Noise Induces Loss Discrepancy Across Groups for Linear Regression

This loss discrepancy across groups is especially problematic in critical applications that impact people's lives (Berk, 2012; Chouldechova, 2017). Despite the vast literature on removing loss discrepancy (Hardt et al., 2016; Khani et al., 2019; Agarwal et al., 2018; Zafar et al., 2017), the direct removal of loss discrepancy might introduce other problems such as intragroup loss discrepancy (Lipton et al., 2018) and adverse long-term impacts (Liu et al., 2018). Therefore, it is important to understand the source of loss discrepancy. Why do such loss discrepancies exist? The literature generally studies sources of loss discrepancy due to an "information deficiency" of one group--that is, one group has, for example, more noise (Corbett-Davies et al., 2017), lessPreliminary work, under review.