The last decade has shed some light on theoretical properties such as their consistency for regression tasks. In the current paper, we propose a new class of very simple learners based on so-called naive trees. These naive trees partition the feature space completely at random and independent of the data. Although counter-intuitive, we prove these naive trees and ensembles are consistent under fairly general assumptions. However, naive trees appear to be too simple for actual application. We therefore analyze their finite sample properties in a simulation and small benchmark study. We find a slow convergence speed and a rather poor predictive performance. Based on these results, we finally discuss to what extent consistency proofs help to justify the application of complex learning algorithms.

翻译：过去十年中，回归任务中树模型的相合性等理论性质已得到部分阐明。本文提出一类基于所谓朴素树的极简学习器。这些朴素树完全随机且独立于数据地对特征空间进行划分。尽管有违直觉，我们证明在相当一般的假设下，这些朴素树及其集成方法是相合的。然而朴素树在实际应用中可能过于简单。因此我们通过模拟实验和小型基准研究分析了其有限样本性质，发现其收敛速度较慢且预测性能较差。基于这些结果，我们最终讨论了相合性证明能在何种程度上为复杂学习算法的应用提供理论依据。