# A Comprehensive View of Fairness through Distributional Stability

arXiv: https://arxiv.org/abs/2609.37061 · HTML: https://mlsanity.com/paper/2609.37061/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018)
- [A survey on domain adaptation theory: learning bounds and theoretical guarantees](https://mlsanity.com/paper/2004.11829/) (2020)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [General Fair Empirical Risk Minimization](https://mlsanity.com/paper/1901.10080/) (2019)
- [Bagging Provides Assumption-free Stability](https://mlsanity.com/paper/2301.12600/) (2023)
- [Fair Bayes-Optimal Classifiers Under Predictive Parity](https://mlsanity.com/paper/2205.07182/) (2022)
- [Chasing Fairness Under Distribution Shift: A Model Weight Perturbation Approach](https://mlsanity.com/paper/2303.03300/) (2023)
- [On the Inductive Biases of Demographic Parity-based Fair Learning Algorithms](https://mlsanity.com/paper/2402.18129/) (2024)
- [On the Vulnerability of Fairness Constrained Learning to Malicious Noise](https://mlsanity.com/paper/2307.11892/) (2023)
- [Finite-Sample and Distribution-Free Fair Classification: Optimal Trade-off Between Excess Risk and Fairness, and the Cost of Group-Blindness](https://mlsanity.com/paper/2410.16477/) (2024)
- [Fair Text Classification via Transferable Representations](https://mlsanity.com/paper/2503.07691/) (2025)
- [Randomized multi-class classification under system constraints: a unified approach via post-processing](https://mlsanity.com/paper/2512.14246/) (2025)

## Abstract (arXiv)

We view fairness as a property of distributional stability. Rather than assessing a predictor under a fixed data distribution, we study how its predictions change under perturbations that modify the composition of protected groups. A predictor is fair if it remains stable under such shifts. Under this perspective, several classical notions of fairness arise as stability with respect to specific perturbations, with the associated unfairness gap given by a Lipschitz constant of a prediction-rate functional. This formulation also yields guarantees that hold uniformly over a range of demographic compositions at test time, without requiring knowledge of the deployment distribution. It leads to a learning procedure based on convex combinations of reweighted predictors, formulated as a second-order cone program, for which we establish generalization bounds. Experiments on standard benchmarks illustrate the approach.