Recent years have witnessed significant advancements in machine learning methods on graphs. However, transferring knowledge effectively from one graph to another remains a critical challenge. This highlights the need for algorithms capable of applying information extracted from a source graph to an unlabeled target graph, a task known as unsupervised graph domain adaptation (GDA). One key difficulty in unsupervised GDA is conditional shift, which hinders transferability. In this paper, we show that conditional shift can be observed only if there exists local dependencies among node features. To support this claim, we perform a rigorous analysis and also further provide generalization bounds of GDA when dependent node features are modeled using markov chains. Guided by the theoretical findings, we propose to improve GDA by decorrelating node features, which can be specifically implemented through decorrelated GCN layers and graph transformer layers. Our experimental results demonstrate the effectiveness of this approach, showing not only substantial performance enhancements over baseline GDA methods but also clear visualizations of small intra-class distances in the learned representations. Our code is available at https://github.com/TechnologyAiGroup/DFT.

Ensemble learning is a pivotal machine learning strategy that combines multiple base learners to achieve prediction accuracy surpassing that of any individual model. Despite its effectiveness, large-scale ensemble learning consumes a considerable amount of resources. Ensemble pruning addresses this issue by selecting a subset of base learners from the original ensemble to form a sub-ensemble, while maintaining or even improving the performance of the original model. However, existing ensemble pruning strategies often rely on heuristic solutions that may fail to capture complex interactions among base learners. To address this limitation, in this work, we model the base learners in an ensemble as a weighted and attributed graph, where node features represent characteristics of each learner and edge weights represent relationships between the base learners. Leveraging this representation, we propose a novel ensemble pruning method based on graph neural networks (GNNs). Our approach incorporates specialized GNN architectures designed for bagging and boosting ensembles. Experimental results demonstrate that our method not only improves prediction accuracy but also significantly reduces inference time across diverse datasets. Our implementation is available at the anonymous repository: https://github.com/TechnologyAiGroup/GRE.

Hyperbolic neural networks (HNNs) are emerging as a promising tool for representing data embedded in non-Euclidean geometries, yet their adoption has been hindered by challenges related to stability and robustness. In this work, we conduct a rigorous Lipschitz analysis for HNNs and propose using Lipschitz regularization as a novel strategy to enhance their robustness. Our comprehensive investigation spans both the Poincaré ball model and the hyperboloid model, establishing Lipschitz bounds for HNN layers. Importantly, our analysis provides detailed insights into the behavior of the Lipschitz bounds as they relate to feature norms, particularly distinguishing between scenarios where features have unit norms and those with large norms. Further, we study regularization using the derived Lipschitz bounds. Our empirical validations demonstrate consistent improvements in HNN robustness against noisy perturbations.

Graph neural networks (GNNs) have shown considerable promise for graph-structured data. However, they are also known to be unstable and vulnerable to perturbations and attacks. Recently, the Lipschitz constant has been adopted as a control on the stability of Euclidean neural networks, but calculating the exact constant is also known to be difficult even for very shallow networks. In this paper, we extend the Lipschitz analysis to graphs by providing a systematic scheme for estimating upper bounds of the Lipschitz constants of GNNs. We also derive concrete bounds for widely used GNN architectures including GCN, GraphSAGE and GAT. We then use these Lipschitz bounds for regularized GNN training for improved stability. Our numerical results on Lipschitz regularization of GNNs not only illustrate enhanced test accuracy under random noise, but also show consistent improvement for state-of-the-art defense methods against adversarial attacks.