Privately Estimating Monotone Statistics in Polynomial Time

• URL: http://arxiv.org/abs/2605.27912v2
• Date: Thu, 28 May 2026 20:19:03 GMT
• Title: Privately Estimating Monotone Statistics in Polynomial Time
• Abstract summary: We study efficient differentially private algorithms for estimating monotone statistics.<n>Our algorithms save a factor of $t$ in sample complexity and pay a factor of $et$ in running time.<n>As an application, we obtain improved results for private eigenvalue estimation, private loss estimation, and privately estimating a single parameter of a high-dimensional model.
• Score: 5.457331995994299
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study efficient differentially private algorithms for estimating monotone statistics, i.e., statistics that are monotone under the addition of new observations. The starting point for our investigation is subsample-and-aggregate: a classical paradigm that partitions the dataset into blocks, estimates the statistic on each block, and then privately aggregates the estimates. While practical and generically applicable, this approach is quite data-hungry. We improve upon this framework for the class of monotone statistics -- compared to subsample-and-aggregate, our algorithms save a factor of $t$ in sample complexity and pay a factor of $e^t$ in running time, where $t>0$ is a tunable parameter. We complement our results with a query-complexity lower bound, showing that our algorithms are essentially optimal for this task. As an application, we obtain improved results for private eigenvalue estimation, private loss estimation, and privately estimating a single parameter of a high-dimensional model, e.g., in linear regression.

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