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Graph Neural Networks (GNNs) have attracted increasing attention in recent years and have achieved excellent performance in semi-supervised node classification tasks. The success of most GNNs relies on one fundamental assumption, i.e., the…

Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by…

Data-driven algorithms can adapt their internal structure or parameters to inputs from unknown application-specific distributions, by learning from a training sample of inputs. Several recent works have applied this approach to problems in…

Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive performance remains unclear. We introduce a family of premetrics that capture different degrees…

Graphs can model real-world, complex systems by representing entities and their interactions in terms of nodes and edges. To better exploit the graph structure, graph neural networks have been developed, which learn entity and edge…

Graph Neural Networks (GNNs) are widely used for node classification tasks but often fail to generalize when training and test nodes come from different distributions, limiting their practicality. To overcome this, recent approaches adopt…

Graph machine learning methods excel at leveraging pairwise relations present in the data. However, graphs are unable to fully capture the multi-way interactions inherent in many complex systems. An effective way to incorporate them is to…

Graph Neural Networks (GNNs) have proven effective in various medical imaging applications, such as automated disease diagnosis. However, due to the local neighborhood aggregation paradigm in message passing which characterizes these…

Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…

Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…

Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry. While extensive research has been done on developing GNN models with superior performance according to a…

Equivariant networks capture the inductive bias about the symmetry of the learning task by building those symmetries into the model. In this paper, we study how equivariance relates to generalization error utilizing PAC Bayesian analysis…

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class…

Fault detection in power distribution grids is critical for ensuring system reliability and preventing costly outages. Moreover, fault detection methodologies should remain robust to evolving grid topologies caused by factors such as…

Cross-graph node classification, utilizing the abundant labeled nodes from one graph to help classify unlabeled nodes in another graph, can be viewed as a domain generalization problem of graph neural networks (GNNs) due to the structure…

Graph convolutional networks (GCNs) are a family of neural network models that perform inference on graph data by interleaving vertex-wise operations and message-passing exchanges across nodes. Concerning the latter, two key questions…

Graph structure learning is a well-established problem that aims at optimizing graph structures adaptive to specific graph datasets to help message passing neural networks (i.e., GNNs) to yield effective and robust node embeddings. However,…

Causal discovery from observational data is challenging, especially with large datasets and complex relationships. Traditional methods often struggle with scalability and capturing global structural information. To overcome these…

Graph neural networks (GNNs) have been applied into a variety of graph tasks. Most existing work of GNNs is based on the assumption that the given graph data is optimal, while it is inevitable that there exists missing or incomplete edges…

Graph classification is an important area in both modern research and industry. Multiple applications, especially in chemistry and novel drug discovery, encourage rapid development of machine learning models in this area. To keep up with…