# On Perfect Obfuscation: Local Information Geometry Analysis

arXiv: https://arxiv.org/abs/2009.04157 · HTML: https://mlsanity.com/paper/2009.04157/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2020.

## Built on by (most cited first, 6 of 6)

- [Bottlenecks CLUB: Unifying Information-Theoretic Trade-offs Among Complexity, Leakage, and Utility](https://mlsanity.com/paper/2207.04895/) (2022)
- [Variational Leakage: The Role of Information Complexity in Privacy Leakage](https://mlsanity.com/paper/2106.02818/) (2021)
- [Fundamental Limits of Perfect Concept Erasure](https://mlsanity.com/paper/2503.20098/) (2025)
- [Deep Variational Privacy Funnel: General Modeling with Applications in Face Recognition](https://mlsanity.com/paper/2401.14792/) (2024)
- [Privacy for Fairness: Information Obfuscation for Fair Representation Learning with Local Differential Privacy](https://mlsanity.com/paper/2402.10473/) (2024)
- [Deep Privacy Funnel Model: From a Discriminative to a Generative Approach with an Application to Face Recognition](https://mlsanity.com/paper/2404.02696/) (2024)

## Abstract (arXiv)

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 chi2-divergence and Kullback-Leibler divergence in the Euclidean information geometry.