Fair PCA, One Component at a Time
This addresses fairness in dimensionality reduction for multi-group data, offering an incremental improvement by ensuring subspace containment.
The paper tackles the Min-Max Fair PCA problem by proposing an iterative method to compute fair principal components that preserve the containment property of standard PCA, showing empirical outperformance over existing approaches.
The Min-Max Fair PCA problem seeks a low-rank representation of multi-group data such that the the approximation error is as balanced as possible across groups. Existing approaches to this problem return a rank-$d$ fair subspace, but lack the fundamental containment property of standard PCA: each rank-$d$ PCA subspace should contain all lower-rank PCA subspaces. To fill this gap, we define fair principal components as directions that minimize the maximum group-wise reconstruction error, subject to orthogonality with previously selected components, and we introduce an iterative method to compute them. This approach preserves the containment property of standard PCA, and reduces to standard \pca for data with a single group. We analyze the theoretical properties of our method and show empirically that it outperforms existing approaches to Min-Max Fair PCA.