Differential Privacy for Sparse Classification Learning
This work addresses privacy concerns in sparse classification for sensitive data, but it is incremental as it adapts existing ADMM and differential privacy techniques.
The paper tackles the problem of ensuring differential privacy in sparse classification learning by introducing a method that adds exponential noise to stable steps of an ADMM-based algorithm, achieving ε-differential privacy even for unstable problems. Numerical studies show the method is effective and efficient for sensitive data analysis.
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 $ε-$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.