# Understanding Fairness and Prediction Error through Subspace Decomposition and Influence Analysis

arXiv: https://arxiv.org/abs/2510.23935 · HTML: https://mlsanity.com/paper/2510.23935/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 53 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [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)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Bias in Bios: A Case Study of Semantic Representation Bias in a High-Stakes Setting](https://mlsanity.com/paper/1901.09451/) (2019)
- [Towards Fairness in Visual Recognition: Effective Strategies for Bias Mitigation](https://mlsanity.com/paper/1911.11834/) (2019)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Towards Debiasing Sentence Representations](https://mlsanity.com/paper/2007.08100/) (2020)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [Linear Adversarial Concept Erasure](https://mlsanity.com/paper/2201.12091/) (2022)
- [Diverse Adversaries for Mitigating Bias in Training](https://mlsanity.com/paper/2101.10001/) (2021)
- [Balancing out Bias: Achieving Fairness Through Balanced Training](https://mlsanity.com/paper/2109.08253/) (2021)
- [Uncovering the Structural Fairness in Graph Contrastive Learning](https://mlsanity.com/paper/2210.03011/) (2022)
- [Optimising Equal Opportunity Fairness in Model Training](https://mlsanity.com/paper/2205.02393/) (2022)
- [FAIRER: Fairness as Decision Rationale Alignment](https://mlsanity.com/paper/2306.15299/) (2023)
- [Towards A Holistic View of Bias in Machine Learning: Bridging Algorithmic Fairness and Imbalanced Learning](https://mlsanity.com/paper/2207.06084/) (2022)
- [On the Maximal Local Disparity of Fairness-Aware Classifiers](https://mlsanity.com/paper/2406.03255/) (2024)

## Abstract (arXiv)

Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness-utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.