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

arXiv: https://arxiv.org/abs/2604.05446 · HTML: https://mlsanity.com/paper/2604.05446/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 73 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 20 of 20)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016)
- [Orthogonal Machine Learning: Power and Limitations](https://mlsanity.com/paper/1711.00342/) (2017)
- [Assumption-Lean and Data-Adaptive Post-Prediction Inference](https://mlsanity.com/paper/2311.14220/) (2023)
- [Semi-Supervised Risk Control via Prediction-Powered Inference](https://mlsanity.com/paper/2412.11174/) (2024)
- [Local Prediction-Powered Inference](https://mlsanity.com/paper/2409.18321/) (2024)
- [Debiased Bayesian inference for average treatment effects](https://mlsanity.com/paper/1909.12078/) (2019)
- [Revisiting inference after prediction](https://mlsanity.com/paper/2306.13746/) (2023)
- [No-harm calibration for generalized Oaxaca-Blinder estimators](https://mlsanity.com/paper/2012.09246/) (2020)
- [Federated Prediction-Powered Inference from Decentralized Data](https://mlsanity.com/paper/2409.01730/) (2024)
- [The Generalized Oaxaca-Blinder Estimator](https://mlsanity.com/paper/2004.11615/) (2020)
- [Debiased calibration estimation using generalized entropy in survey sampling](https://mlsanity.com/paper/2404.01076/) (2024)

## Built on by (most cited first, 1 of 1)

- [Calibeating Prediction-Powered Inference](https://mlsanity.com/paper/2604.21260/) (2026)

## Abstract (arXiv)

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.