This work introduces the Supervised Expectation-Maximization Framework
(SEMF), a versatile and model-agnostic framework that generates prediction
intervals for datasets with complete or missing data. SEMF extends the
Expectation-Maximization (EM) algorithm, traditionally used in unsupervised
learning, to a supervised context, enabling it to extract latent
representations for uncertainty estimation. The framework demonstrates
robustness through extensive empirical evaluation across 11 tabular datasets,
achieving$\unicode{x2013}$in some cases$\unicode{x2013}$narrower normalized
prediction intervals and higher coverage than traditional quantile regression
methods. Furthermore, SEMF integrates seamlessly with existing machine learning
algorithms, such as gradient-boosted trees and neural networks, exemplifying
its usefulness for real-world applications. The experimental results highlight
SEMF's potential to advance state-of-the-art techniques in uncertainty
quantification.

该研究介绍了监督期望最大化框架（SEMF），这是一个多功能且不涉及具体模型的框架，可以为具有完整或缺失数据的数据集生成预测区间。SEMF 将经典的无监督学习中使用的期望最大化（EM）算法扩展到监督环境中，实现了提取不确定性估计的潜在表示。该框架通过在 11 个表格数据集上进行广泛的实证评估，表明其具有稳健性，在某些情况下可以获得比传统分位回归方法更窄的规范化预测区间和更高的覆盖率。此外，SEMF 与现有的机器学习算法（如梯度提升树和神经网络等）无缝集成，展示了其在实际应用中的有用性。实验结果突出了 SEMF 在不确定性量化方面推动最新技术的潜力。