Re-formalization of Individual Fairness

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.