Ask for More Than Bayes Optimal: A Theory of Indecisions for Selective Hypothesis Testing

2024-12-17 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

The paper "Ask for More Than Bayes Optimal: A Theory of Indecisions for Selective Hypothesis Testing," arXiv:2412.12807, last revised 23 Jul 2026, by Mohamed Ndaoud, Peter Radchenko, and Bradley Rava, introduces a novel framework for selective classification and hypothesis testing. This approach enables automated decision systems to abstain from making a decision when uncertainty is high, thereby minimizing "indecisions" – observations not automated – while targeting a specific accuracy. The core idea allows achieving a misclassification rate below the Bayes error rate, particularly in difficult problems. The authors provide a characterization of optimal risk in selective classification, outlining continuity and monotonicity properties crucial for optimal indecision selection. They also extend this concept to the Neyman-Pearson testing framework, where indecision helps control Type II error for a given Type I error probability. A calibration method is proposed, with analysis of excess risk and indecision mass. Experiments on Gaussian mixtures and real datasets confirm that indecision improves selective accuracy.

Key takeaway

For AI Scientists designing automated decision systems in high-risk scenarios, you should integrate indecision mechanisms to enhance system reliability. This approach allows your models to abstain from uncertain classifications, enabling you to achieve misclassification rates below the Bayes error rate. Consider implementing the proposed calibration method to minimize indecision mass while maintaining high target accuracy, particularly when precise error control, like managing Type I and Type II errors in hypothesis testing, is critical for your applications.

Key insights

Selective classification with indecisions allows systems to abstain from uncertain decisions, achieving sub-Bayes error rates.

Principles

• Minimize indecisions for target accuracy.
• Indecision enables sub-Bayes error rates.
• Control Type II error via indecision.

Method

A calibration method is proposed for selective classification and testing, analyzing excess risk and indecision mass produced by accuracy-based calibration.

In practice

• Apply indecision in high-risk scenarios.
• Use indecision to improve selective accuracy.
• Control Type I/II errors in hypothesis testing.

Topics

• Selective Classification
• Hypothesis Testing
• Bayes Error Rate
• Indecision Theory
• Neyman-Pearson Framework
• Error Control

Best for: AI Scientist, Research Scientist, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.