On Perfect Obfuscation: Local Information Geometry Analysis
This work addresses privacy-preserving data release for specific utility tasks, offering a theoretical framework that is incremental in extending existing privacy-utility trade-off methods.
The paper tackles the problem of extracting features from data that maximize information about a utility attribute while perfectly hiding sensitive information, establishing necessary and sufficient conditions for this under perfect obfuscation constraints. It generalizes prior problems like the information bottleneck and privacy funnel, using local information geometry to analyze information coupling and construct modal decompositions.
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 $χ^2$-divergence and Kullback-Leibler divergence in the Euclidean information geometry.