Model-Agnostic and Uncertainty-Aware Dimensionality Reduction in Supervised Learning

2026-01-15

AI Summary

This work proposes the Prediction-based Order Determination (POD) framework to address the limitations of traditional dimension reduction methods, which often rely on model-specific assumptions and neglect predictive utility, thereby failing to accurately estimate the minimal predictive sufficient dimension. POD is the first approach to directly link the selection of dimensionality reduction order with out-of-sample predictive performance, enabling a model-agnostic and consistent estimation of the minimal predictive sufficient dimension while quantifying its uncertainty. By integrating error bound analysis with consistency theory, POD is broadly applicable across diverse supervised learners and dimension reduction tasks. Empirical evaluations on both simulated and real-world datasets demonstrate that POD yields accurate and robust estimates of the reduction order, highlighting its wide applicability and reliability.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• dimensionality reduction
• supervised learning
• predictive order
• model-agnostic
• uncertainty quantification

Innovation

• model-agnostic
• uncertainty-aware
• dimensionality reduction
• predictive order determination
• out-of-sample predictiveness