# Binary Classifier Calibration using an Ensemble of Near Isotonic Regression Models

arXiv: https://arxiv.org/abs/1511.05191 · HTML: https://mlsanity.com/paper/1511.05191/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2015.

## Built on by (most cited first, 21 of 21)

- [Soft Calibration Objectives for Neural Networks](https://mlsanity.com/paper/2108.00106/) (2021)
- [Classifier Calibration: A survey on how to assess and improve predicted class probabilities](https://mlsanity.com/paper/2112.10327/) (2021)
- [Sample-dependent Adaptive Temperature Scaling for Improved Calibration](https://mlsanity.com/paper/2207.06211/) (2022)
- [A Consistent and Differentiable Lp Canonical Calibration Error Estimator](https://mlsanity.com/paper/2210.07810/) (2022)
- [Triggering Failures: Out-Of-Distribution detection by learning from local adversarial attacks in Semantic Segmentation](https://mlsanity.com/paper/2108.01634/) (2021)
- [Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safety](https://mlsanity.com/paper/2104.14235/) (2021)
- [AdaFocal: Calibration-aware Adaptive Focal Loss](https://mlsanity.com/paper/2211.11838/) (2022)
- [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)
- [Confidence Calibration for Object Detection and Segmentation](https://mlsanity.com/paper/2202.12785/) (2022)
- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)
- [MVC-Bench: Benchmarking Calibration of Medical Vision-Language Models](https://mlsanity.com/paper/2608.27004/) (2026)
- [A Log-Linear Time Sequential Optimal Calibration Algorithm for Quantized Isotonic L2 Regression](https://mlsanity.com/paper/2206.00744/) (2022)
- [An Operational Perspective to Fairness Interventions: Where and How to Intervene](https://mlsanity.com/paper/2302.01574/) (2023)
- [Adaptive Calibrator Ensemble for Model Calibration under Distribution Shift](https://mlsanity.com/paper/2303.05331/) (2023)
- [The ACUTE Protocol: Operationalizing Language Model Activations for Better Calibration, Utility, and Trust](https://mlsanity.com/paper/2606.07822/) (2026)
- [Instance-Aware Observer Network for Out-of-Distribution Object Segmentation](https://mlsanity.com/paper/2207.08782/) (2022)
- [Uncertainty Estimation based on Geometric Separation](https://mlsanity.com/paper/2301.04452/) (2023)
- [Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses](https://mlsanity.com/paper/2304.02141/) (2023)
- [Calibrating the Full Predictive Class Distribution of 3D Object Detectors for Autonomous Driving](https://mlsanity.com/paper/2510.01829/) (2025)
- [Multiclass Calibration Assessment and Recalibration of Probability Predictions via the Linear Log Odds Calibration Function](https://mlsanity.com/paper/2602.18573/) (2026)

## Abstract (arXiv)

Learning accurate probabilistic models from data is crucial in many practical tasks in data mining. In this paper we present a new non-parametric calibration method called textitensemble of near isotonic regression (ENIR). The method can be considered as an extension of BBQ, a recently proposed calibration method, as well as the commonly used calibration method based on isotonic regression. ENIR is designed to address the key limitation of isotonic regression which is the monotonicity assumption of the predictions. Similar to BBQ, the method post-processes the output of a binary classifier to obtain calibrated probabilities. Thus it can be combined with many existing classification models. We demonstrate the performance of ENIR on synthetic and real datasets for the commonly used binary classification models. Experimental results show that the method outperforms several common binary classifier calibration methods. In particular on the real data, ENIR commonly performs statistically significantly better than the other methods, and never worse. It is able to improve the calibration power of classifiers, while retaining their discrimination power. The method is also computationally tractable for large scale datasets, as it is O(N log N) time, where N is the number of samples.