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

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

URL: http://arxiv.org/abs/2504.13804v1
Date: Fri, 18 Apr 2025 17:12:15 GMT
Title: Near-optimal algorithms for private estimation and sequential testing of collision probability
Authors: Robert Busa-Fekete, Umar Syed,
Abstract summary: We describe an algorithm that satisfies $(alpha, beta)$-local differential privacy and estimates collision probability with error at most $epsilon$.<n>We also present a sequential testing algorithm for collision probability, which can distinguish between collision probability values that are separated by $epsilon$.
Score: 1.62060928868899
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We present new algorithms for estimating and testing \emph{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 for $\alpha \le 1$, which improves over previous work by a factor of $\frac{1}{\alpha^2}$. We also present a 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.

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