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.
Can a calibration metric be both testable and actionable?
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abstract
Forecast probabilities often serve as critical inputs for binary decision making. In such settings, calibration$\unicode{x2014}$ensuring forecasted probabilities match empirical frequencies$\unicode{x2014}$is essential. Although the common notion of Expected Calibration Error (ECE) provides actionable insights for decision making, it is not testable: it cannot be empirically estimated in many practical cases. Conversely, the recently proposed Distance from Calibration (dCE) is testable, but it is not actionable since it lacks decision-theoretic guarantees needed for high-stakes applications. To resolve this question, we consider Cutoff Calibration Error, a calibration measure that bridges this gap by assessing calibration over intervals of forecasted probabilities. We show that Cutoff Calibration Error is both testable and actionable, and we examine its implications for popular post-hoc calibration methods, such as isotonic regression and Platt scaling.
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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.