# Certifying Some Distributional Fairness with Subpopulation Decomposition

arXiv: https://arxiv.org/abs/2205.15494 · HTML: https://mlsanity.com/paper/2205.15494/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 67 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 30 of 34)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Flexibly Fair Representation Learning by Disentanglement](https://mlsanity.com/paper/1906.02589/) (2019)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Automated Experiments on Ad Privacy Settings: A Tale of Opacity, Choice, and Discrimination](https://mlsanity.com/paper/1408.6491/) (2014)
- [Learning Controllable Fair Representations](https://mlsanity.com/paper/1812.04218/) (2018)
- [Conditional Learning of Fair Representations](https://mlsanity.com/paper/1910.07162/) (2019)
- [Fairness by Learning Orthogonal Disentangled Representations](https://mlsanity.com/paper/2003.05707/) (2020)
- [Learning Certified Individually Fair Representations](https://mlsanity.com/paper/2002.10312/) (2020)
- [How Do Fair Decisions Fare in Long-term Qualification?](https://mlsanity.com/paper/2010.11300/) (2020)
- [Verifying Individual Fairness in Machine Learning Models](https://mlsanity.com/paper/2006.11737/) (2020)
- [Sample Selection for Fair and Robust Training](https://mlsanity.com/paper/2110.14222/) (2021)
- [Probabilistic Verification of Fairness Properties via Concentration](https://mlsanity.com/paper/1812.02573/) (2018)
- [Perfectly Parallel Fairness Certification of Neural Networks](https://mlsanity.com/paper/1912.02499/) (2019)
- [Fair Normalizing Flows](https://mlsanity.com/paper/2106.05937/) (2021)
- [Does enforcing fairness mitigate biases caused by subpopulation shift?](https://mlsanity.com/paper/2011.03173/) (2020)
- [Adaptive Sampling for Minimax Fair Classification](https://mlsanity.com/paper/2103.00755/) (2021)
- [Group Fairness by Probabilistic Modeling with Latent Fair Decisions](https://mlsanity.com/paper/2009.09031/) (2020)
- [Unintended Selection: Persistent Qualification Rate Disparities and Interventions](https://mlsanity.com/paper/2111.01201/) (2021)
- [Latent Space Smoothing for Individually Fair Representations](https://mlsanity.com/paper/2111.13650/) (2021)

## Built on by (most cited first, 11 of 11)

- [FARE: Provably Fair Representation Learning with Practical Certificates](https://mlsanity.com/paper/2210.07213/) (2022)
- [Uncertainty-based Fairness Measures](https://mlsanity.com/paper/2312.11299/) (2023)
- [FairProof : Confidential and Certifiable Fairness for Neural Networks](https://mlsanity.com/paper/2402.12572/) (2024)
- [COLEP: Certifiably Robust Learning-Reasoning Conformal Prediction via Probabilistic Circuits](https://mlsanity.com/paper/2403.11348/) (2024)
- [A Theoretical Approach to Characterize the Accuracy-Fairness Trade-off Pareto Frontier](https://mlsanity.com/paper/2310.12785/) (2023)
- [COMMIT: Certifying Robustness of Multi-Sensor Fusion Systems against Semantic Attacks](https://mlsanity.com/paper/2403.02329/) (2024)
- [LocalStyleFool: Regional Video Style Transfer Attack Using Segment Anything Model](https://mlsanity.com/paper/2403.11656/) (2024)
- [P2NIA: Privacy-Preserving Non-Iterative Auditing](https://mlsanity.com/paper/2504.00874/) (2025)
- [Is On-Device AI Broken and Exploitable? Assessing the Trust and Ethics in Small Language Models](https://mlsanity.com/paper/2406.05364/) (2024)
- [Correct-By-Construction: Certified Individual Fairness through Neural Network Training](https://mlsanity.com/paper/2508.15642/) (2025)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)

## Abstract (arXiv)

Extensive efforts have been made to understand and improve the fairness of machine learning models based on observational metrics, especially in high-stakes domains such as medical insurance, education, and hiring decisions. However, there is a lack of certified fairness considering the end-to-end performance of an ML model. In this paper, we first formulate the certified fairness of an ML model trained on a given data distribution as an optimization problem based on the model performance loss bound on a fairness constrained distribution, which is within bounded distributional distance with the training distribution. We then propose a general fairness certification framework and instantiate it for both sensitive shifting and general shifting scenarios. In particular, we propose to solve the optimization problem by decomposing the original data distribution into analytical subpopulations and proving the convexity of the subproblems to solve them. We evaluate our certified fairness on six real-world datasets and show that our certification is tight in the sensitive shifting scenario and provides non-trivial certification under general shifting. Our framework is flexible to integrate additional non-skewness constraints and we show that it provides even tighter certification under different real-world scenarios. We also compare our certified fairness bound with adapted existing distributional robustness bounds on Gaussian data and demonstrate that our method is significantly tighter.