Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

An Expectation-Maximization Relaxed Method for Privacy Funnel

Lingyi Chen, Jiachuan Ye, Shitong Wu, Huihui Wu, Hao Wu, Wenyi Zhang

TL;DR

The paper tackles the privacy funnel problem of minimizing the information leakage $I(S;Y)$ under a disclosure constraint $I(X;Y)\ge R$ for discrete variables. It introduces an EM-inspired upper-bound relaxation using an auxiliary $q_{ijk}$ to obtain a tractable objective $\tilde{f}(u,r,q)$ while proving its equivalence to the original PF. An alternating expectation minimization (AEM) algorithm with closed-form updates and convergence guarantees via descent estimates and Pinsker's inequality is developed. Numerical results on synthetic and real-world datasets demonstrate accurate PF curves, near-optimal privacy-utility tradeoffs, and improved stability over prior methods. This approach offers efficient, provably convergent solutions and scalable insights for privacy-preserving data release.

Abstract

The privacy funnel (PF) gives a framework of privacy-preserving data release, where the goal is to release useful data while also limiting the exposure of associated sensitive information. This framework has garnered significant interest due to its broad applications in characterization of the privacy-utility tradeoff. Hence, there is a strong motivation to develop numerical methods with high precision and theoretical convergence guarantees. In this paper, we propose a novel relaxation variant based on Jensen's inequality of the objective function for the computation of the PF problem. This model is proved to be equivalent to the original in terms of optimal solutions and optimal values. Based on our proposed model, we develop an accurate algorithm which only involves closed-form iterations. The convergence of our algorithm is theoretically guaranteed through descent estimation and Pinsker's inequality. Numerical results demonstrate the effectiveness of our proposed algorithm.

An Expectation-Maximization Relaxed Method for Privacy Funnel

TL;DR

The paper tackles the privacy funnel problem of minimizing the information leakage under a disclosure constraint for discrete variables. It introduces an EM-inspired upper-bound relaxation using an auxiliary to obtain a tractable objective while proving its equivalence to the original PF. An alternating expectation minimization (AEM) algorithm with closed-form updates and convergence guarantees via descent estimates and Pinsker's inequality is developed. Numerical results on synthetic and real-world datasets demonstrate accurate PF curves, near-optimal privacy-utility tradeoffs, and improved stability over prior methods. This approach offers efficient, provably convergent solutions and scalable insights for privacy-preserving data release.

Abstract

The privacy funnel (PF) gives a framework of privacy-preserving data release, where the goal is to release useful data while also limiting the exposure of associated sensitive information. This framework has garnered significant interest due to its broad applications in characterization of the privacy-utility tradeoff. Hence, there is a strong motivation to develop numerical methods with high precision and theoretical convergence guarantees. In this paper, we propose a novel relaxation variant based on Jensen's inequality of the objective function for the computation of the PF problem. This model is proved to be equivalent to the original in terms of optimal solutions and optimal values. Based on our proposed model, we develop an accurate algorithm which only involves closed-form iterations. The convergence of our algorithm is theoretically guaranteed through descent estimation and Pinsker's inequality. Numerical results demonstrate the effectiveness of our proposed algorithm.
Paper Structure (21 sections, 4 theorems, 39 equations, 2 figures, 1 algorithm)

This paper contains 21 sections, 4 theorems, 39 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Upper Bound Relaxation Variant and Its Equivalence with the Original Model
  4. Upper Bound Relaxation Variant
  5. Equivalence of Optimal Solutions
  6. The Alternating Expectation Minimization Algorithm
  7. Algorithm Derivation and Implementation
  8. Updating $\boldsymbol{q}$ and $\boldsymbol{\zeta}$
  9. Updating $\boldsymbol{u}$ and $\boldsymbol{\alpha},\lambda$
  10. Updating $\boldsymbol{r}$ and $\gamma$
  11. Updating $\boldsymbol{w}$ and $\boldsymbol{\beta}$
  12. Convergence Analysis
  13. Numerical Results
  14. Experiments on A Synthetic Distribution
  15. Experiment on Real-World Datasets
  16. ...and 6 more sections

Key Result

Theorem 1

The optimal values as well as the optimal triples $(\boldsymbol{u}^\star,\boldsymbol{w}^\star,\boldsymbol{r}^\star)$ of original-pf and relaxed-pf are identical.

Figures (2)

  • Figure 1: Comparison of PF curves between the AEM algorithm (red dashed line) and the DRS method (blue dashed line).
  • Figure 2: Performance comparison between the AEM algorithm and the DRS method on two real-world datasets.

Theorems & Definitions (8)

  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 2
  • proof