Differential Privacy for Sparse Classification Learning

TL;DR

This paper introduces a differentially private sparse classification method using ADMM, ensuring privacy in convex and nonconvex models while maintaining effectiveness and efficiency in sensitive data analysis.

Contribution

It develops a novel differential privacy approach for sparse classification leveraging ADMM, with theoretical privacy bounds and practical application to logistic regression models.

Findings

Method achieves $\

$\\epsilon$-differential privacy with theoretical guarantees.

Effective in sensitive data analysis with good performance in numerical studies.

Abstract

In this paper, we present a differential privacy version of convex and nonconvex sparse classification approach. Based on alternating direction method of multiplier (ADMM) algorithm, we transform the solving of sparse problem into the multistep iteration process. Then we add exponential noise to stable steps to achieve privacy protection. By the property of the post-processing holding of differential privacy, the proposed approach satisfies the $\epsilon-$differential privacy even when the original problem is unstable. Furthermore, we present the theoretical privacy bound of the differential privacy classification algorithm. Specifically, the privacy bound of our algorithm is controlled by the algorithm iteration number, the privacy parameter, the parameter of loss function, ADMM pre-selected parameter, and the data size. Finally we apply our framework to logistic regression with $L_1$ regularizer and logistic regression with $L_{1/2}$ regularizer. Numerical studies demonstrate that our method is both effective and efficient which performs well in sensitive data analysis.