Versatile Differentially Private Learning for General Loss Functions

TL;DR

This paper introduces a versatile differentially private mechanism and estimation framework that supports general loss functions, including non-smooth ones, without prior task specification, suitable for online data analysis.

Contribution

It proposes the ZIL privacy mechanism with a unified approach for parameter estimation and inference under differential privacy, applicable to a broad class of loss functions.

Findings

The ZIL mechanism effectively balances privacy and utility.

The DRCL estimator provides consistent, asymptotically normal estimates.

Simulation studies demonstrate the method's practical performance.

Abstract

This paper aims to provide a versatile privacy-preserving release mechanism along with a unified approach for subsequent parameter estimation and statistical inference. We propose the ZIL privacy mechanism based on zero-inflated symmetric multivariate Laplace noise, which requires no prior specification of subsequent analysis tasks, allows for general loss functions under minimal conditions, imposes no limit on the number of analyses, and is adaptable to the increasing data volume in online scenarios. We derive the trade-off function for the proposed ZIL mechanism that characterizes its privacy protection level. Within the M-estimation framework, we propose a novel doubly random corrected loss (DRCL) for the ZIL mechanism, which provides consistent and asymptotic normal M-estimates for the parameters of the target population under differential privacy constraints. The proposed approach is easy to compute without numerical integration and differentiation for noisy data. It is applicable for a general class of loss functions, including non-smooth loss functions like check loss and hinge loss. Simulation studies, including logistic regression and quantile regression, are conducted to evaluate the performance of the proposed method.