Query-Efficient Locally Private Hypothesis Selection via the Scheffe Graph

• URL: http://arxiv.org/abs/2509.16180v1
• Date: Fri, 19 Sep 2025 17:41:15 GMT
• Title: Query-Efficient Locally Private Hypothesis Selection via the Scheffe Graph
• Authors: Gautam Kamath, Alireza F. Pour, Matthew Regehr, David P. Woodruff,
• Abstract summary: We describe an algorithm that satisfies local differential privacy, performs $tildeO(k3/2)$ non-adaptive queries to individuals.<n>We also introduce a new object we dub the Scheff'e graph, which captures structure of the differences between distributions in $Q$.
• Score: 45.975805184376036
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose an algorithm with improved query-complexity for the problem of hypothesis selection under local differential privacy constraints. Given a set of $k$ probability distributions $Q$, we describe an algorithm that satisfies local differential privacy, performs $\tilde{O}(k^{3/2})$ non-adaptive queries to individuals who each have samples from a probability distribution $p$, and outputs a probability distribution from the set $Q$ which is nearly the closest to $p$. Previous algorithms required either $\Omega(k^2)$ queries or many rounds of interactive queries. Technically, we introduce a new object we dub the Scheff\'e graph, which captures structure of the differences between distributions in $Q$, and may be of more broad interest for hypothesis selection tasks.

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