Extending confidence calibration to generalised measures of variation

TL;DR

This paper introduces the Variation Calibration Error (VCE), a new metric for assessing the calibration of machine learning classifiers across various measures of probability variation, extending beyond confidence calibration.

Contribution

The paper proposes the VCE metric, extending calibration assessment to any variation measure, and demonstrates its desirable properties through synthetic examples.

Findings

VCE approaches zero for perfectly calibrated predictions as data increases

VCE outperforms existing entropy-based metrics like UCE in calibration assessment

Numerical examples validate the effectiveness of VCE in different scenarios

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.