Learning a Size-Weight Frontier for Synthetic-Augmented Inference
Field: Machine Learning Authors: Chengpiao Huang, Kaizheng Wang Published: 2026-08-28 arXiv: 2608.28576
Summary
Synthetic data can improve statistical inference when real data are scarce, but naively treating synthetic samples as real data can introduce bias and lead to unreliable inference. We develop a general framework for synthetic-augmented inference across a population of related tasks. It characterizes synthetic augmentation by the number of synthetic observations and their weight. Central to our framework is a size-weight frontier that specifies, for each weight, the largest synthetic sample size for which all smaller sizes attain the target task-marginal coverage. We estimate this frontier from historical tasks, and establish a finite-sample coverage guarantee simultaneously for all size-weight configurations on or below the estimated frontier. In experiments using large language model responses to augment opinion survey data, our procedure attains target coverage and significantly narrows confidence intervals.
Key Ideas
- Synthetic augmentation is characterized by two knobs: the number of synthetic observations and their weight.
- The size-weight frontier defines, for each weight, the maximum synthetic sample size that still guarantees target task-marginal coverage for all smaller sizes.
- The frontier is estimated from historical tasks, with finite-sample coverage guarantees holding simultaneously for all configurations on or below the estimated frontier.
- In LLM-augmented opinion survey experiments, the method reaches target coverage while substantially shrinking confidence intervals.