Better Differentially Private Approximate Histograms and Heavy Hitters using the Misra-Gries Sketch
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909541111693312 |
|---|---|
| author | Lebeda, Christian Janos Tětek, Jakub |
| author_facet | Lebeda, Christian Janos Tětek, Jakub |
| contents | 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 $(\varepsilon,δ)$-differential privacy. It adds noise with magnitude independent of the size of the sketch; 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 $\varepsilon$-differential privacy where the noise scales linearly to the size of the sketch. Finally, we consider a general setting where users can contribute multiple distinct elements. We present a new sketch with maximum error matching the Misra-Gries sketch. For many parameters in this setting our sketch can be released with less noise under $(\varepsilon, δ)$-differential privacy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02457 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Better Differentially Private Approximate Histograms and Heavy Hitters using the Misra-Gries Sketch Lebeda, Christian Janos Tětek, Jakub Data Structures and Algorithms Cryptography and Security Information Retrieval 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 $(\varepsilon,δ)$-differential privacy. It adds noise with magnitude independent of the size of the sketch; 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 $\varepsilon$-differential privacy where the noise scales linearly to the size of the sketch. Finally, we consider a general setting where users can contribute multiple distinct elements. We present a new sketch with maximum error matching the Misra-Gries sketch. For many parameters in this setting our sketch can be released with less noise under $(\varepsilon, δ)$-differential privacy. |
| title | Better Differentially Private Approximate Histograms and Heavy Hitters using the Misra-Gries Sketch |
| topic | Data Structures and Algorithms Cryptography and Security Information Retrieval |
| url | https://arxiv.org/abs/2301.02457 |