Publicly-Verifiable Certificates for Statistical Algorithms

• URL: http://arxiv.org/abs/2607.15528v1
• Date: Fri, 17 Jul 2026 00:32:13 GMT
• Title: Publicly-Verifiable Certificates for Statistical Algorithms
• Abstract summary: We define and study a new notion: Publicly-Verifiable proofs of Statistical Validity (pvCSVs)<n>pvCSVs allow for public, distributionally-robust certification that the result of a learning algorithm is valid.<n>We study proof systems for learning in the SQ model, demonstrating the model's strengths as well as its limitations.
• Score: 2.502327145375967
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Following Goldwasser, Rothblum, Shafer, and Yehudayoff, who defined a framework for interactive proofs of learning [ITCS'21], we initiate the study of non-interactive proofs of learning. We define and study a new notion: Publicly-Verifiable Certificates of Statistical Validity (pvCSVs), which allow for public, distributionally-robust certification that the result of a learning algorithm is valid. In a pvCSV, a learner publishes a hypothesis $h$ and corresponding certificate $π$; then, any user, who holds a user-specific distribution, can read the pair $(h,π)$ and determine efficiently whether the hypothesis is valid according to the user-specific distribution. We construct pvCSVs in the context of Adaptive Statistical Query (SQ) Algorithms. To certify SQ algorithms that makes $k$ adaptive queries, we construct pvCSVs where the sample complexity scales with $O(\log k)$, whereas the sample complexity of the best learning algorithms scale with $\tilde{O}(\sqrt{k})$. More generally, we study proof systems for learning in the SQ model, demonstrating the model's strengths as well as its limitations.

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