An Expectation-Maximization Relaxed Method for Privacy Funnel

TL;DR

This paper introduces a new EM-based relaxation method for the privacy funnel problem, providing a high-precision, convergent algorithm that effectively balances data utility and privacy.

Contribution

It proposes a novel Jensen's inequality-based relaxation for the privacy funnel, with a proven equivalence to the original problem and a closed-form iterative algorithm.

Findings

Algorithm converges with theoretical guarantees

Numerical results show high accuracy and effectiveness

Method efficiently balances privacy and utility

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.