# Differential Privacy for Sparse Classification Learning

arXiv: https://arxiv.org/abs/1908.00780 · HTML: https://mlsanity.com/paper/1908.00780/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2019.

## Built on by (most cited first, 5 of 5)

- [Scaling Up Differentially Private LASSO Regularized Logistic Regression via Faster Frank-Wolfe Iterations](https://mlsanity.com/paper/2310.19978/) (2023)
- [The Challenge of Differentially Private Screening Rules](https://mlsanity.com/paper/2303.10303/) (2023)
- [SoK: A Review of Differentially Private Linear Models For High-Dimensional Data](https://mlsanity.com/paper/2404.01141/) (2024)
- [Sparse Private LASSO Logistic Regression](https://mlsanity.com/paper/2304.12429/) (2023)
- [Differentially Private Iterative Screening Rules for Linear Regression](https://mlsanity.com/paper/2502.18578/) (2025)

## Abstract (arXiv)

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 L1 regularizer and logistic regression with L1/2 regularizer. Numerical studies demonstrate that our method is both effective and efficient which performs well in sensitive data analysis.