  In this paper we revisit the bias-variance decomposition of model error from
the perspective of designing a fair classifier: we are motivated by the widely
held socio-technical belief that noise variance in large datasets in social
domains tracks demographic characteristics such as gender, race, disability,
etc. We propose a conditional-iid (ciid) model built from group-specific
classifiers that seeks to improve on the trade-offs made by a single model (iid
setting). We theoretically analyze the bias-variance decomposition of different
models in the Gaussian Mixture Model, and then empirically test our setup on
the COMPAS and folktables datasets. We instantiate the ciid model with two
procedures that improve "fairness" by conditioning out undesirable effects:
first, by conditioning directly on sensitive attributes, and second, by
clustering samples into groups and conditioning on cluster membership (blind to
protected group membership).
  Our analysis suggests that there might be principled procedures and concrete
real-world use cases under which conditional models are preferred, and our
striking empirical results strongly indicate that non-iid settings, such as the
ciid setting proposed here, might be more suitable for big data applications in
social contexts.
