Distributionally Robust Fair Principal Components via Geodesic Descents
This addresses fairness and robustness issues in PCA for high-stakes applications, representing an incremental improvement over existing methods.
The paper tackles the problem of ensuring fairness and robustness in principal component analysis for domains like college admissions and healthcare by proposing a distributionally robust optimization method that balances total reconstruction error and subgroup error gaps, achieving competitive performance on real-world datasets.
Principal component analysis is a simple yet useful dimensionality reduction technique in modern machine learning pipelines. In consequential domains such as college admission, healthcare and credit approval, it is imperative to take into account emerging criteria such as the fairness and the robustness of the learned projection. In this paper, we propose a distributionally robust optimization problem for principal component analysis which internalizes a fairness criterion in the objective function. The learned projection thus balances the trade-off between the total reconstruction error and the reconstruction error gap between subgroups, taken in the min-max sense over all distributions in a moment-based ambiguity set. The resulting optimization problem over the Stiefel manifold can be efficiently solved by a Riemannian subgradient descent algorithm with a sub-linear convergence rate. Our experimental results on real-world datasets show the merits of our proposed method over state-of-the-art baselines.