PRECISE: PRivacy-loss-Efficient and Consistent Inference based on poSterior quantilEs

Music City Center 

Differential privacy (DP) is a mathematical framework for releasing information with formal privacy guarantees. Despite the existence of various DP procedures for
performing a wide range of statistical analysis and machine learning tasks, methods of good utility are still lacking in obtaining valid statistical inference with DP guarantees. We address this gap by proposing PRivacy-loss-Efficient and Consistent Inference based on poSterior quantilEs (PRECISE). PRECISE is a general-purpose Bayesian approach for constructing privacy-preserving posterior intervals. We establish the Mean-Squared-Error consistency for our proposed private posterior quantiles converging to the population posterior quantile as sample size increases or privacy guarantees weaken. We conduct extensive experiments to compare the utilities of PRECISE with common existing privacy-preserving inferential approaches in various inferential tasks, data types
and sizes, privacy loss levels. The results demonstrated a significant advantage of PRECISE with its nominal coverage and substantially narrower intervals than the existing methods, which are prone to either under-coverage or impractically wide intervals.

Bayesian

differential privacy

privacy-preserving inference

MSE consistency

privacy loss

quantiles 

Section on Bayesian Statistical Science