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.

Weaknesses: Intuitively randomising sensitive feature should lead to fairer results, however, fairness though unawareness poses a risk of unfairness by proxy as there are ways of predicting protected characteristic features from other features [Ruggieri et all, 2010, Adler et al 2016]. Also a continuous analog of fairness through unawareness [Dwark et al 2012] has been proposed via counterfactual fairness [Matt J. Kusner, et al, Counterfactual fairness, 2017]. In the counterfactual fairness, one has to estimate a dependency structure over the features, i.e. a causal graph, in order to create a counterfactual example when changing/flipping observational sensitive feature. To properly evaluate the contribution of the proposed approach, it has to be compared --methodologically and empirically -- not only to fairness through unawareness, but also to counterfactual fairness approaches. Another concern is that very little information is dedicate to the analysis how to estimate p(A Y).

The introduction of randomization tests for the assessment of fairness is very useful, and the proposed method for encouraging fairness in an adversarial learning system is relevant and novel. The discussion phase showed that the paper would benefit in discussing this work in a broader context, beyond parity measures. First, to shortly describe the pros and cons of addressing fairness through these parity measures (also taking the caution words mentioned in the broader impact section). Second, this would allow to better contrast the randomization of the sensitive attribute that is carried out here with "interventions" on the sensitive features. In particular such as (i) a scheme where randomization would be simply used to mask the sensitive attribute, and (ii) a rudimentary assessment of counterfactual fairness that would be obtained by simply flipping the sensitive attribute.

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.