The prediction of multiple numeric outputs at the same time is called multi-target regression (MTR), and it has gained attention during the last decades. This task is a challenging research topic in supervised learning because it poses additional difficulties to traditional single-target regression (STR), and many real-world problems involve the prediction of multiple targets at once. One of the most successful approaches to deal with MTR, although not the only one, consists in transforming the problem in several STR problems, whose outputs will be combined building up the MTR output. In this paper, the Rotation Forest ensemble method, previously proposed for single-label classification and single-target regression, is adapted to MTR tasks and tested with several regressors and data sets. Our proposal rotates the input space in an efficient and novel fashion, avoiding extra rotations forced by MTR problem decomposition. Four approaches for MTR are used: single-target (ST), stacked-single target (SST), Ensembles of Regressor Chains (ERC), and Multi-target Regression via Quantization (MRQ). For assessing the benefits of the proposal, a thorough experimentation with 28 MTR data sets and statistical tests are used, concluding that Rotation Forest, adapted by means of these approaches, outperforms other popular ensembles, such as Bagging and Random Forest.

同时预测多个数值输出称为多目标回归（MTR），在过去的几十年中，它已引起人们的关注。这项任务在监督学习中是一个具有挑战性的研究主题，因为它给传统的单目标回归（STR）带来了额外的困难，并且许多现实世界中的问题都涉及到一次预测多个目标。处理MTR的最成功方法之一（尽管不是唯一一种）在于将问题转换为几个STR问题，其输出将组合起来构成MTR输出。在本文中，以前建议用于单标签分类和单目标回归的旋转森林集成方法适用于MTR任务，并已使用多个回归器和数据集进行了测试。我们的建议以一种有效且新颖的方式旋转输入空间，避免了MTR问题分解所造成的额外旋转。使用MTR的四种方法：单目标（ST），堆叠单目标（SST），回归链集合（ERC）和通过量化进行多目标回归（MRQ）。为了评估该提案的好处，我们使用了28个MTR数据集和统计测试进行了彻底的实验，得出结论认为，通过这些方法改编的轮作林优于其他流行的合奏，例如Bagging和Random Forest。