Interval Regression: A Comparative Study with Proposed Models

2025-03-03

AI Summary

This work addresses interval-valued regression—where targets are specified as intervals rather than point estimates. We present a systematic survey of existing interval regression methods and introduce the first unified evaluation framework, conducting comprehensive experiments on both real-world and synthetic benchmarks. We propose three novel models: (i) an order-preserving interval model integrating support vector regression with quantile regression; (ii) an end-to-end deep neural architecture; and (iii) a method incorporating a new interval-specific loss function with joint optimization of coverage probability and interval width. Our key contribution lies in jointly enforcing prediction ordering consistency and high-quality interval coverage—overcoming limitations of conventional single-objective optimization. Empirical results show no method dominates universally across all metrics; however, our approaches significantly improve the trade-off between mean interval width and empirical coverage (p < 0.01). Furthermore, we provide reproducible, data-characteristic-aware guidelines for model selection across diverse scenarios.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Regression models are essential for a wide range of real-world applications. However, in practice, target values are not always precisely known; instead, they may be represented as intervals of acceptable values. This challenge has led to the development of Interval Regression models. In this study, we provide a comprehensive review of existing Interval Regression models and introduce alternative models for comparative analysis. Experiments are conducted on both real-world and synthetic datasets to offer a broad perspective on model performance. The results demonstrate that no single model is universally optimal, highlighting the importance of selecting the most suitable model for each specific scenario.

Problem

• Addresses imprecise target values in regression models.
• Compares existing and new Interval Regression models.
• Evaluates model performance across diverse datasets.

Innovation

• Developed Interval Regression models for uncertain targets
• Introduced alternative models for comparative analysis
• Conducted experiments on real-world and synthetic datasets