Statistical Approximating Distributions Under Differential Privacy
Main Article Content
Statistics computed from data are viewed as random variables. When they are used for tasks like hypothesis testing and confidence intervals, their true finite sample distributions are often replaced by approximating distributions that are easier to work with (for example, the Gaussian, which results from using approximations justified by the Central Limit Theorem). When data are perturbed by differential privacy, the approximating distributions also need to be modified. Prior work provided various competing methods for creating such approximating distributions with little formal justification beyond the fact that they worked well empirically.
In this paper, we study the question of how to generate statistical approximating distributions for differentially private statistics, provide finite sample guarantees for the quality of the approximations.
Copyright is retained by the authors. By submitting to this journal, the author(s) license the article under the Creative Commons License – Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0), unless choosing a more lenient license (for instance, public domain). For situations not allowed under CC BY-NC-ND, short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Authors of articles published by the journal grant the journal the right to store the articles in its databases for an unlimited period of time and to distribute and reproduce the articles electronically.
National Science Foundation
Grant numbers 1702760. 1228669