论文标题
基于多目标优化的公平主体组件分析中的权衡分析
Analysis of Trade-offs in Fair Principal Component Analysis Based on Multi-objective Optimization
论文作者
论文摘要
在降低维度问题中，采用的技术可能会在不同群体的表示错误之间产生差异。例如，在投影空间中，与另一个类别相比，可以更好地表示特定类。在某些情况下，这种不公平的结果可能引入道德问题。为了克服这种不便，可以在通过主成分分析降低维度时考虑公平度量。但是，提高公平性的解决方案往往会增加总体重建误差。在这种情况下，本文建议通过基于多目标的方法来解决这一权衡。为此，我们采用了与不同群体的表示错误之间差异相关的公平度量。此外，我们研究了是否可以使用经典主体分析的解决方案来找到公平投影。数值实验证明，由于总体重建误差的损失很小，可以实现更公平的结果。
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.
