Learning a Size-Weight Frontier for Synthetic-Augmented Inference
2026-08-28 • Artificial Intelligence
Artificial IntelligenceMachine Learning
AI summaryⓘ
The authors propose a method to improve data analysis when actual data is limited by adding synthetic data carefully. They create a system that balances how much synthetic data to use and how much importance it should have without causing wrong results. Their approach learns this balance from past similar problems and guarantees reliable results within those bounds. They tested it with language model outputs helping survey data, achieving more accurate confidence measures and tighter estimates.
synthetic datastatistical inferenceconfidence intervalscoverage guaranteesize-weight frontierlarge language modelsdata augmentationtask-marginal coveragefinite-sample theory
Authors
Chengpiao Huang, Kaizheng Wang
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.