Energy Trees: Regression and Classification With Structured and Mixed-Type Covariates (2207.04430v2)

Abstract: The increasing complexity of data requires methods and models that can effectively handle intricate structures, as simplifying them would result in loss of information. While several analytical tools have been developed to work with complex data objects in their original form, these tools are typically limited to single-type variables. In this work, we propose energy trees as a regression and classification model capable of accommodating structured covariates of various types. Energy trees leverage energy statistics to extend the capabilities of conditional inference trees, from which they inherit sound statistical foundations, interpretability, scale invariance, and freedom from distributional assumptions. We specifically focus on functional and graph-structured covariates, while also highlighting the model's flexibility in integrating other variable types. Extensive simulation studies demonstrate the model's competitive performance in terms of variable selection and robustness to overfitting. Finally, we assess the model's predictive ability through two empirical analyses involving human biological data. Energy trees are implemented in the R package etree.