Graphs are one of the most natural representations of many real-world data, such as social networks, chemical molecules, and transportation networks. Graph neural networks (GNNs) are deep neural networks (DNNs) that are specially designed for graphs and have aroused great research interest. Recently, GNNs have been theoretically and empirically proven to be effective in learning graph representations and have been widely applied in many scenarios, such as recommendation and drug discovery. Despite its great success in numerous graph-related tasks, GNNs still face a tremendous challenge in terms of out-of-distribution generalization. Specifically, it has been observed that significant performance gaps for GNNs exist between the training graph set and the test graph set in some graph-related tasks. In addition, graph samples can be very diverse, even though coming from the same dataset. They can be different from each other in not only node attributes but graph structures, which makes the out-of-distribution generalization problem in GNNs more challenging and complex than that in traditional deep learning-based methods. Apart from the out-of-distribution generalization problem, GNNs also come across other kinds of challenges when applied in different application scenarios, such as data sparsity and knowledge transfer in the recommendation task. In this dissertation, we aim at alleviating the out-of-distribution generalization problem in GNNs. In particular, two novel frameworks are proposed to improve GNN's out-of-distribution generalization ability from two perspectives, i.e., a novel training perspective, and an advanced learning perspective. Meanwhile, we design a novel GNN-based method to solve the data sparsity challenge in the recommendation application. In addition, we propose an adaptive pre-training framework based on the new GNN-based recommendation method and thus increase the abilities of GNNs in terms of generalization and knowledge transfer in the real-world application of recommendations.
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