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Efficient Edge Rewiring Strategies for Enhancing PageRank Fairness

Changan Liu, Haoxin Sun, Ahad N. Zehmakan, Zhongzhi Zhang

TL;DR

This work tackles fairness in network information access by maximizing PageRank fairness for a disadvantaged group through edge rewiring with a budget. It introduces exact greedy and fast forest-based algorithms, leveraging a novel connection between PageRank and spanning rooted forests, and employs an extended Wilson algorithm for efficient forest sampling. The proposed methods significantly outperform baselines on six real-world networks, with the Fast algorithm handling graphs with millions of nodes in minutes. The approach offers scalable, provably effective improvements to fairness and opens avenues for exploring other PageRank fairness notions and multi-group settings.

Abstract

We study the notion of unfairness in social networks, where a group such as females in a male-dominated industry are disadvantaged in access to important information, e.g. job posts, due to their less favorable positions in the network. We investigate a well-established network-based formulation of fairness called PageRank fairness, which refers to a fair allocation of the PageRank weights among distinct groups. Our goal is to enhance the PageRank fairness by modifying the underlying network structure. More precisely, we study the problem of maximizing PageRank fairness with respect to a disadvantaged group, when we are permitted to rewire a fixed number of edges in the network. Building on a greedy approach, we leverage techniques from fast sampling of rooted spanning forests to devise an effective linear-time algorithm for this problem. To evaluate the accuracy and performance of our proposed algorithm, we conduct a large set of experiments on various real-world network data. Our experiments demonstrate that the proposed algorithm significantly outperforms the existing ones. Our algorithm is capable of generating accurate solutions for networks of million nodes in just a few minutes.

Efficient Edge Rewiring Strategies for Enhancing PageRank Fairness

TL;DR

This work tackles fairness in network information access by maximizing PageRank fairness for a disadvantaged group through edge rewiring with a budget. It introduces exact greedy and fast forest-based algorithms, leveraging a novel connection between PageRank and spanning rooted forests, and employs an extended Wilson algorithm for efficient forest sampling. The proposed methods significantly outperform baselines on six real-world networks, with the Fast algorithm handling graphs with millions of nodes in minutes. The approach offers scalable, provably effective improvements to fairness and opens avenues for exploring other PageRank fairness notions and multi-group settings.

Abstract

We study the notion of unfairness in social networks, where a group such as females in a male-dominated industry are disadvantaged in access to important information, e.g. job posts, due to their less favorable positions in the network. We investigate a well-established network-based formulation of fairness called PageRank fairness, which refers to a fair allocation of the PageRank weights among distinct groups. Our goal is to enhance the PageRank fairness by modifying the underlying network structure. More precisely, we study the problem of maximizing PageRank fairness with respect to a disadvantaged group, when we are permitted to rewire a fixed number of edges in the network. Building on a greedy approach, we leverage techniques from fast sampling of rooted spanning forests to devise an effective linear-time algorithm for this problem. To evaluate the accuracy and performance of our proposed algorithm, we conduct a large set of experiments on various real-world network data. Our experiments demonstrate that the proposed algorithm significantly outperforms the existing ones. Our algorithm is capable of generating accurate solutions for networks of million nodes in just a few minutes.
Paper Structure (18 sections, 8 theorems, 13 equations, 5 figures, 1 table, 3 algorithms)

This paper contains 18 sections, 8 theorems, 13 equations, 5 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Notations
  4. Spanning Forests and Forest Matrix
  5. The PageRank Algorithm
  6. Problem Definition
  7. Exact Greedy Algorithm
  8. Fast Sampling Algorithm
  9. Novel Interpretation for PageRank via Spanning Rooted Forest
  10. Approximating via an Extension of Wilson's Algorithm
  11. Fast Approximation Algorithm
  12. Experiments
  13. Experimental Setup
  14. Effectiveness Evaluation
  15. Efficiency Evaluation
  16. ...and 3 more sections

Key Result

Lemma 2.1

For the PageRank vector $\boldsymbol{\mathbf{\pi}}$, the following relationship holds: $\boldsymbol{\mathbf{\pi}}^{\top}=\boldsymbol{\mathit{v}}^{\top} \boldsymbol{\mathbf{\Pi}}$, where: (i) $\boldsymbol{\mathbf{\Pi}}=\alpha(\boldsymbol{\mathit{I}}-(1-\alpha) \boldsymbol{\mathit{P}})^{-1}$; and (ii)

Figures (5)

  • Figure 1: (a) Illustration of our proposed algorithm Exact (Algorithm 1) which rewires edge $(5,4)$ to $(5,8)$ and the PageRank allocation to the disadvantaged group $S$ changes from $\boldsymbol{\mathbf{\pi}}(S)=0.13$ to $\boldsymbol{\mathbf{\pi}}(S)=0.17$. (The sizes of nodes are determined by their PageRank scores.) (b) Illustration of the loop erase process of Wilson algorithm Wilson1996GeneratingRS, which bases our fast algorithm. The loop $(3,4,5,3)$ is erased.
  • Figure 2: From left to right: a digraph, a spanning tree, a spanning rooted tree and a spanning rooted forest on it (roots are in gray).
  • Figure 3: Comparison of different algorithms in increasing the PR fairness of the disadvantaged group.
  • Figure 4: Wasserstein distances between the PPR ratio of the nodes in $S$ and the PPR ratio of the nodes in $T$.
  • Figure 5: Correlation betweeen $\Delta$ and $\widehat{\Delta}$ for varying $\alpha$. $r_s$ and $r_p$ represent the Spearman and the Pearson coefficients, respectively.

Theorems & Definitions (12)

  • Lemma 2.1
  • Lemma 4.1
  • proof
  • Remark 4.2
  • Lemma 5.1
  • Theorem 5.2
  • Theorem 5.3
  • proof
  • Theorem 5.4
  • Theorem 5.5
  • ...and 2 more