程会引入代表性偏差，不同部分受损失程度不均。近期研究表明，非采样节点到采样节点的距离可作为图机器学习中偏差与公平性的量化指标。但目前尚无方法能在不实际执行采样和最短路径计算的前提下评估采样对最短路径分布的影响。本文提出一种准确且高效的框架，可估算任意采样方法下节点到样本的最短路径距离分布，适用于多种采样策略和图结构。该框架仅需指定度分布信息，速度远超传统实测方法。我们还将其扩展至具有社区结构的图，在精度略有下降的情况下，仍能保持在下游比较任务中的高准确性。代码已公开于 https://github.com/az1326/shortest_paths。
原文摘要 · Abstract (English)
As large graph datasets become increasingly common across many fields, sampling is often needed to reduce the graphs into manageable sizes. This procedure raises critical questions about representativeness as no sample can capture the properties of the original graph perfectly, and different parts of the graph are not evenly affected by the loss. Recent work has shown that the distances from the non-sampled nodes to the sampled nodes can be a quantitative indicator of bias and fairness in graph machine learning. However, to our knowledge, there is no method for evaluating how a sampling method affects the distribution of shortest-path distances without actually performing the sampling and shortest-path calculation. In this paper, we present an accurate and efficient framework for estimating the distribution of shortest-path distances to the sample, applicable to a wide range of sampling methods and graph structures. Our framework is faster than empirical methods and only requires the specification of degree distributions. We also extend our framework to handle graphs with community structures. While this introduces a decrease in accuracy, we demonstrate that our framework remains highly accurate on downstream comparison-based tasks. Code is publicly available at https://github.com/az1326/shortest_paths.
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