超越点预测：分布信息驱动的预测增强推断
Beyond Point Predictions: Distribution-Informed Prediction-Powered Inference
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中文总结 AI 辅助
本文提出分布信息驱动的预测增强推断（DiPPI），利用预测分布替代点预测作为辅助信息，通过分数校准优化使用，理论保证并实证表明其比基于点预测的PPI方法更高效。
中文摘要 AI 辅助
预测增强推断（PPI）通常依赖于未标注数据上的点预测。当预测分布可用时（如在包括大语言模型预测在内的广泛应用中），我们引入了分布信息驱动的预测增强推断（DiPPI），这是一个通用框架，通过使用预测分布作为辅助信息（遵循PPI的精神）来进一步提高统计效率。我们通过分数校准刻画了该信息的最优使用方式，推导了预测分布有限维表示的预言机效率，并为交叉拟合的DiPPI估计器提供了正学习的理论保证。通过模拟和三个真实数据应用，我们表明DiPPI比基于点预测的PPI方法实现了更好的效率。这些增益出现在预测分布包含分数相关信息而点预测部分丢失这些信息的情况下。
英文摘要
Prediction-powered inference (PPI) typically relies on point predictions on unlabeled data. When predictive distributions are available as in a wide range of applications, including predictions from LLMs, we introduce distribution-informed prediction-powered inference (DiPPI), a general framework for further improving statistical efficiency by using predictive distributions as auxiliary information in the spirit of PPI. We characterize the optimal use of this information through score calibration, derive the oracle efficiency for a finite-dimensional representation of the predictive distribution, and provide theoretical guarantees for positive learning with the cross-fitted DiPPI estimator. Through simulations and three real-data applications, we show that DiPPI achieves better efficiency than PPI methods based on point predictions. These gains arise when the predictive distribution contains score-relevant information that is partially lost in point predictions.
发表机构
- Washington University in St. Louis（华盛顿大学圣路易斯分校）
- Emory University（埃默里大学）
机构由 AI 辅助整理，请以论文原文为准。
