Multi-output learning with the task of simultaneously predicting multiple outputs for an input has increasingly attracted interest from researchers due to its wide application. The $k$ nearest neighbor ( $k \text{NN}$ ) algorithm is one of the most popular frameworks for handling multi-output problems. The performance of $k \text{NN}$ depends crucially on the metric used to compute the distance between different instances. However, our experiment results show that the existing advanced metric learning technique cannot provide an appropriate distance metric for multi-output tasks. This paper systematically studies how to efficiently learn an appropriate distance metric for multi-output problems with provable guarantee. In particular, we present a novel large margin metric learning paradigm for multi-output tasks, which projects both the input and output into the same embedding space and then learns a distance metric to discover output dependency such that instances with very different multiple outputs will be moved far away. Several strategies are then proposed to speed up the training and testing time. Moreover, we study the generalization error bound of our method for three learning tasks, which shows that our method converges to the optimal solutions. Experiments on three multi-output learning tasks (multi-label classification, multi-target regression, and multi-concept retrieval) validate the effectiveness and scalability of the proposed method.

中文翻译：

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多输出任务的公制学习

由于其广泛的应用，以同时预测一个输入的多个输出为任务的多输出学习越来越引起研究人员的兴趣。这 $ k $ 最近的邻居 （ $ k \ text {NN} $ ）算法是用于处理多输出问题的最受欢迎的框架之一。的表现 $ k \ text {NN} $ 关键取决于用于计算不同实例之间距离的度量。但是，我们的实验结果表明，现有的高级度量学习技术无法为多输出任务提供合适的距离度量。本文系统地研究了如何有效地为可证明的多输出问题学习合适的距离度量。特别是，我们提出了一种用于多输出任务的新颖的大余量度量学习范例，该模型将输入和输出都投影到相同的嵌入空间中，然后学习距离度量以发现输出依存关系，从而使具有多个不同输出的实例成为移远了。然后提出了几种策略来加快培训和测试时间。而且，我们针对三种学习任务研究了该方法的泛化误差界，这表明我们的方法收敛于最优解。通过对三种多输出学习任务（多标签分类，多目标回归和多概念检索）的实验，验证了该方法的有效性和可扩展性。