Perturbed M-Estimation: A Further Investigation of Robust Statistics for Differential Privacy

TL;DR

This paper introduces Perturbed M-Estimation, a novel approach combining robust statistics with differential privacy to enhance utility while maintaining privacy guarantees, supported by preliminary results indicating improved statistical utility.

Contribution

It proposes a new privacy mechanism using bounded M-Estimators that improves utility in differential privacy applications by reducing outlier influence.

Findings

Preliminary results show improved utility of outputs.

The method effectively reduces outlier influence.

Supports further research in robust statistical tools for DP.

Abstract

Differential Privacy (DP) provides an elegant mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries; it guarantees that whether an individual is in a database or not, the results of a DP procedure should be similar in terms of their probability distribution. While DP mechanisms are provably effective in protecting privacy, they often negatively impact the utility of the query responses, statistics and/or analyses that come as outputs from these mechanisms. To address this problem, we use ideas from the area of robust statistics which aims at reducing the influence of outlying observations on statistical inference. Based on the preliminary known links between differential privacy and robust statistics, we modify the objective perturbation mechanism by making use of a new bounded function and define a bounded M-Estimator with adequate statistical properties. The resulting privacy mechanism, named "Perturbed M-Estimation", shows important potential in terms of improved statistical utility of its outputs as suggested by some preliminary results. These results consequently support the need to further investigate the use of robust statistical tools for differential privacy.