Differentially Private Sliced Inverse Regression: Minimax Optimality and Algorithm

• 成果类型: Article; Early Access
• 署名作者: Xia, Xintao; Zhang, Linjun; Cai, Zhanrui
• 署名单位: Iowa State University; Rutgers University System; Rutgers University New Brunswick; University of Hong Kong
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2555059
• 发表日期: 2025

摘要

Privacy preservation has become a critical concern in high-dimensional data analysis due to the growing prevalence of data-driven applications. Since its proposal, sliced inverse regression has emerged as a widely used statistical technique to reduce the dimensionality of covariates while maintaining sufficient statistical information. In this used, we propose optimally differentially private algorithms specifically designed to address privacy concerns in the context of sufficient dimension reduction. We establish lower bounds for differentially private sliced inverse regression in low and high dimensional settings. Moreover, we develop differentially private algorithms that achieve the minimax lower bounds up to logarithmic factors. Through a combination of simulations and real data analysis, we illustrate the efficacy of these differentially private algorithms in safeguarding privacy while preserving vital information within the reduced dimension space. As a natural extension, we can readily offer analogous lower and upper bounds for differentially private sparse principal component analysis, a topic that may also be of potential interest to the statistics and machine learning community. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.