Private Continual Release of Real-Valued Data Streams

We present a differentially private mechanism to display statistics (e.g., the moving average) of a stream of real valued observations where the bound on each observation is either too conservative or unknown in advance. This is particularly relevant to scenarios of real-time data monitoring and reporting, e.g., energy data through smart meters. Our focus is on real-world data streams whose distribution is light-tailed, meaning that the tail approaches zero at least as fast as the exponential distribution. For such data streams, individual observations are expected to be concentrated below an unknown threshold. Estimating this threshold from the data can potentially violate privacy as it would reveal particular events tied to individuals [1] . On the other hand an overly conservative threshold may impact accuracy by adding more noise than necessary. We construct a utility optimizing differentially private mechanism to release this threshold based on the input stream. Our main advantage over the state-of-the-art algorithms is that the resulting noise added to each observation of the stream is scaled to the threshold instead of a possibly much larger bound; resulting in considerable gain in utility when the difference is significant. Using two real-world datasets, we demonstrate that our mechanism, on average, improves the utility by a factor of 3.5 on the first dataset, and 9 on the other. While our main focus is on continual release of statistics, our mechanism for releasing the threshold can be used in various other applications where a (privacy-preserving) measure of the scale of the input distribution is required. Permission to freely reproduce all or part of this paper for noncommercial purposes is granted provided that copies bear this notice and the full citation on the first page. Reproduction for commercial purposes is strictly prohibited without the prior written consent of the Internet Society, the first-named author (for reproduction of an entire paper only), and the author's employer if the paper was prepared within the scope of employment.