Improved Accuracy for Private Continual Cardinality Estimation in Fully Dynamic Streams via Matrix Factorization
This work addresses the challenge of maintaining privacy in streaming data analysis for applications like network monitoring or social media analytics, offering incremental improvements over prior reductions.
The paper tackles the problem of improving accuracy for differentially-private cardinality estimation in fully dynamic streams with insertions and deletions, by analyzing the sensitivity vectors of difference streams and applying matrix factorization mechanisms, resulting in substantially improved error bounds across various parameters.
We study differentially-private statistics in the fully dynamic continual observation model, where many updates can arrive at each time step and updates to a stream can involve both insertions and deletions of an item. Earlier work (e.g., Jain et al., NeurIPS 2023 for counting distinct elements; Raskhodnikova & Steiner, PODS 2025 for triangle counting with edge updates) reduced the respective cardinality estimation problem to continual counting on the difference stream associated with the true function values on the input stream. In such reductions, a change in the original stream can cause many changes in the difference stream, this poses a challenge for applying private continual counting algorithms to obtain optimal error bounds. We improve the accuracy of several such reductions by studying the associated $\ell_p$-sensitivity vectors of the resulting difference streams and isolating their properties. We demonstrate that our framework gives improved bounds for counting distinct elements, estimating degree histograms, and estimating triangle counts (under a slightly relaxed privacy model), thus offering a general approach to private continual cardinality estimation in streaming settings. Our improved accuracy stems from tight analysis of known factorization mechanisms for the counting matrix in this setting; the key technical challenge is arguing that one can use state-of-the-art factorizations for sensitivity vector sets with the properties we isolate. Empirically and analytically, we demonstrate that our improved error bounds offer a substantial improvement in accuracy for cardinality estimation problems over a large range of parameters.