Resampling methods for Private Statistical Inference

Releasing statistics using sensitive data can hurt the privacy of individuals contributing to the data (Narayanan and Shmatikov, 2008; Dick et al., 2023). Differential privacy (Dwork et al., 2006) is now a widely accepted solution for performing statistical analysis while protecting sensitive data. In the years since its release, researchers have made considerable progress in the development of differentially private estimators for a range of statistical problems such as mean estimation, median estimation, logistic regression (Asi and Duchi, 2020; Chaudhuri et al., 2011). However, deriving a conclusion from a single point estimate--whether an empirical mean or a classifier prediction-- without any consideration of uncertainty can lead to faulty, inaccurate decision-making (Gelman and Loken, 2013). To have any hope of making private statistical tools broadly applicable, we must build the requisite inferential tools. Constructing confidence intervals around a give point estimate is the most basic inferential task. We therefore develop tools to do so for a broad class of statistics of interest with differential privacy.