A0529
Title: Optimal rates of convergence for sliced inverse regression with differential privacy
Authors: Wenbiao Zhao - Beijing Institute of Technology (China) [presenting]
Abstract: Sliced inverse regression (SIR) is a highly efficient paradigm used for dimension reduction by replacing high-dimensional covariates with a limited number of linear combinations. The focus is on the implementation of the classical SIR approach integrated with a Gaussian differential privacy mechanism to estimate the central space while preserving privacy. The tradeoff between statistical accuracy and privacy in sufficient dimension reduction problems is illustrated under both the classical low-dimensional and modern high-dimensional settings. Additionally, the minimax rate of the proposed estimator is achieved with Gaussian differential privacy constraint, and this rate is illustrated to be optimal for multiple index models with a bounded dimension of the central space. Extensive numerical studies on synthetic data sets are conducted to assess the effectiveness of the proposed technique in finite sample scenarios, and real data analysis is presented to showcase its practical application.
