Better Differentially Private Approximate Histograms and Heavy Hitters using the Misra-Gries Sketch

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Abstract

We consider the problem of computing differentially private approximate histograms and heavy hitters in a stream of elements. In the non-private setting, this is often done using the sketch of Misra and Gries [Science of Computer Programming, 1982]. Chan, Li, Shi, and Xu [PETS 2012] describe a differentially private version of the Misra-Gries sketch, but the amount of noise it adds can be large and scales linearly with the size of the sketch: the more accurate the sketch is, the more noise this approach has to add. We present a better mechanism for releasing a Misra-Gries sketch under (ε,δ)-differential privacy. It adds noise with magnitude independent of the size of the sketch size, in fact, the maximum error coming from the noise is the same as the best known in the private non-streaming setting, up to a constant factor. Our mechanism is simple and likely to be practical. We also give a simple post-processing step of the Misra-Gries sketch that does not increase the worst-case error guarantee. It is sufficient to add noise to this new sketch with less than twice the magnitude of the non-streaming setting. This improves on the previous result for ε-differential privacy where the noise scales linearly to the size of the sketch.
OriginalsprogEngelsk
TitelProceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2023
UdgivelsesstedNew York
ForlagAssociation for Computing Machinery
Publikationsdato18 jun. 2023
Sider79-88
ISBN (Trykt)9798400701276
DOI
StatusUdgivet - 18 jun. 2023
BegivenhedSIGMOD/PODS '23: International Conference on Management of Data - Seattle, USA
Varighed: 18 jun. 202323 jun. 2023
Konferencens nummer: 42
https://2023.sigmod.org/

Konference

KonferenceSIGMOD/PODS '23: International Conference on Management of Data
Nummer42
Land/OmrådeUSA
BySeattle
Periode18/06/202323/06/2023
Internetadresse

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