# Fairness Constraints in High-Dimensional Generalized Linear Models

arXiv: https://arxiv.org/abs/2604.16610 · HTML: https://mlsanity.com/paper/2604.16610/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (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)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Fairness without Demographics through Adversarially Reweighted Learning](https://mlsanity.com/paper/2006.13114/) (2020)
- [Towards Fair Classifiers Without Sensitive Attributes: Exploring Biases in Related Features](https://mlsanity.com/paper/2104.14537/) (2021)
- [Fairness without the sensitive attribute via Causal Variational Autoencoder](https://mlsanity.com/paper/2109.04999/) (2021)
- [Pairwise Fairness for Ordinal Regression](https://mlsanity.com/paper/2105.03153/) (2021)
- [Fairness without Sensitive Attributes via Knowledge Sharing](https://mlsanity.com/paper/2409.18470/) (2024)
- [A Scalable Empirical Bayes Approach to Variable Selection in Generalized Linear Models](https://mlsanity.com/paper/1803.09735/) (2018)

## Abstract (arXiv)

Most fairness-aware learning methods assume that sensitive attributes are observed, an assumption that may fail due to privacy, legal, or data-collection constraints. We develop a framework for fairness-aware generalized linear models when the sensitive attribute is latent, possibly multi-category, and the predictors may be high-dimensional. Candidate proxy variables are modeled using Gaussian mixtures for continuous predictors and product-multinomial mixtures for categorical predictors. The resulting posterior group-membership probabilities are used to residualize the predictors and reduce their association with the latent sensitive structure. For continuous outcomes, we use constrained least squares to limit the contribution of the estimated sensitive attribute to prediction variability. For binary outcomes, we use penalized logistic regression to reduce dependence between predicted probabilities and estimated group membership. In high-dimensional settings, the procedure is combined with SEMMS variable selection to obtain sparse models. We establish identifiability and latent-class recovery results for Gaussian and categorical mixtures and derive expressions that quantify the loss of predictive power after residualization.Simulations and real-data applications demonstrate favorable accuracy-fairness performance.