Despite remarkable success in diverse web-based applications, Graph Neural Networks(GNNs) inherit and further exacerbate historical discrimination and social stereotypes, which critically hinder their deployments in high-stake domains such as online clinical diagnosis, financial crediting, etc. However, current fairness research that primarily craft on i.i.d data, cannot be trivially replicated to non-i.i.d. graph structures with topological dependence among samples. Existing fair graph learning typically favors pairwise constraints to achieve fairness but fails to cast off dimensional limitations and generalize them into multiple sensitive attributes; besides, most studies focus on in-processing techniques to enforce and calibrate fairness, constructing a model-agnostic debiasing GNN framework at the pre-processing stage to prevent downstream misuses and improve training reliability is still largely under-explored. Furthermore, previous work on GNNs tend to enhance either fairness or privacy individually but few probe into their interplays. In this paper, we propose a novel model-agnostic debiasing framework named MAPPING (\underline{M}asking \underline{A}nd \underline{P}runing and Message-\underline{P}assing train\underline{ING}) for fair node classification, in which we adopt the distance covariance($dCov$)-based fairness constraints to simultaneously reduce feature and topology biases in arbitrary dimensions, and combine them with adversarial debiasing to confine the risks of attribute inference attacks. Experiments on real-world datasets with different GNN variants demonstrate the effectiveness and flexibility of MAPPING. Our results show that MAPPING can achieve better trade-offs between utility and fairness, and mitigate privacy risks of sensitive information leakage.
Graph contrastive learning (GCL), learning the node representation by contrasting two augmented graphs in a self-supervised way, has attracted considerable attention. GCL is usually believed to learn the invariant representation. However, does this understanding always hold in practice? In this paper, we first study GCL from the perspective of causality. By analyzing GCL with the structural causal model (SCM), we discover that traditional GCL may not well learn the invariant representations due to the non-causal information contained in the graph. How can we fix it and encourage the current GCL to learn better invariant representations? The SCM offers two requirements and motives us to propose a novel GCL method. Particularly, we introduce the spectral graph augmentation to simulate the intervention upon non-causal factors. Then we design the invariance objective and independence objective to better capture the causal factors. Specifically, (i) the invariance objective encourages the encoder to capture the invariant information contained in causal variables, and (ii) the independence objective aims to reduce the influence of confounders on the causal variables. Experimental results demonstrate the effectiveness of our approach on node classification tasks.
Graph condensation has emerged as an intriguing technique to save the expensive training costs of Graph Neural Networks (GNNs) by substituting a condensed small graph with the original graph. Despite the promising results achieved, previous methods usually employ an entangled paradigm of redundant parameters (nodes, edges, GNNs), which incurs complex joint optimization during condensation. This paradigm has considerably impeded the scalability of graph condensation, making it challenging to condense extremely large-scale graphs and generate high-fidelity condensed graphs. Therefore, we propose to disentangle the condensation process into a two-stage GNN-free paradigm, independently condensing nodes and generating edges while eliminating the need to optimize GNNs at the same time. The node condensation module avoids the complexity of GNNs by focusing on node feature alignment with anchors of the original graph, while the edge translation module constructs the edges of the condensed nodes by transferring the original structure knowledge with neighborhood anchors. This simple yet effective approach achieves at least 10 times faster than state-of-the-art methods with comparable accuracy on medium-scale graphs. Moreover, the proposed DisCo can successfully scale up to the Ogbn-papers100M graph containing over 100 million nodes with flexible reduction rates and improves performance on the second-largest Ogbn-products dataset by over 5%. Extensive downstream tasks and ablation study on five common datasets further demonstrate the effectiveness of the proposed DisCo framework. Our code is available at https://github.com/BangHonor/DisCo.
Graph Neural Networks (GNNs) have shown considerable effectiveness in a variety of graph learning tasks, particularly those based on the message-passing approach in recent years. However, their performance is often constrained by a limited receptive field, a challenge that becomes more acute in the presence of sparse graphs. In light of the power series, which possesses infinite expansion capabilities, we propose a novel Graph Power Filter Neural Network (GPFN) that enhances node classification by employing a power series graph filter to augment the receptive field. Concretely, our GPFN designs a new way to build a graph filter with an infinite receptive field based on the convergence power series, which can be analyzed in the spectral and spatial domains. Besides, we theoretically prove that our GPFN is a general framework that can integrate any power series and capture long-range dependencies. Finally, experimental results on three datasets demonstrate the superiority of our GPFN over state-of-the-art baselines.
