Learning a Size-Weight Frontier for Synthetic-Augmented Inference
A research paper proposes a framework for synthetic-augmented inference that uses a size-weight frontier to determine the largest synthetic sample size for a given weight while maintaining target task-marginal coverage. The method is validated using large language model responses to augment opinion survey data, achieving target coverage and narrower confidence intervals.
The paper introduces a general framework for synthetic-augmented inference across related tasks. It characterizes synthetic augmentation by the number of synthetic observations and their weight, and defines a size-weight frontier that specifies the largest synthetic sample size for each weight that still achieves target coverage. The frontier is estimated from historical tasks, and a finite-sample coverage guarantee is provided for all configurations on or below the estimated frontier. Experiments with LLM-augmented opinion survey data show the procedure achieves target coverage and substantially narrows confidence intervals.
The core technical contribution is the size-weight frontier, which provides a principled way to balance synthetic sample size and weight to control coverage. The finite-sample guarantee is simultaneous across all size-weight configurations on or below the estimated frontier, suggesting a robust calibration approach. The method relies on historical task data to estimate the frontier, implying transferability of coverage properties across related tasks.
This framework addresses a key challenge in using synthetic data for statistical inference: avoiding bias from treating synthetic samples as real. It could enable more reliable use of LLM-generated data in survey research and other domains with scarce real data, potentially reducing data collection costs while maintaining statistical validity.
Organizations can use this approach to augment limited real data with synthetic data while preserving statistical guarantees, potentially lowering data acquisition costs and improving decision-making confidence. It is particularly relevant for market research, public opinion polling, and any domain where real data is expensive or scarce.
Next signals include applications to other types of synthetic data beyond LLM responses, extensions to non-survey inference tasks, and empirical validation on larger and more diverse task populations. The method may also influence best practices for synthetic data usage in regulated or high-stakes inference settings.