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Sketches-based join size estimation under local differential privacy

Meifan Zhang, Xin Liu, Lihua Yin

TL;DR

This work addresses private join size estimation under local differential privacy, where large join attribute domains and hash collisions hinder accuracy. It introduces LDPJoinSketch, a Hadamard-enabled sketch-based method that perturbates client data and aggregates server-side sketches to estimate join size, with a proven unbiased estimator and bounded error. Building on this, LDPJoinSketch+ adds a Frequency-Aware Perturbation mechanism to separate high- and low-frequency items, reducing hash-collision error while preserving privacy, resulting in improved accuracy, especially for skewed data. The methods extend to multi-way joins, with experimental results showing clear advantages over existing LDP approaches across diverse datasets and settings, making them practical for private data analysis tasks in real-world systems.

Abstract

Join size estimation on sensitive data poses a risk of privacy leakage. Local differential privacy (LDP) is a solution to preserve privacy while collecting sensitive data, but it introduces significant noise when dealing with sensitive join attributes that have large domains. Employing probabilistic structures such as sketches is a way to handle large domains, but it leads to hash-collision errors. To achieve accurate estimations, it is necessary to reduce both the noise error and hash-collision error. To tackle the noise error caused by protecting sensitive join values with large domains, we introduce a novel algorithm called LDPJoinSketch for sketch-based join size estimation under LDP. Additionally, to address the inherent hash-collision errors in sketches under LDP, we propose an enhanced method called LDPJoinSketch+. It utilizes a frequency-aware perturbation mechanism that effectively separates high-frequency and low-frequency items without compromising privacy. The proposed methods satisfy LDP, and the estimation error is bounded. Experimental results show that our method outperforms existing methods, effectively enhancing the accuracy of join size estimation under LDP.

Sketches-based join size estimation under local differential privacy

TL;DR

This work addresses private join size estimation under local differential privacy, where large join attribute domains and hash collisions hinder accuracy. It introduces LDPJoinSketch, a Hadamard-enabled sketch-based method that perturbates client data and aggregates server-side sketches to estimate join size, with a proven unbiased estimator and bounded error. Building on this, LDPJoinSketch+ adds a Frequency-Aware Perturbation mechanism to separate high- and low-frequency items, reducing hash-collision error while preserving privacy, resulting in improved accuracy, especially for skewed data. The methods extend to multi-way joins, with experimental results showing clear advantages over existing LDP approaches across diverse datasets and settings, making them practical for private data analysis tasks in real-world systems.

Abstract

Join size estimation on sensitive data poses a risk of privacy leakage. Local differential privacy (LDP) is a solution to preserve privacy while collecting sensitive data, but it introduces significant noise when dealing with sensitive join attributes that have large domains. Employing probabilistic structures such as sketches is a way to handle large domains, but it leads to hash-collision errors. To achieve accurate estimations, it is necessary to reduce both the noise error and hash-collision error. To tackle the noise error caused by protecting sensitive join values with large domains, we introduce a novel algorithm called LDPJoinSketch for sketch-based join size estimation under LDP. Additionally, to address the inherent hash-collision errors in sketches under LDP, we propose an enhanced method called LDPJoinSketch+. It utilizes a frequency-aware perturbation mechanism that effectively separates high-frequency and low-frequency items without compromising privacy. The proposed methods satisfy LDP, and the estimation error is bounded. Experimental results show that our method outperforms existing methods, effectively enhancing the accuracy of join size estimation under LDP.
Paper Structure (25 sections, 12 theorems, 25 equations, 15 figures, 2 tables, 5 algorithms)

This paper contains 25 sections, 12 theorems, 25 equations, 15 figures, 2 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Preliminaries
  4. AGMS sketch and Fast-AGMS sketch
  5. Local differential privacy
  6. Hadamard Mechanism
  7. LDPJoinSketch
  8. Client-side of LDPJoinSketch
  9. Server-side of LDPJoinSketch
  10. Analysis of estimation error
  11. LDPJoinSketch+
  12. The framework of LDPJoinSketch+
  13. Frequency-Aware Perturbation
  14. The server-side of LDPJoinSketch+
  15. Extension to multi-way Joins
  16. ...and 10 more sections

Key Result

Theorem 1

LDPJoinSketch satisfies $\epsilon$-LDP.

Figures (15)

  • Figure 1: Sketches-based join size estimation under LDP.
  • Figure 2: Example of LDPJoinSketch
  • Figure 3: Example of LDPJoinSketch+
  • Figure 4: LDPJoinSketch for multi-way join.
  • Figure 5: The Accuracy of Join Size Estimation.
  • ...and 10 more figures

Theorems & Definitions (29)

  • Definition 1
  • Theorem 1
  • proof
  • Example 1
  • Definition 2
  • Theorem 2
  • proof
  • Lemma 1
  • proof
  • Theorem 3
  • ...and 19 more