  Algorithmic fairness is becoming increasingly important in data mining and
machine learning. Among others, a foundational notation is group fairness. The
vast majority of the existing works on group fairness, with a few exceptions,
primarily focus on debiasing with respect to a single sensitive attribute,
despite the fact that the co-existence of multiple sensitive attributes (e.g.,
gender, race, marital status, etc.) in the real-world is commonplace. As such,
methods that can ensure a fair learning outcome with respect to all sensitive
attributes of concern simultaneously need to be developed. In this paper, we
study the problem of information-theoretic intersectional fairness (InfoFair),
where statistical parity, a representative group fairness measure, is
guaranteed among demographic groups formed by multiple sensitive attributes of
interest. We formulate it as a mutual information minimization problem and
propose a generic end-to-end algorithmic framework to solve it. The key idea is
to leverage a variational representation of mutual information, which considers
the variational distribution between learning outcomes and sensitive
attributes, as well as the density ratio between the variational and the
original distributions. Our proposed framework is generalizable to many
different settings, including other statistical notions of fairness, and could
handle any type of learning task equipped with a gradient-based optimizer.
Empirical evaluations in the fair classification task on three real-world
datasets demonstrate that our proposed framework can effectively debias the
classification results with minimal impact to the classification accuracy.
