Adjusting Queries to Statistical Procedures Under Differential Privacy
This work addresses the challenge of balancing privacy and utility in statistical analysis, offering a practical method for analysts to enhance data utility without compromising privacy guarantees, though it appears incremental as it builds on existing mechanisms like the Gaussian mechanism.
The paper tackles the problem of improving statistical inference under differential privacy by allowing analysts to adjust their queries before the agency adds noise, and shows that simple explicit transformations can lead to better inference for given privacy levels.
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$(\varepsilon,δ)$ -- 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$(\varepsilon,δ)$ 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.