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Differentially Private Graph Diffusion with Applications in Personalized PageRanks

Rongzhe Wei, Eli Chien, Pan Li

TL;DR

The paper tackles privacy risks in graph diffusion by introducing edge-level differential privacy through per-iteration Laplace noise and a degree-aware clipping mechanism, leveraging Privacy Amplification by Iteration (PABI) to obtain non-divergent privacy bounds. A novel $\\infty$-Wasserstein distance tracking technique tightens the analysis beyond diameter-based bounds and supports practical use in diffusion-based tasks like Personalized PageRank (PPR). It also proposes a Personalized Edge-level RDP framework to tailor privacy guarantees to a seed node, reducing unnecessary leakage. The approach yields improved utility under stringent privacy budgets, demonstrated through experiments on real networks and ablation studies that validate the design choices, including the degree-based thresholding and the new tracking method. This work advances private diffusion on graphs with practical, scalable guarantees for ranking and proximity tasks.

Abstract

Graph diffusion, which iteratively propagates real-valued substances among the graph, is used in numerous graph/network-involved applications. However, releasing diffusion vectors may reveal sensitive linking information in the data such as transaction information in financial network data. However, protecting the privacy of graph data is challenging due to its interconnected nature. This work proposes a novel graph diffusion framework with edge-level differential privacy guarantees by using noisy diffusion iterates. The algorithm injects Laplace noise per diffusion iteration and adopts a degree-based thresholding function to mitigate the high sensitivity induced by low-degree nodes. Our privacy loss analysis is based on Privacy Amplification by Iteration (PABI), which to our best knowledge, is the first effort that analyzes PABI with Laplace noise and provides relevant applications. We also introduce a novel Infinity-Wasserstein distance tracking method, which tightens the analysis of privacy leakage and makes PABI more applicable in practice. We evaluate this framework by applying it to Personalized Pagerank computation for ranking tasks. Experiments on real-world network data demonstrate the superiority of our method under stringent privacy conditions.

Differentially Private Graph Diffusion with Applications in Personalized PageRanks

TL;DR

The paper tackles privacy risks in graph diffusion by introducing edge-level differential privacy through per-iteration Laplace noise and a degree-aware clipping mechanism, leveraging Privacy Amplification by Iteration (PABI) to obtain non-divergent privacy bounds. A novel -Wasserstein distance tracking technique tightens the analysis beyond diameter-based bounds and supports practical use in diffusion-based tasks like Personalized PageRank (PPR). It also proposes a Personalized Edge-level RDP framework to tailor privacy guarantees to a seed node, reducing unnecessary leakage. The approach yields improved utility under stringent privacy budgets, demonstrated through experiments on real networks and ablation studies that validate the design choices, including the degree-based thresholding and the new tracking method. This work advances private diffusion on graphs with practical, scalable guarantees for ranking and proximity tasks.

Abstract

Graph diffusion, which iteratively propagates real-valued substances among the graph, is used in numerous graph/network-involved applications. However, releasing diffusion vectors may reveal sensitive linking information in the data such as transaction information in financial network data. However, protecting the privacy of graph data is challenging due to its interconnected nature. This work proposes a novel graph diffusion framework with edge-level differential privacy guarantees by using noisy diffusion iterates. The algorithm injects Laplace noise per diffusion iteration and adopts a degree-based thresholding function to mitigate the high sensitivity induced by low-degree nodes. Our privacy loss analysis is based on Privacy Amplification by Iteration (PABI), which to our best knowledge, is the first effort that analyzes PABI with Laplace noise and provides relevant applications. We also introduce a novel Infinity-Wasserstein distance tracking method, which tightens the analysis of privacy leakage and makes PABI more applicable in practice. We evaluate this framework by applying it to Personalized Pagerank computation for ranking tasks. Experiments on real-world network data demonstrate the superiority of our method under stringent privacy conditions.
Paper Structure (27 sections, 14 theorems, 51 equations, 10 figures, 1 table)

This paper contains 27 sections, 14 theorems, 51 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. More Related Works
  3. Preliminaries
  4. Methodology
  5. Preliminaries: Privacy Amplification by Iteration
  6. Private Graph Diffusions
  7. Proof Sketch of Theorem \ref{['thm.privacy_noisy_graph_diffusion']}
  8. Personalized Graph Diffusion Algorithms with Application in PPR Diffusion
  9. Experiments
  10. Evaluating Privacy-Utility Tradeoffs on Ranking Tasks
  11. Ablation Study
  12. Conclusion
  13. Preliminaries
  14. Privacy Guarantees for Noisy Graph Diffusion: Analytical Proofs
  15. Main Proof
  16. ...and 12 more sections

Key Result

Proposition 1

Let $X_K$ and $X'_K$ denote the outputs from $\text{CNI}(X_0, \{\psi_k\}, \{\xi_k\}, \mathcal{B})$ and $\text{CNI}(X_0, \{\psi_k'\}, \{\xi_k'\}, \mathcal{B})$, respectively, where $\xi_k, \xi_k' \sim \mathcal{N}(0, \sigma^2 I_d)$. Define distortion $\rho := \sup_{k,x} \| \psi_k(x) - \psi'_k(x) \|$ a

Figures (10)

  • Figure 1: Illustration of Distortion from Edge Perturbations over Adjacent Graphs for Nodes with Low and High Degrees.
  • Figure 2: RDP vs. Total Diffusion Step $K$ with $\gamma_{1, k} = 0.8, \gamma_{2, k} = 0, \gamma_{3, k} = 0.2, \alpha = 2, \sigma = 0.01$, and $\eta = 10^{-5}$.
  • Figure 3: Setting: Graph Diffusion with $\gamma_{1, k} = 0.8, \gamma_{2, k} = 0, \gamma_{3, k} = 0.2$.
  • Figure 4: Trade-off between NDCG and Personalized Edge-level Privacy.
  • Figure 5: Trade-off between Recall and Personalized Edge-level Privacy.
  • ...and 5 more figures

Theorems & Definitions (19)

  • Definition 1: Edge-level RDPsajadmanesh2023gapchien2024differentially
  • Definition 2: Personalized Edge-level RDPkearns2014mechanismepasto2022differentially
  • Definition 3: Contractive Noisy Iteration (CNI) feldman2018privacy
  • Proposition 1
  • Theorem 1: Privacy Guarantees of Noisy Graph Diffusions
  • Lemma 2: Absorption of Distortion in Laplace Distribution
  • Lemma 3: PABI with $\infty$-Wasserstein Distance Tracking
  • Theorem 4: Privacy Guarantees for Personalized Noisy Graph Diffusions
  • Definition A.1: Shifted Rényi Divergence
  • Lemma A.1: Shift-reduction lemma feldman2018privacy
  • ...and 9 more