A survey arguing that calibration error is best understood as the degree to which two worlds, the predictor's and nature's, can be distinguished, and that this view unifies ECE, smooth calibration, CDL, and distance to calibration.
An elementary predictor obtaining 2 √ T + 1 distance to calibration
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Calibration through the Lens of Indistinguishability
A survey arguing that calibration error is best understood as the degree to which two worlds, the predictor's and nature's, can be distinguished, and that this view unifies ECE, smooth calibration, CDL, and distance to calibration.