  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.
