logicDT: a procedure for identifying response-associated interactions between binary predictors

Interactions between predictors play an important role in many applications. Popular and successful tree-based supervised learning methods such as random forests or logic regression can incorporate interactions associated with the considered outcome without specifying which variables might interact. Nonetheless, these algorithms suffer from certain drawbacks such as limited interpretability of model predictions and difficulties with negligible marginal effects in the case of random forests or not being able to incorporate interactions with continuous variables, being restricted to additive structures between Boolean terms, and not directly considering conjunctions that reveal the interactions in the case of logic regression. We, therefore, propose a novel method called logic decision trees (logicDT) that is specifically tailored to binary input data and helps to overcome the drawbacks of existing methods. The main idea consists of considering sets of Boolean conjunctions, using these terms as input variables for decision trees, and searching for the best performing model. logicDT is also accompanied by a framework for estimating the importance of identified terms, i.e., input variables and interactions between input variables. This new method is compared to other popular statistical learning algorithms in simulations and real data applications. As these evaluations show, logicDT is able to yield high prediction performances while maintaining interpretability.