Simulation-based Differentially Private Inference for Categorical Data

Speaker: Roberto Molinari, Auburn University

Title: Simulation-based Differentially Private Inference for Categorical Data

Abstract:

Differential privacy (DP) provides a mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries: it guarantees that whether an individual is in a database or not, the results of a DP procedure should be similar in terms of their probability distribution. While DP mechanisms are provably effective in protecting privacy, by randomizing outputs they often negatively impact the precision of the statistics computed from them as well as the possibility of performing reliable inference on them. Indeed, even for standard inference tasks, there are few or inexistent solutions to perform reliable tests when DP mechanisms have been applied to the data. To address this problem, in this talk ideas from simulation-based methods are investigated to deliver easily computable and reliable inference quantities for different statistical tasks. Our numerical and theoretical results are described when employing these approaches for inference on discrete/categorical data, starting from the standard one-sample proportion test for which only a few solutions exist in the DP framework. These results are also discussed for a broader collection of tests such as two-proportions, chi-squared tests and log-linear models.