  We present a flexible framework for learning predictive models that
approximately satisfy the equalized odds notion of fairness. This is achieved
by introducing a general discrepancy functional that rigorously quantifies
violations of this criterion. This differentiable functional is used as a
penalty driving the model parameters towards equalized odds. To rigorously
evaluate fitted models, we develop a formal hypothesis test to detect whether a
prediction rule violates this property, the first such test in the literature.
Both the model fitting and hypothesis testing leverage a resampled version of
the sensitive attribute obeying equalized odds, by construction. We demonstrate
the applicability and validity of the proposed framework both in regression and
multi-class classification problems, reporting improved performance over
state-of-the-art methods. Lastly, we show how to incorporate techniques for
equitable uncertainty quantification---unbiased for each group under study---to
communicate the results of the data analysis in exact terms.
