Estimating Numerical Distributions under Local Differential Privacy

Zitao Li*, Tianhao Wang, Milan Lopuhaä-Zwakenberg, Boris Škorić, Ninghui Li

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

58 Citations (Scopus)


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.
Original languageEnglish
Title of host publicationACM SIGMOD 2020
Publication statusPublished - Jun 2020
Externally publishedYes
EventACM SIGMOD International Conference on Management of Data, SIGMOD/PODS 2020 - Hotel Double Tree by Hilton, Portland, United States
Duration: 14 Jun 202019 Jun 2020


ConferenceACM SIGMOD International Conference on Management of Data, SIGMOD/PODS 2020
Abbreviated titleSIGMOD/PODS 2020
Country/TerritoryUnited States


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