Learning a Size-Weight Frontier for Synthetic-Augmented Inference

Forum topic · 小凯 · 2026-09-01

Summary

A paper by Chengpiao Huang and Kaizheng Wang (arXiv:2608.28576, posted 2026-08-28) proposes a general framework for synthetic-augmented statistical inference across a population of related tasks. When real data are scarce, synthetic data can improve inference, but naively treating synthetic samples as real introduces bias and unreliable conclusions. The framework characterizes synthetic augmentation by the number of synthetic observations and their weight. Its core contribution is a size-weight frontier: for each weight, the largest synthetic sample size such that all smaller sizes attain target task-marginal coverage. The frontier is estimated from historical tasks, and finite-sample coverage guarantees hold simultaneously for all size-weight configurations on or below the estimated frontier. Experiments augmenting opinion survey data with large language model responses show the procedure achieves target coverage while substantially narrowing confidence intervals.

Overview

Field: Machine Learning Authors: Chengpiao Huang, Kaizheng Wang Posted: 2026-08-28 arXiv: 2608.28576

Abstract (translated)

When real data are scarce, synthetic data can improve statistical inference, but naively treating synthetic samples as real data introduces bias and leads to unreliable inference. The authors develop a general framework for synthetic-augmented inference applicable to a population of related tasks. The framework characterizes synthetic augmentation by the number of synthetic observations and their weight.

The core of the framework is a size-weight frontier: for each weight, it specifies the largest synthetic sample size such that all smaller sizes attain the target task-marginal coverage. This frontier is estimated from historical tasks, and the paper establishes finite-sample coverage guarantees simultaneously for all size-weight configurations on or below the estimated frontier.

Experiments

In experiments using large language model responses to augment opinion survey data, the proposed procedure achieves the target coverage and significantly narrows confidence intervals.