When learning graph neural networks (GNNs) in node-level prediction tasks, most existing loss functions are applied for each node independently, even if node embeddings and their labels are non-i.i.d. because of their graph structures. To eliminate such inconsistency, in this study we propose a novel Quasi-Wasserstein (QW) loss with the help of the optimal transport defined on graphs, leading to new learning and prediction paradigms of GNNs. In particular, we design a "Quasi-Wasserstein" distance between the observed multi-dimensional node labels and their estimations, optimizing the label transport defined on graph edges. The estimations are parameterized by a GNN in which the optimal label transport may determine the graph edge weights optionally. By reformulating the strict constraint of the label transport to a Bregman divergence-based regularizer, we obtain the proposed Quasi-Wasserstein loss associated with two efficient solvers learning the GNN together with optimal label transport. When predicting node labels, our model combines the output of the GNN with the residual component provided by the optimal label transport, leading to a new transductive prediction paradigm. Experiments show that the proposed QW loss applies to various GNNs and helps to improve their performance in node-level classification and regression tasks.

翻译：在节点级预测任务中学习图神经网络（GNN）时，大多数现有损失函数独立应用于每个节点，即便由于图结构的存在，节点嵌入及其标签并非独立同分布。为消除这种不一致性，本研究借助图上的最优传输理论，提出一种新颖的拟Wasserstein（QW）损失，从而催生GNN的新学习与预测范式。具体而言，我们设计了观测到的多维节点标签与其估计值之间的“拟Wasserstein”距离，优化定义在图边上的标签传输。该估计值由GNN参数化，其中最优标签传输可选择性地决定图边的权重。通过将标签传输的严格约束重构为基于Bregman散度的正则化项，我们得到所提出的拟Wasserstein损失，并配备两种高效求解器，使GNN与最优标签传输得以联合学习。在预测节点标签时，我们的模型将GNN输出与最优标签传输提供的残差分量相结合，形成一种新的直推式预测范式。实验表明，所提出的QW损失可适用于多种GNN，并有助于提升它们在节点级分类与回归任务中的性能。