Aleksandra Slavkovic, Pennsylvania State University

Abstract

Differential Privacy (DP) provides an elegant mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries. However, numerous technical and practical subtleties exist that limit its usability in statistical applications. We introduce the concept of the adjacent output space, where the structure of this space is directly connected to the sensitivity analysis. We provide extensions to the previously proposed K-norm mechanisms and show that the optimal K-Norm mechanism for any problem is determined solely by the adjacent output space. We focus on L1, L2, and L-infinity in particular as well as other K-norms. We implement these mechanisms on linear and logistics regressions, and demonstrate the improvements on data utility. We show that the choice of norm can result in a significant reduction of noise. By choosing one mechanism over another, the same statistical utility can be achieved using half the original privacy budget. These improvements result in higher data usability, more accurate results, and consequently better inference under DP.

(Jordan Awan and Aleksandra Slavkovic)

Video