# Efficient fair PCA for fair representation learning

arXiv: https://arxiv.org/abs/2302.13319 · HTML: https://mlsanity.com/paper/2302.13319/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 26 Feb 2023.

## Builds on (most cited first, 28 of 28)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [Data Decisions and Theoretical Implications when Adversarially Learning Fair Representations](https://mlsanity.com/paper/1707.00075/) (2017)
- [Controllable Invariance through Adversarial Feature Learning](https://mlsanity.com/paper/1705.11122/) (2017)
- [Turning a Blind Eye: Explicit Removal of Biases and Variation from Deep Neural Network Embeddings](https://mlsanity.com/paper/1809.02169/) (2018)
- [Invariant Representations without Adversarial Training](https://mlsanity.com/paper/1805.09458/) (2018)
- [Linear Adversarial Concept Erasure](https://mlsanity.com/paper/2201.12091/) (2022)
- [Learning Controllable Fair Representations](https://mlsanity.com/paper/1812.04218/) (2018)
- [Fairness by Learning Orthogonal Disentangled Representations](https://mlsanity.com/paper/2003.05707/) (2020)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [Conscientious Classification: A Data Scientist's Guide to Discrimination-Aware Classification](https://mlsanity.com/paper/1907.09013/) (2019)
- [Eigenvalue and Generalized Eigenvalue Problems: Tutorial](https://mlsanity.com/paper/1903.11240/) (2019)
- [Fair Normalizing Flows](https://mlsanity.com/paper/2106.05937/) (2021)
- [Gold Doesn't Always Glitter: Spectral Removal of Linear and Nonlinear Guarded Attribute Information](https://mlsanity.com/paper/2203.07893/) (2022)
- [Learning Fair Representation via Distributional Contrastive Disentanglement](https://mlsanity.com/paper/2206.08743/) (2022)
- [Learning Fair Representations via an Adversarial Framework](https://mlsanity.com/paper/1904.13341/) (2019)
- [Convex Formulations for Fair Principal Component Analysis](https://mlsanity.com/paper/1802.03765/) (2018)
- [Gradient Reversal Against Discrimination](https://mlsanity.com/paper/1807.00392/) (2018)
- [Efficient Fair Principal Component Analysis](https://mlsanity.com/paper/1911.04931/) (2019)
- [Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold](https://mlsanity.com/paper/2109.11196/) (2021)
- [Right for the Right Reason: Training Agnostic Networks](https://mlsanity.com/paper/1806.06296/) (2018)
- [Obstructing Classification via Projection](https://mlsanity.com/paper/2105.09047/) (2021)

## Built on by (most cited first, 23 of 23)

- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Adaptive Activation Steering: A Tuning-Free LLM Truthfulness Improvement Method for Diverse Hallucinations Categories](https://mlsanity.com/paper/2406.00034/) (2024)
- [SAE-SSV: Supervised Steering in Sparse Representation Spaces for Reliable Control of Language Models](https://mlsanity.com/paper/2505.16188/) (2025)
- [Evaluating the Fairness of Discriminative Foundation Models in Computer Vision](https://mlsanity.com/paper/2310.11867/) (2023)
- [FairImagen: Post-Processing for Bias Mitigation in Text-to-Image Models](https://mlsanity.com/paper/2510.21363/) (2025)
- [Fair CoVariance Neural Networks](https://mlsanity.com/paper/2409.08558/) (2024)
- [A Joint Matrix Factorization Analysis of Multilingual Representations](https://mlsanity.com/paper/2310.15513/) (2023)
- [Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpoint](https://mlsanity.com/paper/2310.18593/) (2023)
- [Preserving Task-Relevant Information Under Linear Concept Removal](https://mlsanity.com/paper/2506.10703/) (2025)
- [Fair Canonical Correlation Analysis](https://mlsanity.com/paper/2309.15809/) (2023)
- [Surgical Feature-Space Decomposition of LLMs: Why, When and How?](https://mlsanity.com/paper/2405.13039/) (2024)
- [On Socially Fair Low-Rank Approximation and Column Subset Selection](https://mlsanity.com/paper/2412.06063/) (2024)
- [Learning Fair Representations with High-Confidence Guarantees](https://mlsanity.com/paper/2310.15358/) (2023)
- [AdapFair: Ensuring Adaptive Fairness for Machine Learning Operations](https://mlsanity.com/paper/2409.15088/) (2024)
- [FALCON: Fine-grained Activation Manipulation by Contrastive Orthogonal Unalignment for Large Language Model](https://mlsanity.com/paper/2502.01472/) (2025)
- [Hidden Convexity of Fair PCA and Fast Solver via Eigenvalue Optimization](https://mlsanity.com/paper/2503.00299/) (2025)
- [Fair CCA for Fair Representation Learning: An ADNI Study](https://mlsanity.com/paper/2507.09382/) (2025)
- [Enhancing SAE-based Steering via Neighbor Integrated Feature Selection](https://mlsanity.com/paper/2608.28806/) (2026)
- [PLS-based approach for fair representation learning](https://mlsanity.com/paper/2502.16263/) (2025)
- [Fair PCA, One Component at a Time](https://mlsanity.com/paper/2503.21563/) (2025)
- [Incorporating Fairness Constraints into Archetypal Analysis](https://mlsanity.com/paper/2507.12021/) (2025)
- [Fair Representation Learning with Controllable High Confidence Guarantees via Adversarial Inference](https://mlsanity.com/paper/2510.21017/) (2025)
- [Generalizing Fair Top-k Selection: An Integrative Approach](https://mlsanity.com/paper/2603.04689/) (2026)

## Abstract (arXiv)

We revisit the problem of fair principal component analysis (PCA), where the goal is to learn the best low-rank linear approximation of the data that obfuscates demographic information. We propose a conceptually simple approach that allows for an analytic solution similar to standard PCA and can be kernelized. Our methods have the same complexity as standard PCA, or kernel PCA, and run much faster than existing methods for fair PCA based on semidefinite programming or manifold optimization, while achieving similar results.