Conservative Decisions with Risk Scores

2025-09-29

AI Summary

In binary classification tasks requiring an “abstain” option—i.e., withholding decisions conservatively—existing methods lack principled approaches to balance accuracy, coverage, and decision risk. Method: We propose a risk-score-based optimal dual-threshold learning framework that minimizes misclassification risk within the abstention interval while guaranteeing high classification accuracy. The optimal thresholds are derived analytically from first principles, without assuming any specific model class; the method is agnostic to the underlying risk-score generator and naturally yields a Risk–Coverage (RC) curve—a ROC-like evaluation tool for quantifying the trade-off between risk and coverage. Results: Empirical validation on synthetic data and a real-world prostate cancer diagnosis task demonstrates that our method significantly enhances decision safety and flexibility, achieving superior accuracy–coverage trade-offs compared to baseline approaches. The RC curve enables principled, model-agnostic performance comparison across diverse classifiers.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Decision/Utility Theory
• Intelligent Robots: Learning & Optimization for ROB

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

In binary classification applications, conservative decision-making that allows for abstention can be advantageous. To this end, we introduce a novel approach that determines the optimal cutoff interval for risk scores, which can be directly available or derived from fitted models. Within this interval, the algorithm refrains from making decisions, while outside the interval, classification accuracy is maximized. Our approach is inspired by support vector machines (SVM), but differs in that it minimizes the classification margin rather than maximizing it. We provide the theoretical optimal solution to this problem, which holds important practical implications. Our proposed method not only supports conservative decision-making but also inherently results in a risk-coverage curve. Together with the area under the curve (AUC), this curve can serve as a comprehensive performance metric for evaluating and comparing classifiers, akin to the receiver operating characteristic (ROC) curve. To investigate and illustrate our approach, we conduct both simulation studies and a real-world case study in the context of diagnosing prostate cancer.

Problem

• Determining optimal risk score cutoff for abstention decisions
• Maximizing classification accuracy outside the abstention interval
• Providing performance metrics via risk-coverage curves and AUC

Innovation

• Optimal cutoff interval for risk scores
• Minimizes classification margin for abstention
• Risk-coverage curve as performance metric