mlsanityData to 7 Oct 2026

Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold

arXiv 2109.11196 ↗First posted 23 Sep 2021stat.ML cs.CY cs.LGcited by 18

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Abstract (arXiv)

This paper defines fair principal component analysis (PCA) as minimizing the maximum mean discrepancy (MMD) between dimensionality-reduced conditional distributions of different protected classes. The incorporation of MMD naturally leads to an exact and tractable mathematical formulation of fairness with good statistical properties. We formulate the problem of fair PCA subject to MMD constraints as a non-convex optimization over the Stiefel manifold and solve it using the Riemannian Exact Penalty Method with Smoothing (REPMS; Liu and Boumal, 2019). Importantly, we provide local optimality guarantees and explicitly show the theoretical effect of each hyperparameter in practical settings, extending previous results. Experimental comparisons based on synthetic and UCI datasets show that our approach outperforms prior work in explained variance, fairness, and runtime.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 19 of its 52 references that are in the map. First posted on arXiv 23 Sep 2021.

Builds on

19 of 52 references.

References · 19

  1. 2016Equality of Opportunity in Supervised Learningcited by 2,000
  2. 2019A Survey on Bias and Fairness in Machine Learningcited by 1,911
  3. 2014Certifying and removing disparate impactcited by 715
  4. 2016Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatmentcited by 368
  5. 2018Learning Adversarially Fair and Transferable Representationscited by 353
  6. 2018Fair Clustering Through Fairletscited by 176
  7. 2017Data Decisions and Theoretical Implications when Adversarially Learning Fair Representationscited by 165
  8. 2019Fair Algorithms for Clusteringcited by 98
  9. 2018The Price of Fair PCA: One Extra Dimensioncited by 67
  10. 2021Fair Feature Distillation for Visual Recognitioncited by 59
  11. 2019Toward a better trade-off between performance and fairness with kernel-based distribution matchingcited by 36
  12. 2019A Brief Introduction to Manifold Optimizationcited by 35
7 more
  1. 2018Convex Formulations for Fair Principal Component Analysiscited by 20
  2. 2014A Stochastic PCA and SVD Algorithm with an Exponential Convergence Ratecited by 18
  3. 2019Simple algorithms for optimization on Riemannian manifolds with constraintscited by 14
  4. 2013Stochastic Optimization of PCA with Capped MSGcited by 6
  5. 2016Orthogonal Sparse PCA and Covariance Estimation via Procrustes Reformulationcited by 5
  6. 2020Covariance-Robust Dynamic Watermarkingcited by 1
  7. 2021Manifold Optimization for High Accuracy Spatial Location Estimation Using Ultrasound Wavescited by 1

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Citing papers per year: 2022: 3; 2023: 5; 2024: 3; 2025: 7.

18 papers.

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  1. 2023Efficient fair PCA for fair representation learningcited by 23
  2. 2022MMD-B-Fair: Learning Fair Representations with Statistical Testingcited by 13
  3. 2022First-Order Algorithms for Min-Max Optimization in Geodesic Metric Spacescited by 10
  4. 2025Fair Representation Learning for Continuous Sensitive Attributes using Expectation of Integral Probability Metricscited by 7
  5. 2022A novel approach for Fair Principal Component Analysis based on eigendecompositioncited by 6
  6. 2024Fair CoVariance Neural Networkscited by 6
  7. 2023Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpointcited by 5
  8. 2023Last-Iterate Convergence of Adaptive Riemannian Gradient Descent for Equilibrium Computationcited by 2
  9. 2024Specification Overfitting in Artificial Intelligencecited by 2
  10. 2024On Socially Fair Low-Rank Approximation and Column Subset Selectioncited by 2
  11. 2023When Collaborative Filtering is not Collaborative: Unfairness of PCA for Recommendationscited by 1
  12. 2023Learning Fair Representations with High-Confidence Guaranteescited by 1
6 more
  1. 2025Hidden Convexity of Fair PCA and Fast Solver via Eigenvalue Optimizationcited by 1
  2. 2025PLS-based approach for fair representation learningcited by 0
  3. 2025Achieving Fair PCA Using Joint Eigenvalue Decompositioncited by 0
  4. 2025Fair PCA, One Component at a Timecited by 0
  5. 2025Incorporating Fairness Constraints into Archetypal Analysiscited by 0
  6. 2025Fair Representation Learning with Controllable High Confidence Guarantees via Adversarial Inferencecited by 0