# An Exploration of Multicalibration Uniform Convergence Bounds

arXiv: https://arxiv.org/abs/2202.04530 · HTML: https://mlsanity.com/paper/2202.04530/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 9 Feb 2022.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Towards Accountability for Machine Learning Datasets: Practices from Software Engineering and Infrastructure](https://mlsanity.com/paper/2010.13561/) (2020)
- [Rademacher Complexity for Adversarially Robust Generalization](https://mlsanity.com/paper/1810.11914/) (2018)
- [On the Apparent Conflict Between Individual and Group Fairness](https://mlsanity.com/paper/1912.06883/) (2019)
- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [Moment Multicalibration for Uncertainty Estimation](https://mlsanity.com/paper/2008.08037/) (2020)
- [Multi-group Agnostic PAC Learnability](https://mlsanity.com/paper/2105.09989/) (2021)
- [Sample Complexity of Uniform Convergence for Multicalibration](https://mlsanity.com/paper/2005.01757/) (2020)

## Built on by (most cited first, 4 of 4)

- [Comparative Learning: A Sample Complexity Theory for Two Hypothesis Classes](https://mlsanity.com/paper/2211.09101/) (2022)
- [The Sample Complexity of Multicalibration](https://mlsanity.com/paper/2604.21923/) (2026)
- [Optimal Deterministic Multicalibration and Omniprediction](https://mlsanity.com/paper/2606.20557/) (2026)
- [Sample Complexity of Multicalibration for Multilevel Properties](https://mlsanity.com/paper/2608.04288/) (2026)

## Abstract (arXiv)

Recent works have investigated the sample complexity necessary for fair machine learning. The most advanced of such sample complexity bounds are developed by analyzing multicalibration uniform convergence for a given predictor class. We present a framework which yields multicalibration error uniform convergence bounds by reparametrizing sample complexities for Empirical Risk Minimization (ERM) learning. From this framework, we demonstrate that multicalibration error exhibits dependence on the classifier architecture as well as the underlying data distribution. We perform an experimental evaluation to investigate the behavior of multicalibration error for different families of classifiers. We compare the results of this evaluation to multicalibration error concentration bounds. Our investigation provides additional perspective on both algorithmic fairness and multicalibration error convergence bounds. Given the prevalence of ERM sample complexity bounds, our proposed framework enables machine learning practitioners to easily understand the convergence behavior of multicalibration error for a myriad of classifier architectures.