Learning from Interval Targets

2025-10-23

AI Summary

This paper addresses interval-target regression—regression modeling where ground-truth labels are only available as intervals (e.g., due to measurement error or intrinsic uncertainty). To tackle this setting, we propose the min-max learning paradigm: for each labeled interval, we non-convexly maximize the loss over the worst-case label within the interval, then globally minimize the resulting worst-case loss to enhance model robustness. Theoretically, we establish the first non-asymptotic generalization bound for interval regression, grounded in the smoothness of the hypothesis class. Practically, we design a loss function compatible with interval labels and integrate smoothness regularization with efficient non-convex optimization techniques. Extensive experiments on multiple real-world datasets demonstrate that our method significantly outperforms existing interval regression baselines, achieving state-of-the-art performance.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Non-convex Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• 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

We study the problem of regression with interval targets, where only upper and lower bounds on target values are available in the form of intervals. This problem arises when the exact target label is expensive or impossible to obtain, due to inherent uncertainties. In the absence of exact targets, traditional regression loss functions cannot be used. First, we study the methodology of using a loss functions compatible with interval targets, for which we establish non-asymptotic generalization bounds based on smoothness of the hypothesis class that significantly relaxing prior assumptions of realizability and small ambiguity degree. Second, we propose a novel min-max learning formulation: minimize against the worst-case (maximized) target labels within the provided intervals. The maximization problem in the latter is non-convex, but we show that good performance can be achieved with the incorporation of smoothness constraints. Finally, we perform extensive experiments on real-world datasets and show that our methods achieve state-of-the-art performance.

Problem

• Developing regression methods using interval targets instead of exact values
• Establishing generalization bounds for interval-compatible loss functions
• Proposing min-max formulation to handle worst-case interval targets

Innovation

• Using loss functions compatible with interval targets
• Proposing min-max learning with worst-case target labels
• Incorporating smoothness constraints for non-convex optimization