# Learning a Size-Weight Frontier for Synthetic-Augmented Inference

arXiv: https://arxiv.org/abs/2608.28576 · HTML: https://mlsanity.com/paper/2608.28576/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 18 of 18)

- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [WorldValuesBench: A Large-Scale Benchmark Dataset for Multi-Cultural Value Awareness of Language Models](https://mlsanity.com/paper/2404.16308/) (2024)
- [Large Language Models for Market Research: A Data-augmentation Approach](https://mlsanity.com/paper/2412.19363/) (2024)
- [Synthetic Oversampling: Theory and A Practical Approach Using LLMs to Address Data Imbalance](https://mlsanity.com/paper/2406.03628/) (2024)
- [Multi-Armed Bandits With Machine Learning-Generated Surrogate Rewards](https://mlsanity.com/paper/2506.16658/) (2025)
- [How Many Human Survey Respondents is a Large Language Model Worth? An Uncertainty Quantification Perspective](https://mlsanity.com/paper/2502.17773/) (2025)
- [Synthetic-Powered Predictive Inference](https://mlsanity.com/paper/2505.13432/) (2025)
- [AI-Powered Bayesian Inference](https://mlsanity.com/paper/2502.19231/) (2025)
- [Boosting Data Analytics With Synthetic Volume Expansion](https://mlsanity.com/paper/2310.17848/) (2023)
- [Valid Inference with Imperfect Synthetic Data](https://mlsanity.com/paper/2508.06635/) (2025)
- [GLM Inference with AI-Generated Synthetic Data Using Misspecified Linear Regression](https://mlsanity.com/paper/2503.21968/) (2025)
- [General Synthetic-Powered Inference](https://mlsanity.com/paper/2509.20345/) (2025)
- [Synthetic Augmentation in Imbalanced Learning: When It Helps, When It Hurts, and How Much to Add](https://mlsanity.com/paper/2601.16120/) (2026)
- [Harnessing Synthetic Data from Generative AI for Statistical Inference](https://mlsanity.com/paper/2603.05396/) (2026)
- [Model-Free Assessment of Simulator Fidelity via Quantile Curves](https://mlsanity.com/paper/2512.05024/) (2025)
- [Generative Augmented Inference of LLM-generated Data for Market Research: Theory and Empirical Evidence](https://mlsanity.com/paper/2604.14575/) (2026)
- [Allocating Human Oversight in AI-Enabled Analytics](https://mlsanity.com/paper/2604.12497/) (2026)
- [Valid Inference with Synthetic Data via Task Exchangeability](https://mlsanity.com/paper/2606.13629/) (2026)

## Abstract (arXiv)

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.