Learning a Size-Weight Frontier for Synthetic-Augmented Inference

Chengpiao Huang; Kaizheng Wang

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arXiv · 2608.28576

Learning a Size-Weight Frontier for Synthetic-Augmented Inference

Chengpiao Huang·Kaizheng Wang

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Abstract

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 achieves target coverage and substantially narrows confidence intervals.

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Chengpiao Huang, Kaizheng Wang. 2026-08-28. Learning a Size-Weight Frontier for Synthetic-Augmented Inference. https://arxiv.org/abs/2608.28576

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