Contemporary machine learning (ML) techniques surpass traditional statistical methods in terms of their higher predictive power and their capability of processing a larger number of attributes. However, these novel ML algorithms generate models that have a complex structure which makes it difficult for their outputs to be interpreted with high precision. Another important issue is that a highly accurate predictive model might lack fairness by generating outputs that may result in discriminatory outcomes for protected subgroups. Thus, it is imperative to design predictive systems that are not only accurate but also achieve the desired fairness level. When used in certain contexts, predictive models, and strategies that rely on such models, are subject to laws and regulations that ensure fairness.

The objective of this article is to introduce a fairness interpretability framework for measuring and explaining the bias in classification and regression models at the level of a distribution. In our work, we measure the model bias across sub-population distributions in the model output using the Wasserstein metric. To properly quantify the contributions of predictors, we take into account the favorability of both the model and predictors with respect to the non-protected class. The quantification is accomplished by the use of transport theory, which gives rise to the decomposition of the model bias and bias explanations to positive and negative contributions. To gain more insight into the role of favorability and allow for additivity of bias explanations, we adapt techniques from cooperative game theory.