Private Minimum Hellinger Distance Estimation via Hellinger Distance Differential Privacy
For statisticians and machine learning practitioners needing robust estimation with formal privacy guarantees, this work offers a new privacy framework that enables sharper inference than standard differential privacy.
The paper introduces private minimum Hellinger distance estimators that satisfy a new privacy constraint called Hellinger differential privacy, achieving robust and efficient parameter estimation while providing privacy guarantees. Numerical experiments confirm retained robustness under contamination.
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.