Statistical Inference Leveraging Synthetic Data with Distribution-Free Guarantees
This work addresses the problem of limited labeled data for researchers and practitioners in fields like bioinformatics and AI evaluation, offering a flexible method to boost statistical power with synthetic data, though it is incremental as it builds on existing inference procedures.
The paper tackles the challenge of safely using synthetic data to improve statistical inference by introducing the GESPI framework, which enhances sample efficiency while maintaining error guarantees without distributional assumptions, demonstrated on tasks like AlphaFold protein structure prediction and comparing large reasoning models.
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.