Publicly-Verifiable Certificates for Statistical Algorithms

2026-07-16

AI Summary

This work addresses the challenge of efficiently verifying the validity of statistical learning models on a given data distribution without trusting the learner. It introduces publicly verifiable certificates of statistical validity (pvCSVs), establishing the first non-interactive, publicly verifiable proof system for learning that applies to adaptive statistical query (SQ) algorithms. The proposed framework enables any user to verify a model’s performance on their own distribution with a sample complexity of only $O(\log k)$, a significant improvement over the $\tilde{O}(\sqrt{k})$ complexity of standard SQ learning algorithms. This result provides a systematic characterization of the capabilities and limitations of the SQ model in the context of verifiable learning.

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.

Problem

• Publicly-Verifiable Certificates
• Statistical Validity
• Learning Algorithms
• Distributional Robustness
• Statistical Query Model

Innovation

• Publicly-Verifiable Certificates
• Statistical Query Model
• Non-interactive Proofs of Learning
• Sample Complexity
• Distributional Robustness