  We propose a post-processing algorithm for fair classification that mitigates
model bias under a unified family of group fairness criteria covering
statistical parity, equal opportunity, and equalized odds, applicable to
multi-class problems and both attribute-aware and attribute-blind settings. It
achieves fairness by re-calibrating the output score of the given base model
with a "fairness cost" -- a linear combination of the (predicted) group
memberships. Our algorithm is based on a representation result showing that the
optimal fair classifier can be expressed as a linear post-processing of the
loss function and the group predictor, derived via using these as sufficient
statistics to reformulate the fair classification problem as a linear program.
The parameters of the post-processor are estimated by solving the empirical LP.
Experiments on benchmark datasets show the efficiency and effectiveness of our
algorithm at reducing disparity compared to existing algorithms, including
in-processing, especially on larger problems.
