The Staircase Mechanism in Differential Privacy

• Published in: IEEE journal of selected topics in signal processing Vol. 9; no. 7; pp. 1176 - 1184
• Main Authors: Quan Geng, Kairouz, Peter, Sewoong Oh, Viswanath, Pramod
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Data privacy; Laplace equations; Noise; Optimization; Privacy; Probability density function; Probability distribution; Random variables; randomized algorithm; Releasing; Sensitivity; Signal processing; Staircases; Two dimensional
• ISSN: 1932-4553; 1941-0484
• DOI: 10.1109/JSTSP.2015.2425831

Adding Laplacian noise is a standard approach in differential privacy to sanitize numerical data before releasing it. In this paper, we propose an alternative noise adding mechanism: the staircase mechanism, which is a geometric mixture of uniform random variables. The staircase mechanism can replace the Laplace mechanism in each instance in the literature and for the same level of differential privacy, the performance in each instance improves; the improvement is particularly stark in medium-low privacy regimes. We show that the staircase mechanism is the optimal noise adding mechanism in a universal context, subject to a conjectured technical lemma (which we also prove to be true for one and two dimensional data).