Graphon models provide a flexible nonparametric framework for estimating latent connectivity probabilities in networks, enabling a range of downstream applications such as link prediction and data augmentation. However, accurate graphon estimation typically requires a large graph, whereas in practice, one often only observes a small-sized network. One approach to addressing this issue is to adopt a transfer learning framework, which aims to improve estimation in a small target graph by leveraging structural information from a larger, related source graph. In this paper, we propose a novel method, namely GTRANS, a transfer learning framework that integrates neighborhood smoothing and Gromov-Wasserstein optimal transport to align and transfer structural patterns between graphs. To prevent negative transfer, GTRANS includes an adaptive debiasing mechanism that identifies and corrects for target-specific deviations via residual smoothing. We provide theoretical guarantees on the stability of the estimated alignment matrix and demonstrate the effectiveness of GTRANS in improving the accuracy of target graph estimation through extensive synthetic and real data experiments. These improvements translate directly to enhanced performance in downstream applications, such as the graph classification task and the link prediction task.

Unsupervised Graph Domain Adaptation has become a promising paradigm for transferring knowledge from a fully labeled source graph to an unlabeled target graph. Existing graph domain adaptation models primarily focus on the closed-set setting, where the source and target domains share the same label spaces. However, this assumption might not be practical in the real-world scenarios, as the target domain might include classes that are not present in the source domain. In this paper, we investigate the problem of unsupervised open-set graph domain adaptation, where the goal is to not only correctly classify target nodes into the known classes, but also recognize previously unseen node types into the unknown class. Towards this end, we propose a novel framework called GraphRTA, which conducts reprogramming on both the graph and model sides. Specifically, we reprogram the graph by modifying target graph structure and node features, which facilitates better separation of known and unknown classes. Meanwhile, we also perform model reprogramming by pruning domain-specific parameters to reduce bias towards the source graph while preserving parameters that capture transferable patterns across graphs. Additionally, we extend the classifier with an extra dimension for the unknown class, thus eliminating the need of manually specified threshold in open-set recognition. Comprehensive experiments on several public datasets demonstrate that our proposed model can achieve satisfied performance compared with recent state-of-the-art baselines.

Graph neural networks (GNNs) have achieved superior performance in various applications, but training dedicated GNNs can be costly for large-scale graphs. Some recent work started to study the pre-training of GNNs. However, none of them provide theoretical insights into the design of their frameworks, or clear requirements and guarantees towards their transferability. In this work, we establish a theoretically grounded and practically useful framework for the transfer learning of GNNs. Firstly, we propose a novel view towards the essential graph information and advocate the capturing of it as the goal of transferable GNN training, which motivates the design of EGI (Ego-Graph Information maximization) to analytically achieve this goal. Secondly, when node features are structure-relevant, we conduct an analysis of EGI transferability regarding the difference between the local graph Laplacians of the source and target graphs. We conduct controlled synthetic experiments to directly justify our theoretical conclusions. Comprehensive experiments on two real-world network datasets show consistent results in the analyzed setting of direct-transfering, while those on large-scale knowledge graphs show promising results in the more practical setting of transfering with fine-tuning.1

Transferable graph learning involves knowledge transferability from a source graph to a relevant target graph. The major challenge of transferable graph learning is the distribution shift between source and target graphs induced by individual node attributes and complex graph structures. To solve this problem, in this paper, we propose a generic graph-structured Gaussian process framework (GraphGP) for adaptively transferring knowledge across graphs with either homophily or heterophily assumptions. Specifically, GraphGP is derived from a novel graph structure-aware neural network in the limit on the layer width. The generalization analysis of GraphGP explicitly investigates the connection between knowledge transferability and graph domain similarity. Extensive experiments on several transferable graph learning benchmarks demonstrate the efficacy of GraphGP over state-of-the-art Gaussian process baselines.

Graphon models provide a flexible nonparametric framework for estimating latent connectivity probabilities in networks, enabling a range of downstream applications such as link prediction and data augmentation. However, accurate graphon estimation typically requires a large graph, whereas in practice, one often only observes a small-sized network. One approach to addressing this issue is to adopt a transfer learning framework, which aims to improve estimation in a small target graph by leveraging structural information from a larger, related source graph. In this paper, we propose a novel method, namely GTRANS, a transfer learning framework that integrates neighborhood smoothing and Gromov-Wasserstein optimal transport to align and transfer structural patterns between graphs. To prevent negative transfer, GTRANS includes an adaptive debiasing mechanism that identifies and corrects for target-specific deviations via residual smoothing. We provide theoretical guarantees on the stability of the estimated alignment matrix and demonstrate the effectiveness of GTRANS in improving the accuracy of target graph estimation through extensive synthetic and real data experiments. These improvements translate directly to enhanced performance in downstream applications, such as the graph classification task and the link prediction task.

Unsupervised Graph Domain Adaptation has become a promisin g paradigm for transferring knowledge from a fully labeled source graph to an unlabeled target graph. Existing graph domain adaptation models primarily f ocus on the closed-set setting, where the source and target domains share the same l abel spaces. However, this assumption might not be practical in the real-wor ld scenarios, as the target domain might include classes that are not present in t he source domain. In this paper, we investigate the problem of unsupervised open -set graph domain adaptation, where the goal is to not only correctly classify target nodes into the known classes, but also recognize previously unseen node ty pes into the unknown class. Towards this end, we propose a novel framework called GraphRT A, which conducts reprogramming on both the graph and model sides. Sp ecifically, we reprogram the graph by modifying target graph structure and no de features, which facilitates better separation of known and unknown classes . Meanwhile, we also perform model reprogramming by pruning domain-specific par ameters to reduce bias towards the source graph while preserving parameters t hat capture transferable patterns across graphs. Additionally, we extend the cl assifier with an extra dimension for the unknown class, thus eliminating the need o f manually specified threshold in open-set recognition. Comprehensive experim ents on several public datasets demonstrate that our proposed model can achieve sa tisfied performance compared with recent state-of-the-art baselines.