# Fair and Accurate Regression: Strong Formulations and Algorithms

arXiv: https://arxiv.org/abs/2412.17116 · HTML: https://mlsanity.com/paper/2412.17116/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 22 Dec 2024.

## Builds on (most cited first, 25 of 25)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Fairness in Machine Learning](https://mlsanity.com/paper/2012.15816/) (2020)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [A survey on datasets for fairness-aware machine learning](https://mlsanity.com/paper/2110.00530/) (2021)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [Learning Optimal and Fair Decision Trees for Non-Discriminative Decision-Making](https://mlsanity.com/paper/1903.10598/) (2019)
- [Fairness and Accountability Design Needs for Algorithmic Support in High-Stakes Public Sector Decision-Making](https://mlsanity.com/paper/1802.01029/) (2018)
- [Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization](https://mlsanity.com/paper/2004.06152/) (2020)
- [Learning Optimal Fair Classification Trees: Trade-offs Between Interpretability, Fairness, and Accuracy](https://mlsanity.com/paper/2201.09932/) (2022)
- [Rank-one Convexification for Sparse Regression](https://mlsanity.com/paper/1901.10334/) (2019)
- [Fair Generalized Linear Models with a Convex Penalty](https://mlsanity.com/paper/2206.09076/) (2022)
- [Spectral Algorithms for Computing Fair Support Vector Machines](https://mlsanity.com/paper/1710.05895/) (2017)
- [Unbiased Subdata Selection for Fair Classification: A Unified Framework and Scalable Algorithms](https://mlsanity.com/paper/2012.12356/) (2020)
- [On the convex hull of convex quadratic optimization problems with indicators](https://mlsanity.com/paper/2201.00387/) (2022)
- [Safe Screening for Logistic Regression with ℓ0-ℓ2 Regularization](https://mlsanity.com/paper/2202.00467/) (2022)
- [Metrizing Fairness](https://mlsanity.com/paper/2205.15049/) (2022)
- [Fair Decision Rules for Binary Classification](https://mlsanity.com/paper/2107.01325/) (2021)
- [Comparing perspective reformulations for piecewise-convex optimization](https://mlsanity.com/paper/2211.15450/) (2022)
- [Distributionally Fair Stochastic Optimization using Wasserstein Distance](https://mlsanity.com/paper/2402.01872/) (2024)

## Built on by (most cited first, 1 of 1)

- [Fair Regression under Demographic Parity: A Unified Framework](https://mlsanity.com/paper/2601.10623/) (2026)

## Abstract (arXiv)

This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we study the polynomially-solvable single-factor and single-observation subproblems as building blocks and derive their closed convex hull descriptions. Strong formulations obtained for the general fair regression problem in this manner are utilized to solve the problem with a branch-and-bound algorithm exactly or as a relaxation to produce fair and accurate models rapidly. Moreover, to handle large-scale instances, we develop a coordinate descent algorithm motivated by the convex-hull representation of the single-factor fair regression problem to improve a given solution efficiently. Numerical experiments conducted on fair least squares and fair logistic regression problems show competitive statistical performance with state-of-the-art methods while significantly reducing training times.