Differentially Private Population Quantity Estimates via Survey Weight Regularization

In general, it is challenging to release differentially private versions of survey-weighted statistics with low error for acceptable privacy loss. This is because weighted statistics from complex sample survey data can be more sensitive to individual survey response and weight values than unweighted statistics, resulting in DP mechanisms that can add substantial noise to the unbiased estimate of the finite population quantity. On the other hand, simply disregarding the survey weights can result in a biased estimate that also underestimates the sampling variance. Thus, the problem of releasing an accurate survey-weighted estimate essentially involves a trade-off among bias, precision, and privacy. We leverage this trade-off to develop a DP method for estimating finite population quantities. The key step is to privately estimate a hyperparameter that determines how much to regularize or shrink survey weights as a function of privacy loss. We illustrate the differentially private finite population estimation using the Panel Study of Income Dynamics. We show that optimal strategies for releasing DP survey-weighted mean income estimates require orders-of-magnitude less DP noise than naively using the original survey weights without modification. We then discuss its implications for integrating DP into survey research.