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.

翻译：数据复杂性的日益增长要求方法和模型能够有效处理复杂结构，因为简化这些结构会导致信息损失。尽管已有多种分析工具能够处理原始形式的复杂数据对象，但这些工具通常仅限于单一类型变量。本文提出能量树作为一种回归与分类模型，能够适应不同类型的结构化协变量。能量树利用能量统计扩展了条件推断树的能力，继承了其坚实的统计基础、可解释性、尺度不变性以及免于分布假设的特性。我们特别关注函数型和图结构协变量，同时强调该模型在整合其他变量类型方面的灵活性。大量模拟研究表明，该模型在变量选择和抗过拟合方面具有竞争力。最后，我们通过两项涉及人类生物学数据的实证分析评估了模型的预测能力。能量树已在R包etree中实现。