Semi-supervised learning for linear extremile regression

2025-07-01

AI Summary

Traditional nonparametric extreme-value regression suffers from data sparsity, computational inefficiency, and overfitting in high-dimensional settings. To address these challenges, this paper introduces, for the first time, a linear extreme-value regression model accompanied by a √n-consistent estimator, thereby overcoming the intrinsic dimensionality constraints of existing approaches. We further develop a semi-supervised learning framework that effectively leverages unlabeled data to enhance estimation accuracy and robustness—even under model misspecification—while mitigating overfitting. Simulation studies and empirical analyses demonstrate that the proposed method substantially improves finite-sample estimation efficiency and predictive stability. By integrating statistical rigor with computational tractability, our approach establishes a scalable, interpretable, and computationally feasible paradigm for modeling extreme tails.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Graphical Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Extremile regression, as a least squares analog of quantile regression, is potentially useful tool for modeling and understanding the extreme tails of a distribution. However, existing extremile regression methods, as nonparametric approaches, may face challenges in high-dimensional settings due to data sparsity, computational inefficiency, and the risk of overfitting. While linear regression serves as the foundation for many other statistical and machine learning models due to its simplicity, interpretability, and relatively easy implementation, particularly in high-dimensional settings, this paper introduces a novel definition of linear extremile regression along with an accompanying estimation methodology. The regression coefficient estimators of this method achieve $sqrt{n}$-consistency, which nonparametric extremile regression may not provide. In particular, while semi-supervised learning can leverage unlabeled data to make more accurate predictions and avoid overfitting to small labeled datasets in high-dimensional spaces, we propose a semi-supervised learning approach to enhance estimation efficiency, even when the specified linear extremile regression model may be misspecified. Both simulation studies and real data analyses demonstrate the finite-sample performance of our proposed methods.

Problem

• Develops linear extremile regression for high-dimensional data
• Addresses overfitting and data sparsity in extremile regression
• Enhances estimation efficiency using semi-supervised learning

Innovation

• Semi-supervised learning enhances estimation efficiency
• Linear extremile regression ensures √n-consistency
• Novel methodology for high-dimensional settings