Computationally Efficient Wasserstein loss for Structured Labels

Abstract

The problem of estimating the probability distribution of label given a input has been widely studied as Label Distribution Learning (LDL). In this paper, we consider the employment of the Wasserstein distance for LDL where the label has a graph structure. More specifically, we propose to use the Wasserstein distance on tree metrics (tree-Wasserstein) for LDL. The key advantage of the proposed method is that the tree-Wasserstein distance can be efficiently computed only by the tree structure without the distance matrix, while the computation of the Wasserstein distance is expensive. Through experiments on synthetic and real-world datasets, we demonstrate that the proposed method can successfully take the structure of label into account during the training. Moreover, we show that the proposed algorithm is more computationally efficient than the Sinkhorn algorithm based approach.