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Estimating Optimal BER and AUC for Classification.

Ryota Ushio, Takashi Ishida, Masashi Sugiyama· September 3, 2026 View original

Key takeaways

  • New estimators are proposed for Bayes-optimal BER and AUC using soft labels.
  • The framework addresses challenges of unknown class priors and noisy soft labels.
  • It extends the FeeBee framework for practical evaluation of these estimators.
  • These tools help distinguish irreducible error from model deficiencies, especially with imbalanced data.

Who benefits

HealthcareFinanceFraud DetectionAnomaly DetectionQuality Control

Summary

This paper introduces novel soft-label-based estimators for the Bayes-optimal Balanced Error Rate (BER) and Area Under the ROC Curve (AUC) in binary classification. It also extends the FeeBee framework to evaluate these estimators without knowing the true optimum, addressing challenges in imbalanced or noisy datasets.

In machine learning, understanding the theoretical best performance a model can achieve (the Bayes error) is crucial for distinguishing between a model's limitations and the inherent difficulty of a task. While methods exist for estimating optimal accuracy, metrics like Balanced Error Rate (BER) and Area Under the ROC Curve (AUC) are often more appropriate for datasets with class imbalance or noisy labels. This research fills a critical gap by proposing new estimators for the Bayes-optimal BER and AUC, leveraging "soft labels" (probabilistic predictions). The framework accounts for realistic scenarios where true soft labels and class priors are unknown, using isotonic regression and auxiliary hard labels to recover clean soft labels. Furthermore, the paper extends the FeeBee framework, originally for Bayes error, to evaluate these BER and AUC estimators without requiring knowledge of the true optimal values, providing a practical way to assess their effectiveness on real-world data. Both the estimators and the evaluation procedure are validated through experiments on synthetic and real datasets.

Why it matters

Data scientists and ML engineers can use these new estimators and evaluation methods to more accurately assess the true potential of their classification models, especially in challenging scenarios with imbalanced data or noisy annotations, guiding model improvement efforts.

How to implement this in your domain

  1. 1Apply the proposed soft-label-based estimators to calculate optimal BER and AUC for classification tasks.
  2. 2Integrate the extended FeeBee framework into model evaluation pipelines for robust assessment.
  3. 3Utilize isotonic regression with auxiliary hard labels to refine soft labels from noisy sources.
  4. 4Use the estimated optimal metrics to set more realistic performance benchmarks for ML projects.

Original post by Ryota Ushio, Takashi Ishida, Masashi Sugiyama

"arXiv:2609.02304v1 Announce Type: new Abstract: A fundamental quantity in machine learning is the optimal performance achievable by any model on a given task. Estimating this quantity allows us to distinguish the irreducible part of the error from a deficiency of the model, telli…"

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Originally posted by Ryota Ushio, Takashi Ishida, Masashi Sugiyama on X · view source

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