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<p>Model checking evaluates whether a statistical model faithfully captures the underlying data-generating process. Classical tests — such as local-smoothing and empirical-process methods — break down in high dimensions. More recent approaches use predictiveness comparisons with flexible machine-learning model fitting procedures to yield algorithm-agnostic tests, yet they require large labeled samples. The authors introduce a prediction-powered, semi-supervised framework that: 1) Imputes responses for unlabeled data via a pretrained model; 2) Corrects imputation bias with a rectifier calibrated on labeled data; 3) Adaptively balances these components through a data-driven power-tuning parameter. Building on algorithm-agnostic out-of-sample predictiveness comparisons, the proposed method integrates unlabeled information to enhance power. Theoretical analyses and numerical results demonstrate that the proposed test controls Type I error and substantially improves power over fully supervised counterparts, even under imputation-model misspecification.</p>

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Prediction-Powered Model Checking via Predictiveness Comparisons

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Yanhong Liu,
  • Yinxu Jia,
  • Guanghui Wang,
  • Zhaojun Wang,
  • Changliang Zou

摘要

Model checking evaluates whether a statistical model faithfully captures the underlying data-generating process. Classical tests — such as local-smoothing and empirical-process methods — break down in high dimensions. More recent approaches use predictiveness comparisons with flexible machine-learning model fitting procedures to yield algorithm-agnostic tests, yet they require large labeled samples. The authors introduce a prediction-powered, semi-supervised framework that: 1) Imputes responses for unlabeled data via a pretrained model; 2) Corrects imputation bias with a rectifier calibrated on labeled data; 3) Adaptively balances these components through a data-driven power-tuning parameter. Building on algorithm-agnostic out-of-sample predictiveness comparisons, the proposed method integrates unlabeled information to enhance power. Theoretical analyses and numerical results demonstrate that the proposed test controls Type I error and substantially improves power over fully supervised counterparts, even under imputation-model misspecification.