The notion of individual fairness is a formalization of an ethical principle, "Treating like cases alike," which has been argued such as by Aristotle. In a fairness-aware machine learning context, Dwork et al. firstly formalized the notion. In their formalization, a similar pair of data in an unfair space should be mapped to similar positions in a fair space. We propose to re-formalize individual fairness by the statistical independence conditioned by individuals. This re-formalization has the following merits. First, our formalization is compatible with that of Dwork et al. Second, our formalization enables to combine individual fairness with the fairness notion, equalized odds or sufficiency, as well as statistical parity. Third, though their formalization implicitly assumes a pre-process approach for making fair prediction, our formalization is applicable to an in-process or post-process approach.

翻译：个体公平这一概念是对亚里士多德等思想家所提出的“类似情况类似对待”这一伦理原则的形式化。在公平感知机器学习背景下，Dwork等人首先对该概念进行了形式化定义。在他们的形式化框架中，不公平空间中相似的数据对应当被映射到公平空间中的相似位置。我们提出基于个体条件统计独立性对个体公平进行重新形式化。这种重新形式化具有以下优点：首先，我们的形式化与Dwork等人的形式化框架兼容；其次，我们的形式化方法能够将个体公平与均衡几率、充分性等公平概念以及统计均等性相结合；第三，尽管Dwork等人的形式化隐含地假设采用预处理方法实现公平预测，我们的形式化方法同样适用于过程中处理或后处理方案。