In this paper, we present a new explainability formalism designed to explain how each input variable of a test set impacts the predictions of machine learning models. Hence, we propose a group explainability formalism for trained machine learning decision rules, based on their response to the variability of the input variables distribution. In order to emphasize the impact of each input variable, this formalism uses an information theory framework that quantifies the influence of all input-output observations based on entropic projections. This is thus the first unified and model agnostic formalism enabling data scientists to interpret the dependence between the input variables, their impact on the prediction errors, and their influence on the output predictions. Convergence rates of the entropic projections are provided in the large sample case. Most importantly, we prove that computing an explanation in our framework has a low algorithmic complexity, making it scalable to real-life large datasets. We illustrate our strategy by explaining complex decision rules learned by using XGBoost, Random Forest or Deep Neural Network classifiers on various datasets such as Adult income, MNIST and CelebA. We finally make clear its differences with the explainability strategies textit{LIME} and textit{SHAP}, that are based on single observations. Results can be reproduced by using the freely distributed Python toolbox https://gems-ai.com}.
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