On Perfect Obfuscation: Local Information Geometry Analysis

TL;DR

This paper introduces a local information geometry framework to analyze perfect obfuscation in privacy-preserving data release, enabling extraction of utility-relevant features without revealing sensitive information.

Contribution

It generalizes the information bottleneck and privacy funnel problems by providing a geometric analysis for constructing optimal obfuscation strategies under perfect privacy constraints.

Findings

Decomposition of mutual information into orthogonal modes.

Construction of locally sufficient statistics for utility inference.

Development of perfect obfuscation notions using divergence measures.

Abstract

We consider the problem of privacy-preserving data release for a specific utility task under perfect obfuscation constraint. We establish the necessary and sufficient condition to extract features of the original data that carry as much information about a utility attribute as possible, while not revealing any information about the sensitive attribute. This problem formulation generalizes both the information bottleneck and privacy funnel problems. We adopt a local information geometry analysis that provides useful insight into information coupling and trajectory construction of spherical perturbation of probability mass functions. This analysis allows us to construct the modal decomposition of the joint distributions, divergence transfer matrices, and mutual information. By decomposing the mutual information into orthogonal modes, we obtain the locally sufficient statistics for inferences about the utility attribute, while satisfying perfect obfuscation constraint. Furthermore, we develop the notion of perfect obfuscation based on $\chi^2$-divergence and Kullback-Leibler divergence in the Euclidean information geometry.