A Unified Approach to Differentially Private Bayes Point Estimation

TL;DR

This paper introduces a new Bayesian method for parameter estimation that enhances the accuracy-privacy trade-off under differential privacy constraints, outperforming traditional noise-adding techniques.

Contribution

The paper proposes the Unified Bayes Private Point (UBaPP) approach, a novel Bayesian estimation method that improves privacy-accuracy balance under differential privacy.

Findings

UBaPP achieves better accuracy for a given privacy level.

Numerical example demonstrates improved performance over traditional methods.

Method effectively balances privacy and estimation accuracy.

Abstract

Parameter estimation in statistics and system identification relies on data that may contain sensitive information. To protect this sensitive information, the notion of \emph{differential privacy} (DP) has been proposed, which enforces confidentiality by introducing randomization in the estimates. Standard algorithms for differentially private estimation are based on adding an appropriate amount of noise to the output of a traditional point estimation method. This leads to an accuracy-privacy trade off, as adding more noise reduces the accuracy while increasing privacy. In this paper, we propose a new Unified Bayes Private Point (UBaPP) approach to Bayes point estimation of the unknown parameters of a data generating mechanism under a DP constraint, that achieves a better accuracy-privacy trade off than traditional approaches. We verify the performance of our approach on a simple numerical example.