Statistical Inference Leveraging Synthetic Data with Distribution-Free Guarantees

• URL: http://arxiv.org/abs/2509.20345v1
• Date: Wed, 24 Sep 2025 17:37:14 GMT
• Title: Statistical Inference Leveraging Synthetic Data with Distribution-Free Guarantees
• Authors: Meshi Bashari, Yonghoon Lee, Roy Maor Lotan, Edgar Dobriban, Yaniv Romano,
• Abstract summary: High-quality synthetic data presents both opportunities and challenges for statistical inference.<n>This paper introduces a GEneral Synthetic-Powered Inference framework that wraps around any statistical inference procedure.<n>Our framework leverages high-quality synthetic data to boost statistical power, yet adaptively defaults to the standard inference method using only real data.
• Score: 27.512077526249524
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The rapid proliferation of high-quality synthetic data -- generated by advanced AI models or collected as auxiliary data from related tasks -- presents both opportunities and challenges for statistical inference. This paper introduces a GEneral Synthetic-Powered Inference (GESPI) framework that wraps around any statistical inference procedure to safely enhance sample efficiency by combining synthetic and real data. Our framework leverages high-quality synthetic data to boost statistical power, yet adaptively defaults to the standard inference method using only real data when synthetic data is of low quality. The error of our method remains below a user-specified bound without any distributional assumptions on the synthetic data, and decreases as the quality of the synthetic data improves. This flexibility enables seamless integration with conformal prediction, risk control, hypothesis testing, and multiple testing procedures, all without modifying the base inference method. We demonstrate the benefits of our method on challenging tasks with limited labeled data, including AlphaFold protein structure prediction, and comparing large reasoning models on complex math problems.

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