Dimension reduction is a fundamental tool for analyzing high-dimensional data in supervised learning. Traditional methods for estimating intrinsic order often prioritize model-specific structural assumptions over predictive utility. This paper introduces predictive order determination (POD), a model-agnostic framework that determines the minimal predictively sufficient dimension by directly evaluating out-of-sample predictiveness. POD quantifies uncertainty via error bounds for over- and underestimation and achieves consistency under mild conditions. By unifying dimension reduction with predictive performance, POD applies flexibly across diverse reduction tasks and supervised learners. Simulations and real-data analyses show that POD delivers accurate, uncertainty-aware order estimates, making it a versatile component for prediction-centric pipelines.
@article{arxiv.2601.10357,
title = {Model-Agnostic and Uncertainty-Aware Dimensionality Reduction in Supervised Learning},
author = {Yue Yu and Guanghui Wang and Liu Liu and Changliang Zou},
journal= {arXiv preprint arXiv:2601.10357},
year = {2026}
}