Classifier Calibration with ROC-Regularized Isotonic Regression

TL;DR

This paper introduces a new ROC-regularized isotonic regression method for calibrating both binary and multi-class classifiers, ensuring zero calibration error while preserving classifier performance metrics.

Contribution

It proves ROC curve convex hull preservation by IR and extends IR to multi-class calibration with a novel multidimensional binning and monotony regularization.

Findings

IR preserves the ROC convex hull, maintaining classifier performance.

The multi-class extension achieves zero calibration error with ROC surface preservation.

Regularization balances calibration accuracy and overfitting prevention.

Abstract

Calibration of machine learning classifiers is necessary to obtain reliable and interpretable predictions, bridging the gap between model confidence and actual probabilities. One prominent technique, isotonic regression (IR), aims at calibrating binary classifiers by minimizing the cross entropy on a calibration set via monotone transformations. IR acts as an adaptive binning procedure, which allows achieving a calibration error of zero, but leaves open the issue of the effect on performance. In this paper, we first prove that IR preserves the convex hull of the ROC curve -- an essential performance metric for binary classifiers. This ensures that a classifier is calibrated while controlling for overfitting of the calibration set. We then present a novel generalization of isotonic regression to accommodate classifiers with K classes. Our method constructs a multidimensional adaptive binning scheme on the probability simplex, again achieving a multi-class calibration error equal to zero. We regularize this algorithm by imposing a form of monotony that preserves the K-dimensional ROC surface of the classifier. We show empirically that this general monotony criterion is effective in striking a balance between reducing cross entropy loss and avoiding overfitting of the calibration set.