Prediction-Powered Conditional Inference

2026-03-05

AI Summary

This work proposes a nonparametric inference method for conditional functionals—such as the conditional mean—in settings where labeled data are scarce, unlabeled covariates are abundant, and a black-box predictor is available. The approach avoids parametric modeling assumptions by leveraging a data-adaptive kernel localization and a prediction-correction decomposition, which transforms conditional moment estimation into a weighted unconditional moment problem while incorporating the black-box predictor to reduce variance. Theoretical analysis establishes non-asymptotic error bounds, minimax optimal convergence rates, and asymptotic normality, along with an explicit variance decomposition that quantifies the contributions of both the predictor and the unlabeled data. Experiments demonstrate that the resulting confidence intervals achieve accurate coverage and are significantly narrower, marking the first method in a fully nonparametric framework to simultaneously attain validity and efficiency gains.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We study prediction-powered conditional inference in the setting where labeled data are scarce, unlabeled covariates are abundant, and a black-box machine-learning predictor is available. The goal is to perform statistical inference on conditional functionals evaluated at a fixed test point, such as conditional means, without imposing a parametric model for the conditional relationship. Our approach combines localization with prediction-based variance reduction. First, we introduce a reproducing kernel-based localization method that learns a data-adaptive weight function from covariates and reformulates the target conditional moment at the test point as a weighted unconditional moment. Second, we incorporate machine-learning predictions through a correction-based decomposition of this localized moment, yielding a prediction-powered estimator and confidence interval that reduce variance when the predictor is informative while preserving validity regardless of predictor accuracy. We establish nonasymptotic error bounds and minimax-optimal convergence rates for the resulting estimator, prove pointwise asymptotic normality with consistent variance estimation, and provide an explicit variance decomposition that characterizes how machine-learning predictions and unlabeled covariates improve statistical efficiency. Numerical experiments on simulated and real datasets demonstrate valid conditional coverage and substantially sharper confidence intervals than alternative methods.

Problem

• prediction-powered inference
• conditional inference
• label scarcity
• black-box predictor
• nonparametric statistics

Innovation

• prediction-powered inference
• conditional inference
• localization
• variance reduction
• nonparametric statistics