论文标题
线性模型下的人口奇偶校验限制了最小值最佳回归
Demographic Parity Constrained Minimax Optimal Regression under Linear Model
论文作者
论文摘要
我们探讨了在线性模型的上下文中与人口统计奇偶元约束回归问题相关的最小值最佳误差。与Chzhen和Schreuder（2022）提出的模型相比，我们提出的模型涵盖了更广泛的歧视性偏见来源。我们的分析表明，在我们的模型下的人口统计奇偶校验约束的回归问题的最小值最佳错误的特征是$θ（\ frac {dm} {n}）$，其中$ n $表示样本大小，$ d $表示维数，$ m $表示来自灵敏度属性的汇编组的数量。此外，我们证明了最小误差与模型中存在的较大偏差结合增加。
We explore the minimax optimal error associated with a demographic parity-constrained regression problem within the context of a linear model. Our proposed model encompasses a broader range of discriminatory bias sources compared to the model presented by Chzhen and Schreuder (2022). Our analysis reveals that the minimax optimal error for the demographic parity-constrained regression problem under our model is characterized by $Θ(\frac{dM}{n})$, where $n$ denotes the sample size, $d$ represents the dimensionality, and $M$ signifies the number of demographic groups arising from sensitive attributes. Moreover, we demonstrate that the minimax error increases in conjunction with a larger bias present in the model.
