Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold
Abstract
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.
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Junghyun Lee
PhD Student
PhD student at GSAI, KAIST, jointly advised by Prof. Se-Young Yun and Prof. Chulhee Yun. Interested in mathematical and theoretical AI, i.e., essentially any machine learning challenges necessitating mathematical analysis. Recently focused on statistical problems arising from RLHF, including interactive machine learning and low-dimensional structure recovery.