PICPIs: Prediction-Interval-Conditional Prediction Intervals

2026-09-21

AI Summary

本文提出了一种基于预测区间的条件预测区间（PICPIs）方法，以解决非参数不确定性量化中的条件有效性问题，并提供了实用算法和理论保证。

Abstract

A classical question in statistics is which observable quantities to condition on when drawing inferences about unobservable targets. For conformal prediction in nonparametric uncertainty quantification, standard marginal validity offers limited resolution at the prediction values on which decisions are based, and fully conditional guarantees with respect to the covariates are provably unattainable. We address this gap by introducing a prediction-based conditioning framework that we refer to as Prediction-Interval-Conditional Prediction Intervals (PICPIs). Formally, a PICPI is an interval $I$ satisfying a self-consistency condition: $$\mathbb{E} [Y \mid p(X) \in I] \in I,$$ for predictive model $p$, contextual covariate $X$, and outcome $Y$. Thus, an interval simultaneously defines a stratum of prediction values and certifies that the mean outcome in that stratum lies in the same interval. This self-consistency condition yields data-adaptive strata without altering the original prediction. Such intervals can be constructed using practical algorithms. Under regularity of the prediction distribution, the constructed intervals cover all but an arbitrarily small fraction of prediction values and have widths that decrease at rate $n^{-1/3}$, up to logarithmic factors and the prediction error. Moreover, identifying these locally calibrated intervals can, in turn, inform downstream decision-making. We derive inference procedures for PICPIs in probabilistic prediction and multi-class classification, accompanied by theoretical guarantees. Empirical results are provided that compare PICPIs with existing interval-based baselines.

Problem

• conformal prediction
• nonparametric uncertainty quantification
• conditional guarantees
• prediction intervals
• self-consistency condition

Innovation

• Prediction-Interval-Conditional Prediction Intervals
• self-consistency condition
• data-adaptive strata
• nonparametric uncertainty quantification
• probabilistic prediction