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

We study the sequential calibration of estimations in a quantized isotonic L2 regression setting. We start by showing that the optimal calibrated quantized estimations can be acquired from the traditional isotonic L2 regression solution. We modify the traditional PAVA algorithm to create calibrators for both batch and sequential optimization of the quantized isotonic regression problem. Our algorithm can update the optimal quantized monotone mapping for the samples observed so far in linear space and logarithmic time per new unordered sample.