Reviews: The Price of Fair PCA: One Extra dimension

The manuscript proposes a dimensionality reduction method called "fair PCA". The proposed study is based on the observation that, in a data model containing more than one data category ("population" as called by authors), the projection learnt by PCA may yield different reconstruction errors for different populations. This may impair the performance of machine learning algorithms that have access to dimensionality-reduced data obtained via PCA. To address this problem, the authors propose a variant of the PCA algorithm that minimizes the total deviation between the error of the learnt projection and the error of the optimal projection for each population. Quality: The paper is based on an interesting idea with an interesting motivation. The technical content of the paper is of satisfactory depth.