  As an important problem in modern data analytics, classification has
witnessed varieties of applications from different domains. Different from
conventional classification approaches, fair classification concerns the issues
of unintentional biases against the sensitive features (e.g., gender, race).
Due to high nonconvexity of fairness measures, existing methods are often
unable to model exact fairness, which can cause inferior fair classification
outcomes. This paper fills the gap by developing a novel unified framework to
jointly optimize accuracy and fairness. The proposed framework is versatile and
can incorporate different fairness measures studied in literature precisely as
well as can be applicable to many classifiers including deep classification
models. Specifically, in this paper, we first prove Fisher consistency of the
proposed framework. We then show that many classification models within this
framework can be recast as mixed-integer convex programs, which can be solved
effectively by off-the-shelf solvers when the instance sizes are moderate and
can be used as benchmarks to compare the efficiency of approximation
algorithms. We prove that in the proposed framework, when the classification
outcomes are known, the resulting problem, termed "unbiased subdata selection,"
is strongly polynomial-solvable and can be used to enhance the classification
fairness by selecting more representative data points. This motivates us to
develop an iterative refining strategy (IRS) to solve the large-scale
instances, where we improve the classification accuracy and conduct the
unbiased subdata selection in an alternating fashion. We study the convergence
property of IRS and derive its approximation bound. More broadly, this
framework can be leveraged to improve classification models with unbalanced
data by taking F1 score into consideration.
