  We propose a novel algorithm for learning fair representations that can
simultaneously mitigate two notions of disparity among different demographic
subgroups in the classification setting. Two key components underpinning the
design of our algorithm are balanced error rate and conditional alignment of
representations. We show how these two components contribute to ensuring
accuracy parity and equalized false-positive and false-negative rates across
groups without impacting demographic parity. Furthermore, we also demonstrate
both in theory and on two real-world experiments that the proposed algorithm
leads to a better utility-fairness trade-off on balanced datasets compared with
existing algorithms on learning fair representations for classification.