Graph neural networks (GNN) are a powerful tool for combining imaging and non-imaging medical information for node classification tasks. Cross-network node classification extends GNN techniques to account for domain drift, allowing for node classification on an unlabeled target network. In this paper we present OTGCN, a powerful, novel approach to cross-network node classification. This approach leans on concepts from graph convolutional networks to harness insights from graph data structures while simultaneously applying strategies rooted in optimal transport to correct for the domain drift that can occur between samples from different data collection sites. This blended approach provides a practical solution for scenarios with many distinct forms of data collected across different locations and equipment. We demonstrate the effectiveness of this approach at classifying Autism Spectrum Disorder subjects using a blend of imaging and non-imaging data.
Local neighborhoods play a crucial role in embedding generation in graph-based learning. It is commonly believed that nodes ought to have embeddings that resemble those of their neighbors. In this research, we try to carefully expand the concept of similarity from nearby neighborhoods to the entire graph. We provide an extension of similarity that is based on transitivity relations, which enables Graph Neural Networks (GNNs) to capture both global similarities and local similarities over the whole graph. We introduce Transitivity Graph Neural Network (TransGNN), which more than local node similarities, takes into account global similarities by distinguishing strong transitivity relations from weak ones and exploiting them. We evaluate our model over several real-world datasets and showed that it considerably improves the performance of several well-known GNN models, for tasks such as node classification.
We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the need for more effective and specialized approaches grows with the production of graph data with diverse characteristics. In particular, real-world multiplex graphs may exhibit a high number of dimensions, making it difficult to construct a single consensus representation. Furthermore, important information can be hidden in complex latent structures scattered in multiple dimensions. To address these issues, we propose HMGE, a novel embedding method based on hierarchical aggregation for high-dimensional multiplex graphs. Hierarchical aggregation consists of learning a hierarchical combination of the graph dimensions and refining the embeddings at each hierarchy level. Non-linear combinations are computed from previous ones, thus uncovering complex information and latent structures hidden in the multiplex graph dimensions. Moreover, we leverage mutual information maximization between local patches and global summaries to train the model without supervision. This allows to capture of globally relevant information present in diverse locations of the graph. Detailed experiments on synthetic and real-world data illustrate the suitability of our approach to downstream supervised tasks, including link prediction and node classification.
This study utilizes community structures to address node degree biases in message-passing (MP) via learnable graph augmentations and novel graph transformers. Recent augmentation-based methods showed that MP neural networks often perform poorly on low-degree nodes, leading to degree biases due to a lack of messages reaching low-degree nodes. Despite their success, most methods use heuristic or uniform random augmentations, which are non-differentiable and may not always generate valuable edges for learning representations. In this paper, we propose Community-aware Graph Transformers, namely CGT, to learn degree-unbiased representations based on learnable augmentations and graph transformers by extracting within community structures. We first design a learnable graph augmentation to generate more within-community edges connecting low-degree nodes through edge perturbation. Second, we propose an improved self-attention to learn underlying proximity and the roles of nodes within the community. Third, we propose a self-supervised learning task that could learn the representations to preserve the global graph structure and regularize the graph augmentations. Extensive experiments on various benchmark datasets showed CGT outperforms state-of-the-art baselines and significantly improves the node degree biases. The source code is available at https://github.com/NSLab-CUK/Community-aware-Graph-Transformer.
Graph summarization as a preprocessing step is an effective and complementary technique for scalable graph neural network (GNN) training. In this work, we propose the Coarsening Via Convolution Matching (CONVMATCH) algorithm and a highly scalable variant, A-CONVMATCH, for creating summarized graphs that preserve the output of graph convolution. We evaluate CONVMATCH on six real-world link prediction and node classification graph datasets, and show it is efficient and preserves prediction performance while significantly reducing the graph size. Notably, CONVMATCH achieves up to 95% of the prediction performance of GNNs on node classification while trained on graphs summarized down to 1% the size of the original graph. Furthermore, on link prediction tasks, CONVMATCH consistently outperforms all baselines, achieving up to a 2x improvement.
