论文标题
预测的一个示例，该示例符合人口统计学奇偶校验，并在回归的背景下均衡群体风险
An example of prediction which complies with Demographic Parity and equalizes group-wise risks in the context of regression
论文作者
论文摘要
令$（x，s，y）\ in \ mathbb {r}^p \ times \ {1，2 \} \ times \ times \ mathbb {r} $在某些联合分发$ \ mathbb {p} $带有特征vector $ x $，敏感属性$ s $ s $ s $ s $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ y $ $ y $ $ y $ $ y $ $ $ $ y $ n \ in \ in。不产生不同治疗的贝叶斯最佳预测$ f^*$定义为$ f^*（x）= \ mathbb {e} [y | x = x] $。我们提供了一个预测$ x \到f（x）$的非平凡示例，该示例满足了两个常见的群体 - 事实概念：人口统计奇偶\ begin \ begin {align}（f（x）| s = 1）＆\ stackrel {d} {d} {=} {=} {=}（f（x）| s = 2）| s = 2） \ Mathbb {e} [（f^*（x） - f（x））^2 | S = 1] = \ Mathbb {E} [（f^*（x） - f（x））^2 | s = 2]。 \ end {align}据我们所知，这是满足上述的非恒定预测因子的第一个明确构造。我们讨论了这种结果对算法公平的数学概念的更好理解。
Let $(X, S, Y) \in \mathbb{R}^p \times \{1, 2\} \times \mathbb{R}$ be a triplet following some joint distribution $\mathbb{P}$ with feature vector $X$, sensitive attribute $S$ , and target variable $Y$. The Bayes optimal prediction $f^*$ which does not produce Disparate Treatment is defined as $f^*(x) = \mathbb{E}[Y | X = x]$. We provide a non-trivial example of a prediction $x \to f(x)$ which satisfies two common group-fairness notions: Demographic Parity \begin{align} (f(X) | S = 1) &\stackrel{d}{=} (f(X) | S = 2) \end{align} and Equal Group-Wise Risks \begin{align} \mathbb{E}[(f^*(X) - f(X))^2 | S = 1] = \mathbb{E}[(f^*(X) - f(X))^2 | S = 2]. \end{align} To the best of our knowledge this is the first explicit construction of a non-constant predictor satisfying the above. We discuss several implications of this result on better understanding of mathematical notions of algorithmic fairness.
