Efficient Fair Principal Component Analysis

TL;DR

This paper introduces a fairness-aware PCA algorithm that balances dimensionality reduction with fairness constraints, ensuring equitable treatment across sensitive groups while maintaining low reconstruction loss.

Contribution

It proposes an adaptive first-order algorithm based on Pareto optimality for fair PCA, with theoretical guarantees and empirical validation demonstrating improved fairness and efficiency.

Findings

The algorithm guarantees Pareto optimality for fairness and reconstruction loss.

Empirical results show superior performance over state-of-the-art methods.

The method effectively reduces unfairness in downstream classification tasks.

Abstract

It has been shown that dimension reduction methods such as PCA may be inherently prone to unfairness and treat data from different sensitive groups such as race, color, sex, etc., unfairly. In pursuit of fairness-enhancing dimensionality reduction, using the notion of Pareto optimality, we propose an adaptive first-order algorithm to learn a subspace that preserves fairness, while slightly compromising the reconstruction loss. Theoretically, we provide sufficient conditions that the solution of the proposed algorithm belongs to the Pareto frontier for all sensitive groups; thereby, the optimal trade-off between overall reconstruction loss and fairness constraints is guaranteed. We also provide the convergence analysis of our algorithm and show its efficacy through empirical studies on different datasets, which demonstrates superior performance in comparison with state-of-the-art algorithms. The proposed fairness-aware PCA algorithm can be efficiently generalized to multiple group sensitive features and effectively reduce the unfairness decisions in downstream tasks such as classification.