Heterogeneous graph neural networks (HGNs) are prominent approaches to node classification tasks on heterogeneous graphs. Despite the superior performance, insights about the predictions made from HGNs are obscure to humans. Existing explainability techniques are mainly proposed for GNNs on homogeneous graphs. They focus on highlighting salient graph objects to the predictions whereas the problem of how these objects affect the predictions remains unsolved. Given heterogeneous graphs with complex structures and rich semantics, it is imperative that salient objects can be accompanied with their influence paths to the predictions, unveiling the reasoning process of HGNs. In this paper, we develop xPath, a new framework that provides fine-grained explanations for black-box HGNs specifying a cause node with its influence path to the target node. In xPath, we differentiate the influence of a node on the prediction w.r.t. every individual influence path, and measure the influence by perturbing graph structure via a novel graph rewiring algorithm. Furthermore, we introduce a greedy search algorithm to find the most influential fine-grained explanations efficiently. Empirical results on various HGNs and heterogeneous graphs show that xPath yields faithful explanations efficiently, outperforming the adaptations of advanced GNN explanation approaches.
Knowledge Graphs (KGs) such as Resource Description Framework (RDF) data represent relationships between various entities through the structure of triples (<subject, predicate, object>). Knowledge graph embedding (KGE) is crucial in machine learning applications, specifically in node classification and link prediction tasks. KGE remains a vital research topic within the semantic web community. RDF-star introduces the concept of a quoted triple (QT), a specific form of triple employed either as the subject or object within another triple. Moreover, RDF-star permits a QT to act as compositional entities within another QT, thereby enabling the representation of recursive, hyper-relational KGs with nested structures. However, existing KGE models fail to adequately learn the semantics of QTs and entities, primarily because they do not account for RDF-star graphs containing multi-leveled nested QTs and QT-QT relationships. This study introduces RDF-star2Vec, a novel KGE model specifically designed for RDF-star graphs. RDF-star2Vec introduces graph walk techniques that enable probabilistic transitions between a QT and its compositional entities. Feature vectors for QTs, entities, and relations are derived from generated sequences through the structured skip-gram model. Additionally, we provide a dataset and a benchmarking framework for data mining tasks focused on complex RDF-star graphs. Evaluative experiments demonstrated that RDF-star2Vec yielded superior performance compared to recent extensions of RDF2Vec in various tasks including classification, clustering, entity relatedness, and QT similarity.
Recent studies on Graph Neural Networks(GNNs) provide both empirical and theoretical evidence supporting their effectiveness in capturing structural patterns on both homophilic and certain heterophilic graphs. Notably, most real-world homophilic and heterophilic graphs are comprised of a mixture of nodes in both homophilic and heterophilic structural patterns, exhibiting a structural disparity. However, the analysis of GNN performance with respect to nodes exhibiting different structural patterns, e.g., homophilic nodes in heterophilic graphs, remains rather limited. In the present study, we provide evidence that Graph Neural Networks(GNNs) on node classification typically perform admirably on homophilic nodes within homophilic graphs and heterophilic nodes within heterophilic graphs while struggling on the opposite node set, exhibiting a performance disparity. We theoretically and empirically identify effects of GNNs on testing nodes exhibiting distinct structural patterns. We then propose a rigorous, non-i.i.d PAC-Bayesian generalization bound for GNNs, revealing reasons for the performance disparity, namely the aggregated feature distance and homophily ratio difference between training and testing nodes. Furthermore, we demonstrate the practical implications of our new findings via (1) elucidating the effectiveness of deeper GNNs; and (2) revealing an over-looked distribution shift factor on graph out-of-distribution problem and proposing a new scenario accordingly.
