  To avoid discriminatory uses of their data, organizations can learn to map
them into a representation that filters out information related to sensitive
attributes. However, all existing methods in fair representation learning
generate a fairness-information trade-off. To achieve different points on the
fairness-information plane, one must train different models. In this paper, we
first demonstrate that fairness-information trade-offs are fully characterized
by rate-distortion trade-offs. Then, we use this key result and propose SoFaiR,
a single shot fair representation learning method that generates with one
trained model many points on the fairness-information plane. Besides its
computational saving, our single-shot approach is, to the extent of our
knowledge, the first fair representation learning method that explains what
information is affected by changes in the fairness / distortion properties of
the representation. Empirically, we find on three datasets that SoFaiR achieves
similar fairness-information trade-offs as its multi-shot counterparts.
