Locally Fair PageRank: Mean-Field Approximation and One-Step Refinement

2026-09-19

AI Summary

本文针对PageRank在图网络中放大结构差异的问题，提出了一种基于局部传播的公平性PageRank方法，并通过平均场近似和一步修正机制提高了其在大规模图上的可扩展性和准确性。

Abstract

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 $\mathcal{O}(m+n)$.

Problem

• Locally Fair PageRank
• structural disparities
• fairness-aware ranking
• large graphs
• mean-field approximation

Innovation

• Locally Fair PageRank
• mean-field approximation
• One-Step Refinement
• fairness-aware ranking
• scalability