# Discretization-free Multicalibration through Loss Minimization over Tree Ensembles

arXiv: https://arxiv.org/abs/2505.17435 · HTML: https://mlsanity.com/paper/2505.17435/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 19 of 19)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Skin Lesion Analysis Toward Melanoma Detection: A Challenge at the 2017 International Symposium on Biomedical Imaging (ISBI), Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1710.05006/) (2017)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Nuanced Metrics for Measuring Unintended Bias with Real Data for Text Classification](https://mlsanity.com/paper/1903.04561/) (2019)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [BCN20000: Dermoscopic Lesions in the Wild](https://mlsanity.com/paper/1908.02288/) (2019)
- [Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration](https://mlsanity.com/paper/2107.05719/) (2021)
- [Smooth ECE: Principled Reliability Diagrams via Kernel Smoothing](https://mlsanity.com/paper/2309.12236/) (2023)
- [Low-Degree Multicalibration](https://mlsanity.com/paper/2203.01255/) (2022)
- [Multicalibration as Boosting for Regression](https://mlsanity.com/paper/2301.13767/) (2023)
- [A Unifying Perspective on Multi-Calibration: Game Dynamics for Multi-Objective Learning](https://mlsanity.com/paper/2302.10863/) (2023)
- [Loss Minimization Yields Multicalibration for Large Neural Networks](https://mlsanity.com/paper/2304.09424/) (2023)
- [HappyMap: A Generalized Multi-calibration Method](https://mlsanity.com/paper/2303.04379/) (2023)
- [Fair Risk Control: A Generalized Framework for Calibrating Multi-group Fairness Risks](https://mlsanity.com/paper/2405.02225/) (2024)
- [Bridging Multicalibration and Out-of-distribution Generalization Beyond Covariate Shift](https://mlsanity.com/paper/2406.00661/) (2024)

## Built on by (most cited first, 7 of 7)

- [MCGrad: Multicalibration at Web Scale](https://mlsanity.com/paper/2509.19884/) (2025)
- [Multiclass Local Calibration with the Jensen-Shannon Distance](https://mlsanity.com/paper/2510.26566/) (2025)
- [On the Convergence of Multicalibration Gradient Boosting](https://mlsanity.com/paper/2602.06773/) (2026)
- [Divide et Calibra: Multiclass Local Calibration via Vector Quantization](https://mlsanity.com/paper/2605.21060/) (2026)
- [Auditability and the Landscape of Distance to Multicalibration](https://mlsanity.com/paper/2509.16930/) (2025)
- [Augmented Feature Boosting for Multicalibration](https://mlsanity.com/paper/2609.33891/) (2026)
- [A CaLLM Judge is a Better Judge: Mitigating Bias in LLM-as-a-judge](https://mlsanity.com/paper/2610.18108/) (2026)

## Abstract (arXiv)

In recent years, multicalibration has emerged as a desirable learning objective for ensuring that a predictor is calibrated across a rich collection of overlapping subpopulations. Existing approaches typically achieve multicalibration by discretizing the predictor's output space and iteratively adjusting its output values. However, this discretization approach departs from the standard empirical risk minimization (ERM) pipeline, introduces rounding error and additional sensitive hyperparameter, and may distort the predictor's outputs in ways that hinder downstream decision-making. In this work, we propose a discretization-free multicalibration method that directly optimizes an empirical risk objective over an ensemble of depth-two decision trees. Our ERM approach can be implemented using off-the-shelf tree ensemble learning methods such as LightGBM. Our algorithm provably achieves multicalibration, provided that the data distribution satisfies a technical condition we term as loss saturation. Across multiple datasets, our empirical evaluation shows that this condition is always met in practice. Our discretization-free algorithm consistently matches or outperforms existing multicalibration approaches--even when evaluated using a discretization-based multicalibration metric that shares its discretization granularity with the baselines.