Stratification of uncertainties recalibrated by isotonic regression and its impact on calibration error statistics
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Abstract Post hoc recalibration of prediction uncertainties of machine learning regression problems by isotonic regression might present a problem for bin-based calibration error statistics (e.g. ENCE). Isotonic regression often produces stratified uncertainties, i.e. subsets of uncertainties with identical numerical values. Partitioning of the resulting data into equal-sized bins introduces an aleatoric component to the estimation of bin-based calibration statistics. The partitioning of stratified data into bins depends on the order of the data, which is typically an uncontrolled property of calibration test/validation sets. The tie-braking method of the ordering algorithm used for binning might also introduce an aleatoric component. I show on an example how this might significantly affect the calibration diagnostics.
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