Abstract:
This work tackles the issue of fairness in the context of generative
procedures, such as image super-resolution, which entail different
definitions from the standard classification setting. Moreover,
while traditional group fairness definitions are typically defined
with respect to specified protected groups -- camouflaging the
fact that these groupings are artificial and carry historical and
political motivations -- we emphasize that there are no ground
truth identities. For instance, should South and East Asians be
viewed as a single group or separate groups? Should we consider one
race as a whole or further split by gender? Choosing which groups
are valid and who belongs in them is an impossible dilemma and being
``fair'' with respect to Asians may require being ``unfair'' with
respect to South Asians. This motivates the introduction of
definitions that allow algorithms to be \emph{oblivious} to the
relevant groupings.
We define several intuitive notions of group fairness and study
their incompatibilities and trade-offs. We show that the natural
extension of demographic parity is strongly dependent on the
grouping, and \emph{impossible} to achieve obliviously. On the
other hand, the conceptually new definition we introduce,
Conditional Proportional Representation, can be achieved obliviously
through Posterior Sampling. Our experiments validate our
theoretical results and achieve fair image reconstruction using
state-of-the-art generative models.
