# Private Counting of Distinct Elements in the Turnstile Model and Extensions

arXiv: https://arxiv.org/abs/2408.11637 · HTML: https://mlsanity.com/paper/2408.11637/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Aug 2024.

## Built on by (most cited first, 1 of 1)

- [The Binary Tree Mechanism is Optimal for Differentially Private Continual Counting](https://mlsanity.com/paper/2607.00876/) (2026)

## Abstract (arXiv)

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 (ε,δ)-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 (ε,δ)-differential privacy and item-level ε-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].