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[2509.20345] Statistical Inference Leveraging Synthetic Data with Distribution-Free Guarantees
Summary
This article presents the GEneral Synthetic-Powered Inference (GESPI) framework, which enhances statistical inference by integrating synthetic and real data while ensuring distribution-free guarantees.
Why It Matters
As synthetic data becomes increasingly prevalent in statistical analysis, understanding how to leverage it effectively is crucial. This framework addresses the challenges of integrating synthetic data into traditional inference methods, potentially improving outcomes in various applications, including machine learning and hypothesis testing.
Key Takeaways
- GESPI framework enhances statistical power by combining synthetic and real data.
- The method adapts to the quality of synthetic data, ensuring reliability.
- Applicable to various statistical procedures like hypothesis testing and risk control.
- Demonstrated effectiveness in tasks with limited labeled data, such as protein structure prediction.
- Offers a distribution-free approach, making it versatile across different scenarios.
Statistics > Methodology arXiv:2509.20345 (stat) [Submitted on 24 Sep 2025 (v1), last revised 18 Feb 2026 (this version, v2)] Title:Statistical Inference Leveraging Synthetic Data with Distribution-Free Guarantees Authors:Meshi Bashari, Yonghoon Lee, Roy Maor Lotan, Edgar Dobriban, Yaniv Romano View a PDF of the paper titled Statistical Inference Leveraging Synthetic Data with Distribution-Free Guarantees, by Meshi Bashari and 4 other authors View PDF HTML (experimental) 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 bene...