The Minimax Rate of Perturbed Second-Order Calibration
The paper analyzes estimating second-order calibration error for binary classification when a small perturbation is applied to classifier outputs. It proposes an estimator using polynomial regression on perturbed scores, achieving a minimax rate of Oh(log3/2 n/√n), matching the lower bound up to logarithmic factors. This method also introduces a second-order Platt scaling procedure for recalibration.