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

arXiv: https://arxiv.org/abs/2206.00744 · HTML: https://mlsanity.com/paper/2206.00744/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 49 references that are in the map.
- First posted on arXiv 1 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Binary Classifier Calibration using an Ensemble of Near Isotonic Regression Models](https://mlsanity.com/paper/1511.05191/) (2015)
- [Sequential Outlier Detection based on Incremental Decision Trees](https://mlsanity.com/paper/1803.03674/) (2018)
- [Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Error](https://mlsanity.com/paper/2108.08780/) (2021)
- [Efficient, Anytime Algorithms for Calibration with Isotonic Regression under Strictly Convex Losses](https://mlsanity.com/paper/2111.00468/) (2021)

## Built on by (most cited first, 1 of 1)

- [Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses](https://mlsanity.com/paper/2304.02141/) (2023)

## Abstract (arXiv)

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.