Private Minimum Hellinger Distance Estimation via Hellinger Distance Differential Privacy

TL;DR

This paper introduces a new privacy-preserving estimation method based on Hellinger distance that maintains robustness and efficiency, suitable for privacy-sensitive applications.

Contribution

It develops the concept of Hellinger differential privacy and provides algorithms for private parameter estimation with theoretical and empirical validation.

Findings

Estimators satisfy Hellinger differential privacy while remaining robust.

Algorithms for private gradient descent and Newton-Raphson are proposed.

Numerical experiments confirm robustness under contamination.

Abstract

Objective functions based on Hellinger distance yield robust and efficient estimators of model parameters. Motivated by privacy and regulatory requirements encountered in contemporary applications, we derive in this paper \emph{private minimum Hellinger distance estimators}. The estimators satisfy a new privacy constraint, namely, Hellinger differential privacy, while retaining the robustness and efficiency properties. We demonstrate that Hellinger differential privacy shares several features of standard differential privacy while allowing for sharper inference. Additionally, for computational purposes, we also develop Hellinger differentially private gradient descent and Newton-Raphson algorithms. We illustrate the behavior of our estimators in finite samples using numerical experiments and verify that they retain robustness properties under gross-error contamination.