Speaker: Xintao Xia, Graduate Student, Department of Statistics, Iowa State University

Title: Differentially Private Sliced Inverse Regression 

Abstract: Privacy preservation has become a critical concern in high-dimensional data analysis due to the growing prevalence of data-driven applications. Proposed by Li (1991), sliced inverse regression has been a popular statistical tool that reduces the dimension of the covariates while preserving sufficient statistical information. In this paper, we propose optimal differentially private algorithms specifically tailored for addressing privacy concerns in sufficient dimension reduction. We establish lower bounds for differentially private sliced inverse regression in both low and high-dimensional settings. Additionally, we design differentially private algorithms that achieve the minimax lower bounds up to logarithmic factors. Through simulations and real data analysis, we demonstrate the effectiveness of these differentially private algorithms in preserving privacy while retaining essential information in the reduced dimension space. As a straightforward extension, we can easily provide similar lower and upper bounds for differentially private sparse principal component analysis, which may also be of potential interest to the statistics and machine learning community.