# Towards Provably Fair Machine Learning: Bayesian Approaches For Consistent and Transparent Predictions

arXiv: https://arxiv.org/abs/2606.12615 · HTML: https://mlsanity.com/paper/2606.12615/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 10 Jun 2026.

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

- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Fair Bayesian Optimization](https://mlsanity.com/paper/2006.05109/) (2020)
- [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021)
- [Bayesian Modeling of Intersectional Fairness: The Variance of Bias](https://mlsanity.com/paper/1811.07255/) (2018)
- [A Causal Bayesian Networks Viewpoint on Fairness](https://mlsanity.com/paper/1907.06430/) (2019)
- [Fair admission risk prediction with proportional multicalibration](https://mlsanity.com/paper/2209.14613/) (2022)
- [Fair Classifiers that Abstain without Harm](https://mlsanity.com/paper/2310.06205/) (2023)
- [Interpretable and Fair Mechanisms for Abstaining Classifiers](https://mlsanity.com/paper/2503.18826/) (2025)

## Abstract (arXiv)

ML classifiers deployed in high-stakes domains produce predictions whose quality varies systematically across subgroups. For granular subgroups defined by intersections of multiple features, predictions are often inconsistent with the observed data: the model's outputs contradict the evidence available for that subgroup. This problem is exacerbated by regularisation, which improves aggregate performance by collapsing small subgroups into larger groups, disproportionately affecting demographic minorities. We define two requirements for consistent prediction: determinism (identical individuals receive identical predictions) and statistical consistency (we cannot reject, at significance level alpha, the hypothesis that the predictions for a subgroup were drawn from the Bayesian optimal target distribution inferred for that subgroup). From these requirements we derive the Fair Bayesian classifier, which enforces both across every group and subgroup simultaneously and abstains whenever no consistent deterministic prediction is possible. On three benchmark datasets (Adult, COMPAS, and Bank Marketing), standard classifiers produce statistically inconsistent predictions for a substantial proportion of subgroups. Our classifier achieves zero consistency error by construction while exceeding baseline accuracy and multicalibration on every dataset tested. Statistical consistency provides a principled foundation for prediction quality with direct implications for algorithmic fairness. Minority demographics are disproportionately concentrated in small subgroups, precisely where frequentist inference is least reliable; addressing this inference problem is therefore a necessary step toward fair ML. By enforcing Bayesian consistency at the finest resolution the data supports, the our classifier demonstrates that exhaustive subgroup fairness with principled abstention is achievable in practice.