Prediction-Powered Conditional Inference

TL;DR

This paper introduces a novel prediction-powered inference method that leverages machine learning predictions and unlabeled data to improve the accuracy and efficiency of conditional functional estimation without assuming parametric models.

Contribution

It develops a kernel-based localization technique combined with prediction correction to produce valid, efficient confidence intervals for conditional functionals in scarce-label settings.

Findings

Achieves minimax-optimal convergence rates.

Provides valid confidence intervals with improved precision.

Demonstrates effectiveness on real and simulated data.

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.