  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.
