Bayes-Optimal BER and AUC: Estimation and Evaluation of Estimators

• URL: http://arxiv.org/abs/2609.02304v1
• Date: Wed, 02 Sep 2026 08:49:23 GMT
• Title: Bayes-Optimal BER and AUC: Estimation and Evaluation of Estimators
• Abstract summary: A fundamental quantity in machine learning is the optimal performance achievable by any model on a given task.<n>Recent work has shown that the Bayes error, or equivalently the optimal accuracy, can be estimated from soft labels in binary classification.<n>We propose soft-label-based estimators for the optimal BER and AUC.
• Score: 47.001801756596926
• License: http://creativecommons.org/licenses/by/4.0/
• 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, telling us how much room for improvement remains. Recent work has shown that the Bayes error, or equivalently the optimal accuracy, can be estimated from soft labels in binary classification. However, accuracy is often a poor summary of performance in settings with severe class imbalance or noisy annotations, where metrics such as the balanced error rate (BER) and the area under the ROC curve (AUC) are more appropriate. We address this gap with two complementary contributions. (i) Estimation. We propose soft-label-based estimators for the optimal BER and AUC. We first consider the clean setting in which true soft labels and the class prior are known, and then extend the estimators to a more realistic setting in which the class prior is unknown and the observed soft labels are corrupted by an unknown order-preserving transformation, possibly followed by additive noise. In the latter setting, we approximately recover the clean soft labels via isotonic regression with auxiliary hard labels, estimate the class prior with a clipped mean of the hard labels, and derive finite-sample error bounds for the resulting plug-in estimators. (ii) Evaluation. Since the optimum is unobservable on real datasets, evaluating any such estimator is itself nontrivial. We extend the FeeBee framework, originally proposed for evaluating Bayes-error estimators, to the optimal BER and AUC. The resulting procedure provides practical evaluation scores without requiring knowledge of the optimum, and applies to any estimator of the optimal BER or AUC, not only our proposed ones. Experiments on synthetic and real-world datasets validate both the estimators and the evaluation procedure.

Related papers

• Practical estimation of the optimal classification error with soft labels and calibration [47.001801756596926]
  We extend a previous work that utilizes soft labels for estimating the Bayes error, the optimal error rate.<n>We tackle a more challenging problem setting: estimation with corrupted soft labels.<n>Our method is instance-free, i.e., we do not assume access to any input instances.
  arXiv  Detail & Related papers  (2025-05-27T06:04:57Z)
• C-Learner: Constrained Learning for Causal Inference [4.370964009390564]
  We propose a novel debiasing approach that achieves the best weighting of both worlds, producing stable plug-in estimates.<n>Our constrained learning framework solves for the best plug-in estimator under the constraint that the first-order error with respect to the plugged-in quantity is zero.
  arXiv  Detail & Related papers  (2024-05-15T16:38:28Z)
• Data-Driven Estimation of the False Positive Rate of the Bayes Binary Classifier via Soft Labels [25.40796153743837]
  We propose an estimator for the false positive rate (FPR) of the Bayes classifier, that is, the optimal classifier with respect to accuracy, from a given dataset. We develop effective FPR estimators by leveraging a denoising technique and the Nadaraya-Watson estimator.
  arXiv  Detail & Related papers  (2024-01-27T20:41:55Z)
• Model Calibration in Dense Classification with Adaptive Label Perturbation [44.62722402349157]
  Existing dense binary classification models are prone to being over-confident. We propose Adaptive Label Perturbation (ASLP) which learns a unique label perturbation level for each training image. ASLP can significantly improve calibration degrees of dense binary classification models on both in-distribution and out-of-distribution data.
  arXiv  Detail & Related papers  (2023-07-25T14:40:11Z)
• Optimizing Partial Area Under the Top-k Curve: Theory and Practice [151.5072746015253]
  We develop a novel metric named partial Area Under the top-k Curve (AUTKC) AUTKC has a better discrimination ability, and its Bayes optimal score function could give a correct top-K ranking with respect to the conditional probability. We present an empirical surrogate risk minimization framework to optimize the proposed metric.
  arXiv  Detail & Related papers  (2022-09-03T11:09:13Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• Robust Importance Sampling for Error Estimation in the Context of Optimal Bayesian Transfer Learning [13.760785726194591]
  We introduce a novel class of Bayesian minimum mean-square error (MMSE) estimators for optimal Bayesian transfer learning (OBTL) We employ the proposed estimator to evaluate the classification accuracy of a broad family of classifiers that span diverse learning capabilities. Experimental results based on both synthetic data as well as real-world RNA sequencing (RNA-seq) data show that our proposed OBTL error estimation scheme clearly outperforms standard error estimators.
  arXiv  Detail & Related papers  (2021-09-05T19:11:33Z)
• Evaluating State-of-the-Art Classification Models Against Bayes Optimality [106.50867011164584]
  We show that we can compute the exact Bayes error of generative models learned using normalizing flows. We use our approach to conduct a thorough investigation of state-of-the-art classification models.
  arXiv  Detail & Related papers  (2021-06-07T06:21:20Z)
• Exploiting Sample Uncertainty for Domain Adaptive Person Re-Identification [137.9939571408506]
  We estimate and exploit the credibility of the assigned pseudo-label of each sample to alleviate the influence of noisy labels. Our uncertainty-guided optimization brings significant improvement and achieves the state-of-the-art performance on benchmark datasets.
  arXiv  Detail & Related papers  (2020-12-16T04:09:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.