The goal of metric learning is to learn a good distance metric that can capture the relationships among instances, and its importance has long been recognized in many fields. An implicit assumption in the traditional settings of metric learning is that the associated labels of the instances are deterministic. However, in many real-world applications, the associated labels come naturally with probabilities instead of deterministic values, which makes it difficult for the existing metric-learning methods to work well in these applications. To address this challenge, in this article, we study how to effectively learn the distance metric from datasets that contain probabilistic information, and then propose several novel metric-learning mechanisms for two types of probabilistic labels, i.e., the instance-wise probabilistic label and the group-wise probabilistic label. Compared with the existing metric-learning methods, our proposed mechanisms are capable of learning distance metrics directly from the probabilistic labels with high accuracy. We also theoretically analyze the proposed mechanisms and conduct extensive experiments on real-world datasets to verify the desirable properties of these mechanisms.

中文翻译：

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从概率信息中学习距离度量

度量学习的目标是学习一个很好的距离度量，可以捕捉到实例之间的关系，其重要性早已在许多领域得到认可。度量学习的传统设置中的一个隐含假设是实例的相关标签是确定性的。然而，在许多现实世界的应用程序中，相关标签自然而然地带有概率而不是确定性值，这使得现有的度量学习方法很难在这些应用程序中很好地工作。为了应对这一挑战，在本文中，我们研究了如何从包含概率信息的数据集中有效地学习距离度量，然后针对两种类型的概率标签提出了几种新颖的度量学习机制，即 实例概率标签和分组概率标签。与现有的度量学习方法相比，我们提出的机制能够直接从概率标签中以高精度学习距离度量。我们还从理论上分析了所提出的机制，并对现实世界的数据集进行了广泛的实验，以验证这些机制的理想特性。