MEC: Machine-Learning-Assisted Generalized Entropy Calibration for Semi-Supervised Mean Estimation

TL;DR

MEC is a novel semi-supervised inference method that enhances uncertainty quantification and efficiency by calibrating machine learning predictors with a Bregman projection-based reweighting scheme.

Contribution

It introduces MEC, a calibration-weighted, cross-fitted variant of PPI that improves robustness and efficiency under weaker assumptions.

Findings

MEC attains the semiparametric efficiency bound under weaker conditions.

MEC achieves near-nominal coverage in simulations and real data.

MEC produces tighter confidence intervals than existing methods.

Abstract

Obtaining high-quality labels is costly, whereas unlabeled covariates are often abundant, motivating semi-supervised inference methods with reliable uncertainty quantification. Prediction-powered inference (PPI) leverages a machine-learning predictor trained on a small labeled sample to improve efficiency, but it can lose efficiency under model misspecification and suffer from coverage distortions due to label reuse. We introduce Machine-Learning-Assisted Generalized Entropy Calibration (MEC), a cross-fitted, calibration-weighted variant of PPI. MEC improves efficiency by reweighting labeled samples to better align with the target population, using a principled calibration framework based on Bregman projections. This yields robustness to affine transformations of the predictor and relaxes requirements for validity by replacing conditions on raw prediction error with weaker projection-error conditions. As a result, MEC attains the semiparametric efficiency bound under weaker assumptions than existing PPI variants. Across simulations and a real-data application, MEC achieves near-nominal coverage and tighter confidence intervals than CF-PPI and vanilla PPI.