Preserving Target Distributions With Differentially Private Count Mechanisms

TL;DR

This paper introduces a novel two-stage framework for privatizing count tables that preserves distribution accuracy, featuring a new cyclic Laplace mechanism and an efficient constructor algorithm, improving privacy-utility tradeoffs.

Contribution

It formalizes a distribution-focused approach to differential privacy, proposing a new cyclic Laplace mechanism and a transition matrix constructor algorithm for better count privatization.

Findings

The cyclic Laplace mechanism outperforms existing histogram mechanisms.

The transition matrix approach achieves favorable tradeoffs in accuracy and runtime.

Experiments demonstrate practical advantages of the fixed-point method.

Abstract

Differentially private mechanisms are increasingly used to publish tables of counts, where each entry represents the number of individuals belonging to a particular category. A distribution of counts summarizes the information in the count column, unlinking counts from categories. This object is useful for answering a class of research questions, but it is subject to statistical biases when counts are privatized with standard mechanisms. This motivates a novel design criterion we term accuracy of distribution. This study formalizes a two-stage framework for privatizing tables of counts that balances accuracy of distribution with two standard criteria of accuracy of counts and runtime. In the first stage, a distribution privatizer generates an estimate for the true distribution of counts. We introduce a new mechanism, called the cyclic Laplace, specifically tailored to distributions of counts, that outperforms existing general-purpose differentially private histogram mechanisms. In the second stage, a constructor algorithm generates a count mechanism, represented as a transition matrix, whose fixed-point is the privatized distribution of counts. We develop a mathematical theory that describes such transition matrices in terms of simple building blocks we call epsilon-scales. This theory informs the design of a new constructor algorithm that generates transition matrices with favorable properties more efficiently than standard optimization algorithms. We explore the practicality of our framework with a set of experiments, highlighting situations in which a fixed-point method provides a favorable tradeoff among performance criteria.