Differentially Private Continual Release of Histograms and Related Queries

Monika Henzinger, A. R. Sricharan, Teresa Anna Steiner
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1990-1998, 2025.

Abstract

We study privately releasing column sums of a $d$-dimensional table with entries from a universe $\chi$ undergoing $T$ row updates, called histogram under continual release. Our mechanisms give better additive $\ell_\infty$-error than existing mechanisms for a large class of queries and input streams. Our first contribution is an output-sensitive mechanism in the insertions-only model ($\chi = \\{0,1\\}$) for maintaining (i) the histogram or (ii) queries that do not require maintaining the entire histogram, such as the maximum or minimum column sum, the median, or any quantiles. The mechanism has an additive error of $O(d\log^2 (dq^*)+\log T)$ whp, where $q^*$ is the maximum output value over all time steps on this dataset. The mechanism does not require $q^*$ as input. This breaks the $\Omega(d \log T)$ bound of prior work when $q^* \ll T$. Our second contribution is a mechanism for the turnstile model that admits negative entry updates ($\chi = \\{-1, 0,1\\}$). This mechanism has an additive error of $O(d \log^2 (dK) + \log T)$ whp, where $K$ is the number of times two consecutive data rows differ, and the mechanism does not require $K$ as input. This is useful when monitoring inputs that only vary under unusual circumstances. For $d=1$ this gives the first private mechanism with error $O(\log^2 K + \log T)$ for continual counting in the turnstile model, improving on the $O(\log^2 n + \log T)$ error bound by Dwork, Naor, Reingold, Rothblum (ASIACRYPT 2015), where $n$ is the number of ones in the stream, as well as allowing negative entries, while Dwork et al. (2015) can only handle nonnegative entries ($\chi=\\{0,1\\}$).

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-henzinger25a, title = {Differentially Private Continual Release of Histograms and Related Queries}, author = {Henzinger, Monika and Sricharan, A. R. and Steiner, Teresa Anna}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {1990--1998}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/henzinger25a/henzinger25a.pdf}, url = {https://proceedings.mlr.press/v258/henzinger25a.html}, abstract = {We study privately releasing column sums of a $d$-dimensional table with entries from a universe $\chi$ undergoing $T$ row updates, called histogram under continual release. Our mechanisms give better additive $\ell_\infty$-error than existing mechanisms for a large class of queries and input streams. Our first contribution is an output-sensitive mechanism in the insertions-only model ($\chi = \\{0,1\\}$) for maintaining (i) the histogram or (ii) queries that do not require maintaining the entire histogram, such as the maximum or minimum column sum, the median, or any quantiles. The mechanism has an additive error of $O(d\log^2 (dq^*)+\log T)$ whp, where $q^*$ is the maximum output value over all time steps on this dataset. The mechanism does not require $q^*$ as input. This breaks the $\Omega(d \log T)$ bound of prior work when $q^* \ll T$. Our second contribution is a mechanism for the turnstile model that admits negative entry updates ($\chi = \\{-1, 0,1\\}$). This mechanism has an additive error of $O(d \log^2 (dK) + \log T)$ whp, where $K$ is the number of times two consecutive data rows differ, and the mechanism does not require $K$ as input. This is useful when monitoring inputs that only vary under unusual circumstances. For $d=1$ this gives the first private mechanism with error $O(\log^2 K + \log T)$ for continual counting in the turnstile model, improving on the $O(\log^2 n + \log T)$ error bound by Dwork, Naor, Reingold, Rothblum (ASIACRYPT 2015), where $n$ is the number of ones in the stream, as well as allowing negative entries, while Dwork et al. (2015) can only handle nonnegative entries ($\chi=\\{0,1\\}$).} }
Endnote
%0 Conference Paper %T Differentially Private Continual Release of Histograms and Related Queries %A Monika Henzinger %A A. R. Sricharan %A Teresa Anna Steiner %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-henzinger25a %I PMLR %P 1990--1998 %U https://proceedings.mlr.press/v258/henzinger25a.html %V 258 %X We study privately releasing column sums of a $d$-dimensional table with entries from a universe $\chi$ undergoing $T$ row updates, called histogram under continual release. Our mechanisms give better additive $\ell_\infty$-error than existing mechanisms for a large class of queries and input streams. Our first contribution is an output-sensitive mechanism in the insertions-only model ($\chi = \\{0,1\\}$) for maintaining (i) the histogram or (ii) queries that do not require maintaining the entire histogram, such as the maximum or minimum column sum, the median, or any quantiles. The mechanism has an additive error of $O(d\log^2 (dq^*)+\log T)$ whp, where $q^*$ is the maximum output value over all time steps on this dataset. The mechanism does not require $q^*$ as input. This breaks the $\Omega(d \log T)$ bound of prior work when $q^* \ll T$. Our second contribution is a mechanism for the turnstile model that admits negative entry updates ($\chi = \\{-1, 0,1\\}$). This mechanism has an additive error of $O(d \log^2 (dK) + \log T)$ whp, where $K$ is the number of times two consecutive data rows differ, and the mechanism does not require $K$ as input. This is useful when monitoring inputs that only vary under unusual circumstances. For $d=1$ this gives the first private mechanism with error $O(\log^2 K + \log T)$ for continual counting in the turnstile model, improving on the $O(\log^2 n + \log T)$ error bound by Dwork, Naor, Reingold, Rothblum (ASIACRYPT 2015), where $n$ is the number of ones in the stream, as well as allowing negative entries, while Dwork et al. (2015) can only handle nonnegative entries ($\chi=\\{0,1\\}$).
APA
Henzinger, M., Sricharan, A.R. & Steiner, T.A.. (2025). Differentially Private Continual Release of Histograms and Related Queries. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1990-1998 Available from https://proceedings.mlr.press/v258/henzinger25a.html.

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