# Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses

arXiv: https://arxiv.org/abs/2304.02141 · HTML: https://mlsanity.com/paper/2304.02141/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 9 of 9)

- [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)
- [Recursive Experts: An Efficient Optimal Mixture of Learning Systems in Dynamic Environments](https://mlsanity.com/paper/2009.09249/) (2020)
- [Nonparametric Extrema Analysis in Time Series for Envelope Extraction, Peak Detection and Clustering](https://mlsanity.com/paper/2109.02082/) (2021)
- [Low Regret Binary Sampling Method for Efficient Global Optimization of Univariate Functions](https://mlsanity.com/paper/2201.07164/) (2022)
- [Efficient, Anytime Algorithms for Calibration with Isotonic Regression under Strictly Convex Losses](https://mlsanity.com/paper/2111.00468/) (2021)
- [A Log-Linear Time Sequential Optimal Calibration Algorithm for Quantized Isotonic L2 Regression](https://mlsanity.com/paper/2206.00744/) (2022)

## Abstract (arXiv)

This paper focuses on optimal unimodal transformation of the score outputs of a univariate learning model under linear loss functions. We demonstrate that the optimal mapping between score values and the target region is a rectangular function. To produce this optimal rectangular fit for the observed samples, we propose a sequential approach that can its estimation with each incoming new sample. Our approach has logarithmic time complexity per iteration and is optimally efficient.