# The Price of Fair PCA: One Extra Dimension

arXiv: https://arxiv.org/abs/1811.00103 · HTML: https://mlsanity.com/paper/1811.00103/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2018.

## Built on by (most cited first, 30 of 67)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [On Tilted Losses in Machine Learning: Theory and Applications](https://mlsanity.com/paper/2109.06141/) (2021)
- [The Road to Explainability is Paved with Bias: Measuring the Fairness of Explanations](https://mlsanity.com/paper/2205.03295/) (2022)
- [Evaluating Fairness of Machine Learning Models Under Uncertain and Incomplete Information](https://mlsanity.com/paper/2102.08410/) (2021)
- [Fairness for Image Generation with Uncertain Sensitive Attributes](https://mlsanity.com/paper/2106.12182/) (2021)
- [A Sociotechnical View of Algorithmic Fairness](https://mlsanity.com/paper/2110.09253/) (2021)
- [Efficient fair PCA for fair representation learning](https://mlsanity.com/paper/2302.13319/) (2023)
- [Teacher's pet: understanding and mitigating biases in distillation](https://mlsanity.com/paper/2106.10494/) (2021)
- [Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold](https://mlsanity.com/paper/2109.11196/) (2021)
- [Scalable Spectral Clustering with Group Fairness Constraints](https://mlsanity.com/paper/2210.16435/) (2022)
- [Through the Data Management Lens: Experimental Analysis and Evaluation of Fair Classification](https://mlsanity.com/paper/2101.07361/) (2021)
- [Is Fairness Only Metric Deep? Evaluating and Addressing Subgroup Gaps in Deep Metric Learning](https://mlsanity.com/paper/2203.12748/) (2022)
- [Wasserstein Robust Classification with Fairness Constraints](https://mlsanity.com/paper/2103.06828/) (2021)
- [Distributionally Robust Fair Principal Components via Geodesic Descents](https://mlsanity.com/paper/2202.03071/) (2022)
- [Pareto Efficient Fairness in Supervised Learning: From Extraction to Tracing](https://mlsanity.com/paper/2104.01634/) (2021)
- [Constant-Factor Approximation Algorithms for Socially Fair k-Clustering](https://mlsanity.com/paper/2206.11210/) (2022)
- [Pairwise Fairness for Ordinal Regression](https://mlsanity.com/paper/2105.03153/) (2021)
- [A novel approach for Fair Principal Component Analysis based on eigendecomposition](https://mlsanity.com/paper/2208.11362/) (2022)
- [Fair CoVariance Neural Networks](https://mlsanity.com/paper/2409.08558/) (2024)
- [Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpoint](https://mlsanity.com/paper/2310.18593/) (2023)
- [Fairness-Aware Estimation of Graphical Models](https://mlsanity.com/paper/2408.17396/) (2024)
- [Lexicographically Fair Learning: Algorithms and Generalization](https://mlsanity.com/paper/2102.08454/) (2021)
- [Feature-based Individual Fairness in k-Clustering](https://mlsanity.com/paper/2109.04554/) (2021)
- [A Survey of Learning Criteria Going Beyond the Usual Risk](https://mlsanity.com/paper/2110.04996/) (2021)
- [Fair Column Subset Selection](https://mlsanity.com/paper/2306.04489/) (2023)
- [Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances](https://mlsanity.com/paper/2405.15441/) (2024)
- [Minimax Group Fairness in Strategic Classification](https://mlsanity.com/paper/2410.02513/) (2024)
- [MAFT: Efficient Model-Agnostic Fairness Testing for Deep Neural Networks via Zero-Order Gradient Search](https://mlsanity.com/paper/2412.20086/) (2024)
- [Modification-Fair Cluster Editing](https://mlsanity.com/paper/2112.03183/) (2021)
- [On the Exactness of Dantzig-Wolfe Relaxation for Rank Constrained Optimization Problems](https://mlsanity.com/paper/2210.16191/) (2022)

## Abstract (arXiv)

We investigate whether the standard dimensionality reduction technique of PCA inadvertently produces data representations with different fidelity for two different populations. We show on several real-world data sets, PCA has higher reconstruction error on population A than on B (for example, women versus men or lower- versus higher-educated individuals). This can happen even when the data set has a similar number of samples from A and B. This motivates our study of dimensionality reduction techniques which maintain similar fidelity for A and B. We define the notion of Fair PCA and give a polynomial-time algorithm for finding a low dimensional representation of the data which is nearly-optimal with respect to this measure. Finally, we show on real-world data sets that our algorithm can be used to efficiently generate a fair low dimensional representation of the data.