We introduce a universal framework for characterizing the statistical efficiency of a statistical
estimation problem with differential privacy guarantees. Our framework, which we call High-
dimensional Propose-Test-Release (HPTR), builds upon three crucial components: the
exponential mechanism, robust statistics, and the Propose-Test-Release mechanism.
Connecting all these together is the concept of resilience, which is central to robust statistical
estimation. Resilience guides the design of the algorithm, the sensitivity analysis, and the …

We show by means of several examples that robust statistical estimators present an
excellent starting point for differentially private estimators. Our algorithms use a new
paradigm for differentially private mechanisms, which we call Propose-Test-Release (PTR),
and for which we give a formal definition and general composition theorems.