# Local Distribution Obfuscation via Probability Coupling

## TL;DR

This paper proposes a new local distribution obfuscation method using probability coupling that enhances privacy by adding noise proportional to distribution differences, optimizing utility while ensuring divergence-based privacy.

## Contribution

It introduces a coupling mechanism for local distribution obfuscation that generalizes distribution privacy to divergence and optimizes utility using auxiliary information.

## Key findings

- Probabilistic perturbation should be proportional to Earth mover's distance.
- The coupling mechanism provides divergence distribution privacy.
- The method balances privacy and utility effectively.

## Abstract

We introduce a general model for the local obfuscation of probability distributions by probabilistic perturbation, e.g., by adding differentially private noise, and investigate its theoretical properties. Specifically, we relax a notion of distribution privacy (DistP) by generalizing it to divergence, and propose local obfuscation mechanisms that provide divergence distribution privacy. To provide f-divergence distribution privacy, we prove that probabilistic perturbation noise should be added proportionally to the Earth mover's distance between the probability distributions that we want to make indistinguishable. Furthermore, we introduce a local obfuscation mechanism, which we call a coupling mechanism, that provides divergence distribution privacy while optimizing the utility of obfuscated data by using exact/approximate auxiliary information on the input distributions we want to protect.