Estimating Numerical Distributions under Local Differential Privacy
Zitao Lia, Tianhao Wanga, Milan Lopuhaä-Zwakenbergb, Ninghui Lia, Boris Škorićb
- aPurdue University, West Lafayette, IN, USA
- bEindhoven University of Technology, Eindhoven, Netherlands
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Abstract
When collecting information, local differential privacy (LDP) relieves the concern of privacy leakage from users' perspective, as user's private information is randomized before sent to the aggregator. We study the problem of recovering the distribution over a numerical domain while satisfying LDP. While one can discretize a numerical domain and then apply the protocols developed for categorical domains, we show that taking advantage of the numerical nature of the domain results in better trade-off of privacy and utility. We introduce a new reporting mechanism, called the square wave (SW) mechanism, which exploits the numerical nature in reporting. We also develop an Expectation Maximization with Smoothing (EMS) algorithm, which is applied to aggregated histograms from the SW mechanism to estimate the original distributions. Extensive experiments demonstrate that our proposed approach, SW with EMS, consistently outperforms other methods in a variety of utility metrics.
TL;DRThis work introduces a new reporting mechanism, called the square wave (SW) mechanism, which exploits the numerical nature in reporting and develops an Expectation Maximization with Smoothing algorithm, which is applied to aggregated histograms from the SW mechanism to estimate the original distributions. (Semantic Scholar)