The Shapley Value of coalition of variables provides better explanations

While Shapley Values (SV) are one of the gold standard for interpreting machine learning models, we show that they are still poorly understood, in particular in the presence of categorical variables or of variables of low importance. For instance, we show that the popular practice that consists in summing the SV of dummy variables is false as it provides wrong estimates of all the SV in the model and implies spurious interpretations. Based on the identification of null and active coalitions, and a coalitional version of the SV, we provide a correct computation and inference of important variables. Moreover, a Python library (All the experiments and simulations can be reproduced with the publicly available library \emph{Active Coalition of Variables} https://github.com/acvicml/ACV) that computes reliably conditional expectations and SV for tree-based models, is implemented and compared with state-of-the-art algorithms on toy models and real data sets.