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Artificial intelligence models and methods commonly lack causalinterpretability. Despite the advancements in interpretable machine learning(IML) methods, they frequently assign importance to features which lack causalinfluence on the outcome variable. Selecting causally relevant features amongthose identified as relevant by these methods, or even before model training,would offer a solution. Feature selection methods utilizing informationtheoretical quantities have been successful in identifying statisticallyrelevant features. However, the information theoretical quantities they arebased on do not incorporate causality, rendering them unsuitable for suchscenarios. To address this challenge, this article proposes informationtheoretical quantities that incorporate the causal structure of the system,which can be used to evaluate causal importance of features for some givenoutcome variable. Specifically, we introduce causal versions of entropy andmutual information, termed causal entropy and causal information gain, whichare designed to assess how much control a feature provides over the outcomevariable. These newly defined quantities capture changes in the entropy of avariable resulting from interventions on other variables. Fundamental resultsconnecting these quantities to the existence of causal effects are derived. Theuse of causal information gain in feature selection is demonstrated,highlighting its superiority over standard mutual information in revealingwhich features provide control over a chosen outcome variable. Ourinvestigation paves the way for the development of methods with improvedinterpretability in domains involving causation.

Causal Entropy and Information Gain for Measuring Causal Control