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.

本文提出一种在主成分分析中内在于目标函数中的公正准则的分布式稳健优化问题，通过采用超越最小二乘意义的子群重构误差之间的重构误差差异，平衡了总体重建误差和子群之间的重建误差差异，以及实验证明该方法较其他现有方法有明显优势。