  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.
