Near-optimal algorithms for private estimation and sequential testing of collision probability

Robert Istvan Busa-Fekete, Umar Syed

Primary Area: societal considerations including fairness, safety, privacy

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Keywords: Differentially privacy, collision probability

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.

Abstract: We present new algorithms for estimating and testing collision probability, a fundamental measure of the spread of a discrete distribution that is widely used in many scientific fields. We describe an algorithm that satisfies $(\alpha, \beta)$-local differential privacy and estimates collision probability with error at most $\epsilon$ using $\tilde{O}\left(\frac{\log(1/\beta)}{\alpha^2 \epsilon^2}\right)$ samples, which improves over previous work by a factor of $\frac{1}{\alpha^2}$. We also present the first sequential testing algorithm for collision probability, which can distinguish between collision probability values that are separated by $\epsilon$ using $\tilde{O}(\frac{1}{\epsilon^2})$ samples, even when $\epsilon$ is unknown. Our algorithms have nearly the optimal sample complexity and in experiments we show that they require significantly fewer samples than previous methods.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 1482