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.

翻译：降维是监督学习中分析高维数据的基本工具。传统估计本征维数的方法往往优先考虑模型特定的结构假设，而非预测效用。本文提出预测性维数确定（POD），这是一种模型无关的框架，通过直接评估样本外预测能力来确定最小预测充分维数。POD通过高估和低估的误差界来量化不确定性，并在温和条件下实现一致性。通过将降维与预测性能相统一，POD可灵活应用于各种降维任务和监督学习器。仿真和真实数据分析表明，POD能提供准确且具有不确定性感知的维数估计，使其成为以预测为中心的流程中一个通用组件。