Noise Reduction for Pufferfish Privacy: A Practical Noise Calibration Method

TL;DR

This paper presents a practical noise calibration method that improves data utility under pufferfish privacy by reducing noise compared to traditional mechanisms, especially effective at low privacy budgets.

Contribution

It introduces a relaxed noise calibration approach that alleviates overly strict conditions in the $1$-Wasserstein mechanism, providing a general algorithm with proven noise reduction and utility gains.

Findings

Achieves 47% to 87% utility improvement in experiments

Proves existence of strict noise reduction for all privacy budgets

Shows equivalence of worst-case mechanism to $ ext{l}_1$-sensitivity method

Abstract

This paper introduces a relaxed noise calibration method to enhance data utility while attaining pufferfish privacy. This work builds on the existing $1$-Wasserstein (Kantorovich) mechanism by alleviating the existing overly strict condition that leads to excessive noise, and proposes a practical mechanism design algorithm as a general solution. We prove that a strict noise reduction by our approach always exists compared to $1$-Wasserstein mechanism for all privacy budgets $\epsilon$ and prior beliefs, and the noise reduction (also represents improvement on data utility) gains increase significantly for low privacy budget situations--which are commonly seen in real-world deployments. We also analyze the variation and optimality of the noise reduction with different prior distributions. Moreover, all the properties of the noise reduction still exist in the worst-case $1$-Wasserstein mechanism we introduced, when the additive noise is largest. We further show that the worst-case $1$-Wasserstein mechanism is equivalent to the $\ell_1$-sensitivity method. Experimental results on three real-world datasets demonstrate $47\%$ to $87\%$ improvement in data utility.