# Fair PCA, One Component at a Time

arXiv: https://arxiv.org/abs/2503.21563 · HTML: https://mlsanity.com/paper/2503.21563/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 27 Mar 2025.

## Builds on (most cited first, 16 of 16)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Minimax Pareto Fairness: A Multi Objective Perspective](https://mlsanity.com/paper/2011.01821/) (2020)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [Active Sampling for Min-Max Fairness](https://mlsanity.com/paper/2006.06879/) (2020)
- [Efficient fair PCA for fair representation learning](https://mlsanity.com/paper/2302.13319/) (2023)
- [Convex Formulations for Fair Principal Component Analysis](https://mlsanity.com/paper/1802.03765/) (2018)
- [Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold](https://mlsanity.com/paper/2109.11196/) (2021)
- [My Fair Bandit: Distributed Learning of Max-Min Fairness with Multi-player Bandits](https://mlsanity.com/paper/2002.09808/) (2020)
- [The Frank-Wolfe algorithm: a short introduction](https://mlsanity.com/paper/2311.05313/) (2023)
- [Fair Principal Component Analysis and Filter Design](https://mlsanity.com/paper/2002.06557/) (2020)
- [Online Learning Demands in Max-min Fairness](https://mlsanity.com/paper/2012.08648/) (2020)
- [A novel approach for Fair Principal Component Analysis based on eigendecomposition](https://mlsanity.com/paper/2208.11362/) (2022)
- [Fair principal component analysis (PCA): minorization-maximization algorithms for Fair PCA, Fair Robust PCA and Fair Sparse PCA](https://mlsanity.com/paper/2305.05963/) (2023)
- [On Socially Fair Low-Rank Approximation and Column Subset Selection](https://mlsanity.com/paper/2412.06063/) (2024)
- [Hidden Convexity of Fair PCA and Fast Solver via Eigenvalue Optimization](https://mlsanity.com/paper/2503.00299/) (2025)

## Abstract (arXiv)

The Min-Max Fair PCA problem seeks a low-rank representation of multi-group data such that the the approximation error is as balanced as possible across groups. Existing approaches to this problem return a rank-d fair subspace, but lack the fundamental containment property of standard PCA: each rank-d PCA subspace should contain all lower-rank PCA subspaces. To fill this gap, we define fair principal components as directions that minimize the maximum group-wise reconstruction error, subject to orthogonality with previously selected components, and we introduce an iterative method to compute them. This approach preserves the containment property of standard PCA, and reduces to standard pca for data with a single group. We analyze the theoretical properties of our method and show empirically that it outperforms existing approaches to Min-Max Fair PCA.