Provably Minimum-Length Conformal Prediction Sets for Ordinal Classification

2025-11-20

AI Summary

Existing conformal prediction methods for ordinal classification often rely on heuristic designs or strong distributional assumptions (e.g., unimodality), compromising model- and distribution-freedom, and lack systematic analysis of the coverage-efficiency trade-off. This work proposes the first model-agnostic and distribution-agnostic framework for well-calibrated ordinal prediction, formulating ordinal classification as an instance-wise minimum-length coverage problem. We design a linear-time sliding-window algorithm to construct locally optimal prediction sets and introduce length regularization to enhance set compactness. Evaluated on four cross-domain benchmark datasets, our method reduces average prediction set size by 15% compared to state-of-the-art approaches, demonstrating superior efficiency, robustness, and generalization capability while maintaining rigorous marginal calibration.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• 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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Ordinal classification has been widely applied in many high-stakes applications, e.g., medical imaging and diagnosis, where reliable uncertainty quantification (UQ) is essential for decision making. Conformal prediction (CP) is a general UQ framework that provides statistically valid guarantees, which is especially useful in practice. However, prior ordinal CP methods mainly focus on heuristic algorithms or restrictively require the underlying model to predict a unimodal distribution over ordinal labels. Consequently, they provide limited insight into coverage-efficiency trade-offs, or a model-agnostic and distribution-free nature favored by CP methods. To this end, we fill this gap by propose an ordinal-CP method that is model-agnostic and provides instance-level optimal prediction intervals. Specifically, we formulate conformal ordinal classification as a minimum-length covering problem at the instance level. To solve this problem, we develop a sliding-window algorithm that is optimal on each calibration data, with only a linear time complexity in K, the number of label candidates. The local optimality per instance further also improves predictive efficiency in expectation. Moreover, we propose a length-regularized variant that shrinks prediction set size while preserving coverage. Experiments on four benchmark datasets from diverse domains are conducted to demonstrate the significantly improved predictive efficiency of the proposed methods over baselines (by 15% decrease on average over four datasets).

Problem

• Develops conformal prediction for ordinal classification with optimal interval coverage
• Creates model-agnostic method providing instance-level minimum-length prediction sets
• Improves predictive efficiency while maintaining statistical coverage guarantees

Innovation

• Model-agnostic conformal prediction for ordinal classification
• Sliding-window algorithm with linear time complexity
• Length-regularized variant preserving coverage guarantees