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

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This paper defines fair principal component analysis (PCA) as minimizing the maximum mean discrepancy (MMD) between the 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). Importantly, we provide a local optimality guarantee 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.
Publisher
Association for the Advancement of Artificial Intelligence (AAAI)
Issue Date
2022-02-24
Language
English
Citation

36th AAAI Conference on Artificial Intelligence, AAAI-22, pp.7363 - 7371

ISSN
2159-5399
DOI
10.1609/aaai.v36i7.20699
URI
http://hdl.handle.net/10203/298776
Appears in Collection
EE-Conference Papers(학술회의논문)
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