Adjusting Queries to Statistical Procedures Under Differential Privacy

TL;DR

This paper explores how analysts can improve statistical inference by adjusting vector queries under differential privacy constraints, using simple transformations to enhance informativeness of noisy responses.

Contribution

It introduces methods for adjusting queries with explicit transformations to improve inference under DP$(\varepsilon,\delta)$ privacy guarantees.

Findings

Adjusting queries can lead to more accurate statistical inference.

Simple explicit transformations can significantly improve data utility under privacy constraints.

The approach provides practical guidance for analysts working with differentially private data.

Abstract

We consider a dataset $S$ held by an agency, and a vector query of interest, $f(S) \in \mathbb{R}^k$, to be posed by an analyst, which contains the information required for certain planned statistical inference. The agency releases the requested vector query with noise that guarantees a given level of Differential Privacy -- DP$(\varepsilon,\delta)$ -- using the well-known Gaussian mechanism. The analyst can choose to pose the vector query $f(S)$ or to adjust it by a suitable transformation that can make the agency's response more informative. For any given level of privacy DP$(\varepsilon,\delta)$ decided by the agency, we study natural situations where the analyst can achieve better statistical inference by adjusting the query with a suitable simple explicit transformation.