In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

翻译：近年来，算法公平性的多种概念相继涌现。其中一种概念是个体公平性（IF），要求相似的个体获得相似的处理。与此同时，矩阵估计（ME）已成为处理含缺失值噪声数据的自然范式。本文中，我们将这两个概念联系起来。研究发现，使用矩阵估计对数据进行预处理，可在不牺牲算法性能的前提下提升其个体公平性。具体而言，我们证明，采用一种名为奇异值阈值法（SVT）的常见矩阵估计方法预处理数据，能在适当条件下提供强个体公平性保障。进一步研究表明，在类似条件下，SVT预处理还能产生一致且近似极小化最优的估计结果。因此，在所述条件下，矩阵估计预处理步骤不会增加基算法的预测误差，即不会引入公平性与性能之间的权衡。我们通过合成数据与真实数据验证了这些结论。