Valid Inference with Synthetic Data via Task Exchangeability

2026-06-12 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Research Methodology & Innovation, Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

This work introduces statistical principles for valid inference using synthetic data, addressing concerns about bias and misspecification. Researchers Lezhi Tan and Tijana Zrnic propose "task exchangeability," a condition requiring identification of historical tasks with real data that are mathematically exchangeable with the current task of interest. Their methods enable formal coverage guarantees for confidence intervals, even with highly misspecified synthetic data. The framework was demonstrated on public opinion surveys using LLM-generated "silicon samples" (e.g., ANES feeling-thermometer scores, Pew presidential approval) and AI model evaluation with autoraters (e.g., Arena win rates). Experiments showed task-exchangeability intervals covered true estimands at desired rates (e.g., 97% for ANES at 0.15 alpha, 100% for Pew at 0.2 alpha, 100% for AI evaluation at 0.1 alpha), significantly outperforming naive synthetic-only intervals which often failed to cover the truth (e.g., 3% for ANES, 0% for Pew, 19% for AI evaluation).

Key takeaway

For Data Scientists or Research Scientists evaluating models or conducting social science research with synthetic data, you should adopt the task exchangeability framework to ensure statistical validity. Instead of treating synthetic data as real, calibrate its inherent biases by identifying historical tasks where real-world data is available. This approach, demonstrated to achieve robust coverage (e.g., 97-100% in experiments) where naive methods fail, allows you to generate reliable confidence intervals and make provably valid inferences, even with imperfect synthetic datasets.

Key insights

Task exchangeability enables valid statistical inference from synthetic data by calibrating real-synthetic discrepancies using historical tasks.

Principles

• Synthetic data inference requires assumptions relating real and synthetic distributions.
• Task exchangeability allows historical error calibration for new tasks.
• Coverage guarantees degrade gracefully with approximate exchangeability.

Method

Construct a naive synthetic-data confidence interval, then expand it by a gap inferred from historical tasks where both real and synthetic data were available, using task exchangeability to ensure coverage.

In practice

• Calibrate LLM-generated "silicon samples" for public opinion surveys.
• Validate AI model win rates using autoraters and historical model data.
• Use weighted calibration for tasks with varying relevance.

Topics

• Synthetic Data
• Statistical Inference
• Task Exchangeability
• Confidence Intervals
• LLM Evaluation
• Public Opinion Research

Best for: AI Scientist, Research Scientist, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.