发表机构
Mehta Family School of Data Science and Artificial Intelligence, Indian Institute of Technology Roorkee; LIACS, Leiden University（印度理工学院鲁尔基分校梅塔数据科学与人工智能学院; 莱顿大学计算科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对PageRank放大网络结构性差异的问题，提出局部公平PageRank的平均场近似与单步细化机制，将迭代图规模传播降为线性时间节点级估计，在六个真实网络上验证了评分一致性与公平性保留。
AI 中文摘要
基于图的排名方法（如PageRank）可能放大网络中的结构性差异，从而促使针对敏感群体的公平感知排名机制的出现。局部公平PageRank（LFPR）通过局部传播实现公平性，但精确计算需要反复迭代直至收敛，限制了其在大规模图上的可扩展性。我们开发了一个可扩展的分析框架，用于近似邻域局部公平PageRank和均匀局部公平PageRank。通过引入群体感知的异质平均场表示，该框架将结构相似的节点聚合成度类，并推导出平稳LFPR评分的闭式近似，避免了对公平感知转移矩阵的重复传播。我们开发了一种单步细化（ORF）机制，该机制将公平感知传播算子应用于平均场估计一次，结合了节点特定的邻域信息，无需迭代收敛。波动性分析刻画了围绕平均场解的度相关变异性，并表明变异系数随着入度的增加而减小。平均场近似将精确LFPR的计算成本从迭代的图规模传播降低为线性时间的节点级估计，而ORF只需一次图遍历。在六个真实世界网络上的实验表明，与精确LFPR评分和排名高度一致，保留了群体级公平性，并大幅减少了运行时间。平均场近似将复杂度降低至$\mathcal{O}(n)$，而ORF以$\mathcal{O}(m+n)$的复杂度提高了准确性。
英文摘要
Graph-based ranking methods such as PageRank can amplify structural disparities in networks, motivating fairness-aware ranking mechanisms for sensitive groups. Locally Fair PageRank (LFPR) enforces fairness through local propagation, but exact computation requires repeated iterations until convergence, limiting scalability on large graphs. We develop a scalable analytical framework for approximating Neighborhood Locally Fair PageRank and Uniform Locally Fair PageRank. By introducing a group-aware heterogeneous mean-field representation, the framework aggregates structurally similar nodes into degree classes and derives closed-form approximations of stationary LFPR scores, avoiding repeated propagation over the fairness-aware transition matrix. We develop a One-Step Refinement (ORF) mechanism that applies the fairness-aware propagation operator once to the mean-field estimate, incorporating node-specific neighborhood information without iterative convergence. The fluctuation analysis characterizes degree-dependent variability around the mean-field solution and shows that the coefficient of variation decreases with increasing in-degree. The mean-field approximation reduces the computational cost of exact LFPR from iterative graph-scale propagation to linear-time node-level estimation, while ORF requires one graph traversal. Experiments on six real-world networks show strong agreement with exact LFPR scores and rankings, preservation of group-level fairness, and substantial runtime reductions. The mean-field approximation reduces complexity to $\mathcal{O}(n)$, while ORF improves accuracy with $\mathcal{O}(m+n)$.
