# Fairness Uncertainty Quantification: How certain are you that the model is fair?

arXiv: https://arxiv.org/abs/2304.13950 · HTML: https://mlsanity.com/paper/2304.13950/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 15 of 15)

- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018)
- [Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks](https://mlsanity.com/paper/2006.07322/) (2020)
- [Implicit regularization for deep neural networks driven by an Ornstein-Uhlenbeck like process](https://mlsanity.com/paper/1904.09080/) (2019)
- [Statistical Inference for Model Parameters in Stochastic Gradient Descent](https://mlsanity.com/paper/1610.08637/) (2016)
- [Quantifying Uncertainty in Deep Spatiotemporal Forecasting](https://mlsanity.com/paper/2105.11982/) (2021)
- [Averaging Stochastic Gradient Descent on Riemannian Manifolds](https://mlsanity.com/paper/1802.09128/) (2018)
- [Asymptotic Optimality in Stochastic Optimization](https://mlsanity.com/paper/1612.05612/) (2016)
- [Stochastic First-order Methods for Convex and Nonconvex Functional Constrained Optimization](https://mlsanity.com/paper/1908.02734/) (2019)
- [Online Covariance Matrix Estimation in Stochastic Gradient Descent](https://mlsanity.com/paper/2002.03979/) (2020)
- [Deeply Uncertain: Comparing Methods of Uncertainty Quantification in Deep Learning Algorithms](https://mlsanity.com/paper/2004.10710/) (2020)
- [Review of Mathematical frameworks for Fairness in Machine Learning](https://mlsanity.com/paper/2005.13755/) (2020)
- [Modeling Techniques for Machine Learning Fairness: A Survey](https://mlsanity.com/paper/2111.03015/) (2021)
- [Statistical inference for individual fairness](https://mlsanity.com/paper/2103.16714/) (2021)

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

- [Statistical Inference for Fairness Auditing](https://mlsanity.com/paper/2305.03712/) (2023)
- [Uncertainty-based Fairness Measures](https://mlsanity.com/paper/2312.11299/) (2023)
- [Online covariance estimation for stochastic gradient descent under Markovian sampling](https://mlsanity.com/paper/2308.01481/) (2023)
- [Fairness Hacking: The Malicious Practice of Shrouding Unfairness in Algorithms](https://mlsanity.com/paper/2311.06826/) (2023)

## Abstract (arXiv)

Fairness-aware machine learning has garnered significant attention in recent years because of extensive use of machine learning in sensitive applications like judiciary systems. Various heuristics, and optimization frameworks have been proposed to enforce fairness in classification citedel2020review where the later approaches either provides empirical results or provides fairness guarantee for the exact minimizer of the objective function citecelis2019classification. In modern machine learning, Stochastic Gradient Descent (SGD) type algorithms are almost always used as training algorithms implying that the learned model, and consequently, its fairness properties are random. Hence, especially for crucial applications, it is imperative to construct Confidence Interval (CI) for the fairness of the learned model. In this work we provide CI for test unfairness when a group-fairness-aware, specifically, Disparate Impact (DI), and Disparate Mistreatment (DM) aware linear binary classifier is trained using online SGD-type algorithms. We show that asymptotically a Central Limit Theorem holds for the estimated model parameter of both DI and DM-aware models. We provide online multiplier bootstrap method to estimate the asymptotic covariance to construct online CI. To do so, we extend the known theoretical guarantees shown on the consistency of the online bootstrap method for unconstrained SGD to constrained optimization which could be of independent interest. We illustrate our results on synthetic and real datasets.