When handling streaming graphs, existing graph representation learning models encounter a catastrophic forgetting problem, where previously learned knowledge of these models is easily overwritten when learning with newly incoming graphs. In response, Continual Graph Learning (CGL) emerges as a novel paradigm enabling graph representation learning from streaming graphs. Our prior work, Condense and Train (CaT) is a replay-based CGL framework with a balanced continual learning procedure, which designs a small yet effective memory bankn for replaying. Although the CaT alleviates the catastrophic forgetting problem, there exist three issues: (1) The graph condensation only focuses on labelled nodes while neglecting abundant information carried by unlabelled nodes; (2) The continual training scheme of the CaT overemphasises on the previously learned knowledge, limiting the model capacity to learn from newly added memories; (3) Both the condensation process and replaying process of the CaT are time-consuming. In this paper, we propose a PsUdo-label guided Memory bAnk (PUMA) CGL framework, extending from the CaT to enhance its efficiency and effectiveness by overcoming the above-mentioned weaknesses and limits. To fully exploit the information in a graph, PUMA expands the coverage of nodes during graph condensation with both labelled and unlabelled nodes. Furthermore, a training-from-scratch strategy is proposed to upgrade the previous continual learning scheme for a balanced training between the historical and the new graphs. Besides, PUMA uses a one-time prorogation and wide graph encoders to accelerate the graph condensation and the graph encoding process in the training stage to improve the efficiency of the whole framework. Extensive experiments on six datasets for the node classification task demonstrate the state-of-the-art performance and efficiency over existing methods.
The Adam optimizer is a popular choice in contemporary deep learning, due to its strong empirical performance. However we observe that in privacy sensitive scenarios, the traditional use of Differential Privacy (DP) with the Adam optimizer leads to sub-optimal performance on several tasks. We find that this performance degradation is due to a DP bias in Adam's second moment estimator, introduced by the addition of independent noise in the gradient computation to enforce DP guarantees. This DP bias leads to a different scaling for low variance parameter updates, that is inconsistent with the behavior of non-private Adam. We propose DP-AdamBC, an optimization algorithm which removes the bias in the second moment estimation and retrieves the expected behaviour of Adam. Empirically, DP-AdamBC significantly improves the optimization performance of DP-Adam by up to 3.5% in final accuracy in image, text, and graph node classification tasks.
Recently, many carefully crafted graph representation learning methods have achieved impressive performance on either strong heterophilic or homophilic graphs, but not both. Therefore, they are incapable of generalizing well across real-world graphs with different levels of homophily. This is attributed to their neglect of homophily in heterophilic graphs, and vice versa. In this paper, we propose a two-fold filtering mechanism to extract homophily in heterophilic graphs and vice versa. In particular, we extend the graph heat equation to perform heterophilic aggregation of global information from a long distance. The resultant filter can be exactly approximated by the Possion-Charlier (PC) polynomials. To further exploit information at multiple orders, we introduce a powerful graph convolution PC-Conv and its instantiation PCNet for the node classification task. Compared with state-of-the-art GNNs, PCNet shows competitive performance on well-known homophilic and heterophilic graphs. Our implementation is available at https://github.com/uestclbh/PC-Conv.
Graph Neural Networks (GNNs) have become mainstream methods for solving the semi-supervised node classification problem. However, due to the uneven location distribution of labeled nodes in the graph, labeled nodes are only accessible to a small portion of unlabeled nodes, leading to the \emph{under-reaching} issue. In this study, we firstly reveal under-reaching by conducting an empirical investigation on various well-known graphs. Then, we demonstrate that under-reaching results in unsatisfactory distribution alignment between labeled and unlabeled nodes through systematic experimental analysis, significantly degrading GNNs' performance. To tackle under-reaching for GNNs, we propose an architecture-agnostic method dubbed NodeMixup. The fundamental idea is to (1) increase the reachability of labeled nodes by labeled-unlabeled pairs mixup, (2) leverage graph structures via fusing the neighbor connections of intra-class node pairs to improve performance gains of mixup, and (3) use neighbor label distribution similarity incorporating node degrees to determine sampling weights for node mixup. Extensive experiments demonstrate the efficacy of NodeMixup in assisting GNNs in handling under-reaching. The source code is available at \url{https://github.com/WeigangLu/NodeMixup}.
