# Group Fairness by Probabilistic Modeling with Latent Fair Decisions

arXiv: https://arxiv.org/abs/2009.09031 · HTML: https://mlsanity.com/paper/2009.09031/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2020.

## Built on by (most cited first, 22 of 22)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Tractable Control for Autoregressive Language Generation](https://mlsanity.com/paper/2304.07438/) (2023)
- [Tractable Regularization of Probabilistic Circuits](https://mlsanity.com/paper/2106.02264/) (2021)
- [Scaling Up Probabilistic Circuits by Latent Variable Distillation](https://mlsanity.com/paper/2210.04398/) (2022)
- [Scaling Tractable Probabilistic Circuits: A Systems Perspective](https://mlsanity.com/paper/2406.00766/) (2024)
- [Image Inpainting via Tractable Steering of Diffusion Models](https://mlsanity.com/paper/2401.03349/) (2023)
- [Lossless Compression with Probabilistic Circuits](https://mlsanity.com/paper/2111.11632/) (2021)
- [Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuits](https://mlsanity.com/paper/2302.08086/) (2023)
- [Latent Space Smoothing for Individually Fair Representations](https://mlsanity.com/paper/2111.13650/) (2021)
- [Sparse Probabilistic Circuits via Pruning and Growing](https://mlsanity.com/paper/2211.12551/) (2022)
- [Certifying Some Distributional Fairness with Subpopulation Decomposition](https://mlsanity.com/paper/2205.15494/) (2022)
- [A Compositional Atlas for Algebraic Circuits](https://mlsanity.com/paper/2412.05481/) (2024)
- [Scaling Probabilistic Circuits via Monarch Matrices](https://mlsanity.com/paper/2506.12383/) (2025)
- [Restructuring Tractable Probabilistic Circuits](https://mlsanity.com/paper/2411.12256/) (2024)
- [How to Square Tensor Networks and Circuits Without Squaring Them](https://mlsanity.com/paper/2512.17090/) (2025)
- [Rethinking Probabilistic Circuit Parameter Learning](https://mlsanity.com/paper/2505.19982/) (2025)
- [On the Hardness of Approximating Distributions with Tractable Probabilistic Models](https://mlsanity.com/paper/2506.01281/) (2025)
- [PFAttack: Stealthy Attack Bypassing Group Fairness in Federated Learning](https://mlsanity.com/paper/2410.06509/) (2024)
- [The Gradient of Algebraic Model Counting](https://mlsanity.com/paper/2502.18406/) (2025)
- [BaBE: Enhancing Fairness via Estimation of Latent Explaining Variables](https://mlsanity.com/paper/2307.02891/) (2023)
- [Anti-Matthew FL: Bridging the Performance Gap in Federated Learning to Counteract the Matthew Effect](https://mlsanity.com/paper/2309.16338/) (2023)
- [A Probabilistic Circuit-Induced Pseudo-Metric for Out-of-Distribution Detection](https://mlsanity.com/paper/2608.09117/) (2026)

## Abstract (arXiv)

Machine learning systems are increasingly being used to make impactful decisions such as loan applications and criminal justice risk assessments, and as such, ensuring fairness of these systems is critical. This is often challenging as the labels in the data are biased. This paper studies learning fair probability distributions from biased data by explicitly modeling a latent variable that represents a hidden, unbiased label. In particular, we aim to achieve demographic parity by enforcing certain independencies in the learned model. We also show that group fairness guarantees are meaningful only if the distribution used to provide those guarantees indeed captures the real-world data. In order to closely model the data distribution, we employ probabilistic circuits, an expressive and tractable probabilistic model, and propose an algorithm to learn them from incomplete data. We evaluate our approach on a synthetic dataset in which observed labels indeed come from fair labels but with added bias, and demonstrate that the fair labels are successfully retrieved. Moreover, we show on real-world datasets that our approach not only is a better model than existing methods of how the data was generated but also achieves competitive accuracy.