arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.06137cs.LGstat.ML
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基于多目标优化的公平主成分分析的权衡分析

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

University of Campinas(坎皮纳斯大学)

Guilherme D. Pelegrina, Renan D. B. Brotto, Leonardo T. Duarte, Romis Attux, João M. T. Romano

摘要:

在降维问题中,所采用的技术可能会产生不同组的表征误差之间的差异。例如,在投影空间中,一个特定的类可以比另一个类更好地表示。在某些情况下,这种不公平的结果可能会引起道德问题。为了克服这种不便,可以考虑公平性措施时,通过主成分分析进行降维。然而,增加公平性的解决方案往往会增加整体重建误差。在这种情况下,本文提出了一种基于多目标的方法来解决这种权衡。为此,我们采用了公平的措施与不同组的代表性错误之间的差距。此外,我们调查,如果一个经典的主成分分析的解决方案可以用来找到一个公平的投影。数值实验证明,一个更公平的结果,可以实现一个非常小的损失,在整体重建误差。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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