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Poster
Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising
Borja de Balle Pigem · Yu-Xiang Wang

Thu Jul 12 09:15 AM -- 12:00 PM (PDT) @ Hall B #206
in Posters Thu »
The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important limitations. Our analysis reveals that the variance formula for the original mechanism is far from tight in the high privacy regime ($\varepsilon \to 0$) and it cannot be extended to the low privacy regime ($\varepsilon \to \infty$). We address these limitations by developing an optimal Gaussian mechanism whose variance is calibrated directly using the Gaussian cumulative density function instead of a tail bound approximation. We also propose to equip the Gaussian mechanism with a post-processing step based on adaptive estimation techniques by leveraging that the distribution of the perturbation is known. Our experiments show that analytical calibration removes at least a third of the variance of the noise compared to the classical Gaussian mechanism, and that denoising dramatically improves the accuracy of the Gaussian mechanism in the high-dimensional regime.
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Author Information

Borja de Balle Pigem (Amazon Research)
Yu-Xiang Wang (UC Santa Barbara)
Yu-Xiang Wang

Yu-Xiang Wang is the Eugene Aas Assistant Professor of Computer Science at UCSB. He runs the Statistical Machine Learning lab and co-founded the UCSB Center for Responsible Machine Learning. He is also visiting Amazon Web Services. Yu-Xiang’s research interests include statistical theory and methodology, differential privacy, reinforcement learning, online learning and deep learning.

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