Metric learning from probabilistic labels

Metric learning aims to learn a good distance metric that can capture the relationships among instances, and its importance has long been recognized in many fields. In the traditional settings of metric learning, an implicit assumption 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. Thus, the existing metric learning methods cannot work well in these applications. To tackle this challenge, in this paper, we study how to effectively learn the distance metric from datasets that contain probabilistic information, and then propose two 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 two proposed mechanisms and provide theoretical bounds on the sample complexity for both of them. Additionally, extensive experiments based on real-world datasets are conducted to verify the desirable properties of the proposed mechanisms.