提出新方法MEC，提升半监督均值估计的精度与鲁棒性。
MEC: Machine-Learning-Assisted Generalized Entropy Calibration for Semi-Supervised Mean Estimation
- 用贝格曼投影校准权重，优化标签样本分布匹配
- 在模拟和真实数据中实现近名义覆盖率与更窄置信区间
- 对预测器变换更鲁棒，弱化了对模型正确性的要求
获取高质量标签成本高，而未标注协变量往往丰富，推动了需要可靠不确定性量化的半监督推断方法发展。预测驱动推断（PPI）利用小规模标签样本训练的机器学习预测器提升效率，但在模型误设下可能损失效率，并因标签重用导致覆盖偏差。本文提出机器学习辅助广义熵校准（MEC），一种交叉拟合、校准加权的PPI变体。MEC通过基于贝格曼投影的原理性校准框架，重新加权标签样本以更好匹配目标总体，提升效率。该方法对预测器的仿射变换具有鲁棒性，将原始预测误差条件替换为更弱的投影误差条件，从而放宽有效性要求。结果表明，MEC在弱于现有PPI变体的假设下达到半参数效率界。在模拟和真实数据应用中，MEC实现了近名义覆盖率，并获得比交叉拟合PPI（CF-PPI）和原始PPI更窄的置信区间。
原文摘要 · Abstract (English)
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.
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