Fair Streaming Principal Component Analysis: Statistical and Algorithmic
  Viewpoint
Junghyun Lee Hanseul Cho Se-Young Yun Chulhee Yun
Fair Principal Component Analysis (PCA) is a problem setting where we aim to
perform PCA while making the resulting representation fair in that the
projected distributions, conditional on the sensitive attributes, match one
another. However, existing approaches to fair PCA have two main problems:
theoretically, there has been no statistical foundation of fair PCA in terms of
learnability; practically, limited memory prevents us from using existing
approaches, as they explicitly rely on full access to the entire data. On the
theoretical side, we rigorously formulate fair PCA using a new notion called
\emph{probably approximately fair and optimal} (PAFO) learnability. On the
practical side, motivated by recent advances in streaming algorithms for
addressing memory limitation, we propose a new setting called \emph{fair
streaming PCA} along with a memory-efficient algorithm, fair noisy power method
(FNPM). We then provide its {\it statistical} guarantee in terms of
PAFO-learnability, which is the first of its kind in fair PCA literature.
Lastly, we verify the efficacy and memory efficiency of our algorithm on
real-world datasets.