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We study the sequential calibration of estimations in a quantized isotonic L2regression setting. We start by showing that the optimal calibrated quantizedestimations can be acquired from the traditional isotonic L2 regressionsolution. We modify the traditional PAVA algorithm to create calibrators forboth batch and sequential optimization of the quantized isotonic regressionproblem. Our algorithm can update the optimal quantized monotone mapping forthe samples observed so far in linear space and logarithmic time per newunordered sample.

A Log-Linear Time Sequential Optimal Calibration Algorithm for Quantized Isotonic L2 Regression