Several applications of supervised learning involve the prediction of multiple continuous target variables from a dataset. When the target variables exhibit statistical dependencies among them, a multi-target regression (MTR) modelling permits to improve the predictive performance in comparison to induce a separate model for each target. Apart from describing the dependencies among the targets, the MTR methods could offer better performance and less overfitting than traditional single-target (ST) methods. A group of MTR methods have addressed this demand, but there are still many possibilities for further improvements. This paper presents a novel MTR method called Deep Structure for Tracking Asynchronous Regressor Stacking (DSTARS), which overcomes some existing gaps in the current solutions. DSTARS extends the Stacked Single-Target (SST) approach by combining multiple stacked regressors into a deep structure. In this sense, it is able to boost the predictive performance by successively improving the predictions for the targets. Besides, DSTARS exploits the dependency of each target individually by tracking an asynchronous number of stacked regressors. Additionally, our proposal explores the inter-targets dependencies by exposing and measuring them through a nonlinear metric of variable importance. We compared DSTARS to SST, Ensemble of Regressor Chains (ERC) and Multi-objective Random Forest (MORF). Also, the ST strategy with different algorithms was used to compute independent regressions for each target. We used Random Forest (RF) and Support Vector Machine (SVM) as base-learners to investigate the prediction capability of algorithms belonging to different machine learning paradigms. The experiments carried out on eighteen diverse datasets showed that the proposed method was significantly better than the other compared approaches.

监督学习的几种应用涉及从数据集中预测多个连续目标变量。当目标变量在它们之间表现出统计依赖性时，多目标回归（MTR）建模与为每个目标引入单独的模型相比，可以改善预测性能。除了描述目标之间的依赖性之外，MTR方法比传统的单目标（ST）方法可以提供更好的性能和更少的过拟合。一组MTR方法已经解决了这一需求，但是仍有许多进一步改进的可能性。本文提出了一种新颖的MTR方法，称为深度结构，用于跟踪异步回归堆栈（DSTARS），它克服了当前解决方案中存在的一些不足。DSTARS通过将多个堆叠式回归器组合到一个深层结构中，扩展了堆叠式单目标（SST）方法。从这个意义上讲，它可以通过连续改进目标的预测来提高预测性能。此外，DSTARS通过跟踪异步数量的堆栈回归器来单独利用每个目标的依赖性。此外，我们的建议通过使用可变重要性的非线性指标来公开和测量目标之间的依存关系，从而探索这些目标之间的依存关系。我们将DSTARS与SST，回归链集合（ERC）和多目标随机森林（MORF）进行了比较。而且，采用具有不同算法的ST策略来计算每个目标的独立回归。我们使用随机森林（RF）和支持向量机（SVM）作为基础学习者，以研究属于不同机器学习范例的算法的预测能力。在18个不同的数据集上进行的实验表明，该方法明显优于其他比较方法。