Private Counting of Distinct Elements in the Turnstile Model and Extensions
<|reference_start|>Private Counting of Distinct Elements in the Turnstile Model and Extensions: Privately counting distinct elements in a stream is a fundamental data analysis problem with many applications in machine learning. In the turnstile model, Jain et al. [NeurIPS2023] initiated the study of this problem parameterized by the maximum flippancy of any element, i.e., the number of times that the count of an element changes from 0 to above 0 or vice versa. They give an item-level $(\epsilon,\delta)$-differentially private algorithm whose additive error is tight with respect to that parameterization. In this work, we show that a very simple algorithm based on the sparse vector technique achieves a tight additive error for item-level $(\epsilon,\delta)$-differential privacy and item-level $\epsilon$-differential privacy with regards to a different parameterization, namely the sum of all flippancies. Our second result is a bound which shows that for a large class of algorithms, including all existing differentially private algorithms for this problem, the lower bound from item-level differential privacy extends to event-level differential privacy. This partially answers an open question by Jain et al. [NeurIPS2023].<|reference_end|>
@article{henzinger2024private,
    title={Private Counting of Distinct Elements in the Turnstile Model and
  Extensions},
    author={Monika Henzinger and A. R. Sricharan and Teresa Anna Steiner},
    journal={arXiv preprint arXiv:2408.11637},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.11637},
    primaryClass={cs.DS cs.CR}
}