TCE: A Test-Based Approach to Measuring Calibration Error

Takuo Matsubara, Niek Tax, Richard Mudd, Ido Guy

Keywords: calibration error, statistical test, reliability diagram, optimal binning, imbalanced classification

TL;DR: We propose a new calibration error metric called TCE that offers (i) a clear interpretation, (ii) a consistent scale robust to class imbalance, and (iii) an informative visual representation.

Abstract: This paper proposes a new metric to measure the calibration error of probabilistic binary classifiers, called test-based calibration error (TCE). TCE incorporates a novel loss function based on a statistical test to examine the extent to which model predictions differ from probabilities estimated from data. It offers (i) a clear interpretation, (ii) a consistent scale that is unaffected by class imbalance, and (iii) an enhanced visual representation with respect to the standard reliability diagram. In addition, we introduce an optimality criterion for the binning procedure of calibration error metrics based on a minimal estimation error of the empirical probabilities. We provide a novel computational algorithm for optimal bins under bin-size constraints. We demonstrate properties of TCE through a range of experiments, including multiple real-world imbalanced datasets and ImageNet 1000.