Learning Distance Metrics from Probabilistic Information

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.