Counterfactual explainability and analysis of variance

Existing tools for explaining complex models and systems are associational rather than causal and do not provide mechanistic understanding. We propose a new notion called counterfactual explainability for causal attribution that is motivated by the concept of genetic heritability in twin studies. Counterfactual explainability extends methods for global sensitivity analysis (including the functional analysis of variance and Sobol's indices), which assumes independent explanatory variables, to dependent explanations by using a directed acyclic graphs to describe their causal relationship. Therefore, this explanability measure directly incorporates causal mechanisms by construction. Under a comonotonicity assumption, we discuss methods for estimating counterfactual explainability and apply them to a real dataset dataset to explain income inequality by gender, race, and educational attainment.