Learning from triplet comparison data has been extensively studied in the context of metric learning, where we want to learn a distance metric between two instances, and ordinal embedding, where we want to learn an embedding in a Euclidean space of the given instances that preserve the comparison order as much as possible. Unlike fully labeled data, triplet comparison data can be collected in a more accurate and human-friendly way. Although learning from triplet comparison data has been considered in many applications, an important fundamental question of whether we can learn a classifier only from triplet comparison data without all the labels has remained unanswered. In this letter, we give a positive answer to this important question by proposing an unbiased estimator for the classification risk under the empirical risk minimization framework. Since the proposed method is based on the empirical risk minimization framework, it inherently has the advantage that any surrogate loss function and any model, including neural networks, can be easily applied. Furthermore, we theoretically establish an estimation error bound for the proposed empirical risk minimizer. Finally, we provide experimental results to show that our method empirically works well and outperforms various baseline methods.

中文翻译：

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三元组比较数据的分类

从三元组比较数据中学习已经在度量学习的背景下进行了广泛的研究，我们想学习两个实例之间的距离度量，以及序数嵌入，我们想在给定实例的欧几里德空间中学习嵌入，以保留比较顺序尽可能。与完全标记的数据不同，三元组比较数据可以以更准确和人性化的方式收集。尽管在许多应用中已经考虑从三元组比较数据中学习，但我们是否可以仅从没有所有标签的三元组比较数据中学习分类器的重要基本问题仍未得到解答。在这封信中，我们通过在经验风险最小化框架下提出分类风险的无偏估计量，对这个重要问题给出了肯定的回答。由于所提出的方法基于经验风险最小化框架，因此它固有的优点是可以轻松应用任何替代损失函数和任何模型，包括神经网络。此外，我们在理论上为所提出的经验风险最小化器建立了估计误差界限。最后，我们提供了实验结果，以表明我们的方法在经验上运行良好并且优于各种基线方法。