Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and the associated threshold. This greedy approach trains trees very fast, but, by its nature, their classification accuracy may not be competitive against other state-of-the-art procedures. Moreover, controlling critical issues, such as the misclassification rates in each of the classes, is difficult. To address these shortcomings, optimal decision trees have been recently proposed in the literature, which use discrete decision variables to model the path each observation will follow in the tree. Instead, we propose a new approach based on continuous optimization. Our classifier can be seen as a randomized tree, since at each node of the decision tree a random decision is made. The computational experience reported demonstrates the good performance of our procedure.

分类和回归树（CART）是现代统计和机器学习中的现成技术。传统上，CART是通过贪婪过程构建的，顺序确定分割预测变量和关联的阈值。这种贪婪的方法可以非常快速地训练树木，但是从本质上来说，它们的分类准确性可能无法与其他最新技术相抗衡。此外，很难控制关键问题，例如每个类别中的错误分类率。为了解决这些缺点，最近在文献中提出了最佳决策树，该决策树使用离散的决策变量来建模每个观察结果在树中遵循的路径。相反，我们提出了一种基于连续优化的新方法。我们的分类器可以看作是一棵随机树，因为在决策树的每个节点上都做出了随机决策。报告的计算经验证明了我们的程序的良好性能。