Analysis of Trade-offs in Fair Principal Component Analysis Based on Multi-objective Optimization

TL;DR

This paper explores balancing fairness and accuracy in Principal Component Analysis by using multi-objective optimization to reduce disparities between groups while maintaining low reconstruction error.

Contribution

It introduces a multi-objective approach to incorporate fairness into PCA and evaluates the potential of classical PCA solutions for fair projections.

Findings

Fairer PCA solutions with minimal increase in reconstruction error

Multi-objective optimization effectively balances fairness and accuracy

Classical PCA solutions can be adapted for fairness

Abstract

In dimensionality reduction problems, the adopted technique may produce disparities between the representation errors of different groups. For instance, in the projected space, a specific class can be better represented in comparison with another one. In some situations, this unfair result may introduce ethical concerns. Aiming at overcoming this inconvenience, a fairness measure can be considered when performing dimensionality reduction through Principal Component Analysis. However, a solution that increases fairness tends to increase the overall re-construction error. In this context, this paper proposes to address this trade-off by means of a multi-objective-based approach. For this purpose, we adopt a fairness measure associated with the disparity between the representation errors of different groups. Moreover, we investigate if the solution of a classical Principal Component Analysis can be used to find a fair projection. Numerical experiments attest that a fairer result can be achieved with a very small loss in the overall reconstruction error.