Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold
This work addresses fairness in dimensionality reduction for machine learning applications, representing an incremental improvement with specific gains in efficiency and performance.
The paper tackles fair principal component analysis by minimizing maximum mean discrepancy between protected classes, formulating it as a non-convex optimization over the Stiefel manifold and solving it with the Riemannian Exact Penalty Method with Smoothing. Experimental results show it outperforms prior work in explained variance, fairness, and runtime on synthetic and UCI datasets.
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.