There has been significant progress in improving the performance of graph neural networks (GNNs) through enhancements in graph data, model architecture design, and training strategies. For fairness in graphs, recent studies achieve fair representations and predictions through either graph data pre-processing (e.g., node feature masking, and topology rewiring) or fair training strategies (e.g., regularization, adversarial debiasing, and fair contrastive learning). How to achieve fairness in graphs from the model architecture perspective is less explored. More importantly, GNNs exhibit worse fairness performance compared to multilayer perception since their model architecture (i.e., neighbor aggregation) amplifies biases. To this end, we aim to achieve fairness via a new GNN architecture. We propose \textsf{F}air \textsf{M}essage \textsf{P}assing (FMP) designed within a unified optimization framework for GNNs. Notably, FMP \textit{explicitly} renders sensitive attribute usage in \textit{forward propagation} for node classification task using cross-entropy loss without data pre-processing. In FMP, the aggregation is first adopted to utilize neighbors' information and then the bias mitigation step explicitly pushes demographic group node presentation centers together. In this way, FMP scheme can aggregate useful information from neighbors and mitigate bias to achieve better fairness and prediction tradeoff performance. Experiments on node classification tasks demonstrate that the proposed FMP outperforms several baselines in terms of fairness and accuracy on three real-world datasets. The code is available in {\url{https://github.com/zhimengj0326/FMP}}.
This paper introduces a new approach to address the issue of class imbalance in graph neural networks (GNNs) for learning on graph-structured data. Our approach integrates imbalanced node classification and Bias-Variance Decomposition, establishing a theoretical framework that closely relates data imbalance to model variance. We also leverage graph augmentation technique to estimate the variance, and design a regularization term to alleviate the impact of imbalance. Exhaustive tests are conducted on multiple benchmarks, including naturally imbalanced datasets and public-split class-imbalanced datasets, demonstrating that our approach outperforms state-of-the-art methods in various imbalanced scenarios. This work provides a novel theoretical perspective for addressing the problem of imbalanced node classification in GNNs.
Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering remarkable performance across various tasks, e.g., hypergraph node classification. However, these models struggle to capture global structural information due to their reliance on local message passing. To address this challenge, we propose a novel hypergraph learning framework, HyperGraph Transformer (HyperGT). HyperGT uses a Transformer-based neural network architecture to effectively consider global correlations among all nodes and hyperedges. To incorporate local structural information, HyperGT has two distinct designs: i) a positional encoding based on the hypergraph incidence matrix, offering valuable insights into node-node and hyperedge-hyperedge interactions; and ii) a hypergraph structure regularization in the loss function, capturing connectivities between nodes and hyperedges. Through these designs, HyperGT achieves comprehensive hypergraph representation learning by effectively incorporating global interactions while preserving local connectivity patterns. Extensive experiments conducted on real-world hypergraph node classification tasks showcase that HyperGT consistently outperforms existing methods, establishing new state-of-the-art benchmarks. Ablation studies affirm the effectiveness of the individual designs of our model.
Transformers have recently emerged as powerful neural networks for graph learning, showcasing state-of-the-art performance on several graph property prediction tasks. However, these results have been limited to small-scale graphs, where the computational feasibility of the global attention mechanism is possible. The next goal is to scale up these architectures to handle very large graphs on the scale of millions or even billions of nodes. With large-scale graphs, global attention learning is proven impractical due to its quadratic complexity w.r.t. the number of nodes. On the other hand, neighborhood sampling techniques become essential to manage large graph sizes, yet finding the optimal trade-off between speed and accuracy with sampling techniques remains challenging. This work advances representation learning on single large-scale graphs with a focus on identifying model characteristics and critical design constraints for developing scalable graph transformer (GT) architectures. We argue such GT requires layers that can adeptly learn both local and global graph representations while swiftly sampling the graph topology. As such, a key innovation of this work lies in the creation of a fast neighborhood sampling technique coupled with a local attention mechanism that encompasses a 4-hop reception field, but achieved through just 2-hop operations. This local node embedding is then integrated with a global node embedding, acquired via another self-attention layer with an approximate global codebook, before finally sent through a downstream layer for node predictions. The proposed GT framework, named LargeGT, overcomes previous computational bottlenecks and is validated on three large-scale node classification benchmarks. We report a 3x speedup and 16.8% performance gain on ogbn-products and snap-patents, while we also scale LargeGT on ogbn-papers100M with a 5.9% performance improvement.