The Price of Fair PCA: One Extra Dimension

TL;DR

This paper examines how standard PCA can produce biased data representations for different populations and proposes a Fair PCA method that ensures similar fidelity across groups, demonstrated on real-world datasets.

Contribution

The paper introduces a polynomial-time algorithm for Fair PCA that balances reconstruction error across populations, improving fairness in dimensionality reduction.

Findings

PCA often has higher reconstruction error for certain populations.

The proposed Fair PCA algorithm reduces disparity in data fidelity.

Real-world data experiments show effective fair representations.

Abstract

We investigate whether the standard dimensionality reduction technique of PCA inadvertently produces data representations with different fidelity for two different populations. We show on several real-world data sets, PCA has higher reconstruction error on population A than on B (for example, women versus men or lower- versus higher-educated individuals). This can happen even when the data set has a similar number of samples from A and B. This motivates our study of dimensionality reduction techniques which maintain similar fidelity for A and B. We define the notion of Fair PCA and give a polynomial-time algorithm for finding a low dimensional representation of the data which is nearly-optimal with respect to this measure. Finally, we show on real-world data sets that our algorithm can be used to efficiently generate a fair low dimensional representation of the data.