Year: 2026
Type: preprint
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 target 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 an RKHS localization method that learns a data-adaptive weight from covariates and reformulates the target conditional moment at the target 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, in the abundant-unlabeled regime, 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.
Source: arXiv (Cornell University)
Authors: Sui, Yang, Zhou, Jin, Zhou, Hua, Dai, Xiaowu
Institution: University of California, Los Angeles
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7134267372
Cites:
Cited by:
Related to: