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This paper defines fair principal component analysis (PCA) as minimizing themaximum mean discrepancy (MMD) between dimensionality-reduced conditionaldistributions of different protected classes. The incorporation of MMDnaturally leads to an exact and tractable mathematical formulation of fairnesswith good statistical properties. We formulate the problem of fair PCA subjectto MMD constraints as a non-convex optimization over the Stiefel manifold andsolve it using the Riemannian Exact Penalty Method with Smoothing (REPMS; Liuand Boumal, 2019). Importantly, we provide local optimality guarantees andexplicitly show the theoretical effect of each hyperparameter in practicalsettings, extending previous results. Experimental comparisons based onsynthetic and UCI datasets show that our approach outperforms prior work inexplained variance, fairness, and runtime.

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