Extending confidence calibration to generalised measures of variation

2026-02-13

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Security and Privacy: Large-scale security measurements

Abstract

We propose the Variation Calibration Error (VCE) metric for assessing the calibration of machine learning classifiers. The metric can be viewed as an extension of the well-known Expected Calibration Error (ECE) which assesses the calibration of the maximum probability or confidence. Other ways of measuring the variation of a probability distribution exist which have the advantage of taking into account the full probability distribution, for example the Shannon entropy. We show how the ECE approach can be extended from assessing confidence calibration to assessing the calibration of any metric of variation. We present numerical examples upon synthetic predictions which are perfectly calibrated by design, demonstrating that, in this scenario, the VCE has the desired property of approaching zero as the number of data samples increases, in contrast to another entropy-based calibration metric (the UCE) which has been proposed in the literature.

Problem

• confidence calibration
• Expected Calibration Error
• Variation Calibration Error
• probability distribution
• entropy

Innovation

• Variation Calibration Error
• Expected Calibration Error
• confidence calibration
• probability distribution
• Shannon entropy