Graph neural networks (GNNs) have shown superiority in many prediction tasks over graphs due to their impressive capability of capturing nonlinear relations in graph-structured data. However, for node classification tasks, often, only marginal improvement of GNNs over their linear counterparts has been observed. Previous works provide very few understandings of this phenomenon. In this work, we resort to Bayesian learning to deeply investigate the functions of non-linearity in GNNs for node classification tasks. Given a graph generated from the statistical model CSBM, we observe that the max-a-posterior estimation of a node label given its own and neighbors' attributes consists of two types of non-linearity, a possibly non-linear transformation of node attributes and a ReLU-activated feature aggregation from neighbors. The latter surprisingly matches the type of non-linearity used in many GNN models. By further imposing Gaussian assumption on node attributes, we prove that the superiority of those ReLU activations is only significant when the node attributes are far more informative than the graph structure, which nicely matches many previous empirical observations. A similar argument can be achieved when there is a distribution shift of node attributes between the training and testing datasets. Finally, we verify our theory on both synthetic and real-world networks.
Contrastive learning has shown great promise in the field of graph representation learning. By manually constructing positive/negative samples, most graph contrastive learning methods rely on the vector inner product based similarity metric to distinguish the samples for graph representation. However, the handcrafted sample construction (e.g., the perturbation on the nodes or edges of the graph) may not effectively capture the intrinsic local structures of the graph. Also, the vector inner product based similarity metric cannot fully exploit the local structures of the graph to characterize the graph difference well. To this end, in this paper, we propose a novel adaptive subgraph generation based contrastive learning framework for efficient and robust self-supervised graph representation learning, and the optimal transport distance is utilized as the similarity metric between the subgraphs. It aims to generate contrastive samples by capturing the intrinsic structures of the graph and distinguish the samples based on the features and structures of subgraphs simultaneously. Specifically, for each center node, by adaptively learning relation weights to the nodes of the corresponding neighborhood, we first develop a network to generate the interpolated subgraph. We then construct the positive and negative pairs of subgraphs from the same and different nodes, respectively. Finally, we employ two types of optimal transport distances (i.e., Wasserstein distance and Gromov-Wasserstein distance) to construct the structured contrastive loss. Extensive node classification experiments on benchmark datasets verify the effectiveness of our graph contrastive learning method.
Active speaker detection (ASD) in videos with multiple speakers is a challenging task as it requires learning effective audiovisual features and spatial-temporal correlations over long temporal windows. In this paper, we present SPELL, a novel spatial-temporal graph learning framework that can solve complex tasks such as ASD. To this end, each person in a video frame is first encoded in a unique node for that frame. Nodes corresponding to a single person across frames are connected to encode their temporal dynamics. Nodes within a frame are also connected to encode inter-person relationships. Thus, SPELL reduces ASD to a node classification task. Importantly, SPELL is able to reason over long temporal contexts for all nodes without relying on computationally expensive fully connected graph neural networks. Through extensive experiments on the AVA-ActiveSpeaker dataset, we demonstrate that learning graph-based representations can significantly improve the active speaker detection performance owing to its explicit spatial and temporal structure. SPELL outperforms all previous state-of-the-art approaches while requiring significantly lower memory and computational resources. Our code is publicly available at https://github.com/SRA2/SPELL
Personalized PageRank (PPR) is a fundamental tool in unsupervised learning of graph representations such as node ranking, labeling, and graph embedding. However, while data privacy is one of the most important recent concerns, existing PPR algorithms are not designed to protect user privacy. PPR is highly sensitive to the input graph edges: the difference of only one edge may cause a big change in the PPR vector, potentially leaking private user data. In this work, we propose an algorithm which outputs an approximate PPR and has provably bounded sensitivity to input edges. In addition, we prove that our algorithm achieves similar accuracy to non-private algorithms when the input graph has large degrees. Our sensitivity-bounded PPR directly implies private algorithms for several tools of graph learning, such as, differentially private (DP) PPR ranking, DP node classification, and DP node embedding. To complement our theoretical analysis, we also empirically verify the practical performances of our algorithms.
Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2\%$\uparrow$ in prediction accuracy over four datasets therein.
As the field of Graph Neural Networks (GNN) continues to grow, it experiences a corresponding increase in the need for large, real-world datasets to train and test new GNN models on challenging, realistic problems. Unfortunately, such graph datasets are often generated from online, highly privacy-restricted ecosystems, which makes research and development on these datasets hard, if not impossible. This greatly reduces the amount of benchmark graphs available to researchers, causing the field to rely only on a handful of publicly-available datasets. To address this problem, we introduce a novel graph generative model, Computation Graph Transformer (CGT) that learns and reproduces the distribution of real-world graphs in a privacy-controlled way. More specifically, CGT (1) generates effective benchmark graphs on which GNNs show similar task performance as on the source graphs, (2) scales to process large-scale graphs, (3) incorporates off-the-shelf privacy modules to guarantee end-user privacy of the generated graph. Extensive experiments across a vast body of graph generative models show that only our model can successfully generate privacy-controlled, synthetic substitutes of large-scale real-world graphs that can be effectively used to benchmark GNN models.
When dealing with tabular data, models based on decision trees are a popular choice due to their high accuracy on these data types, their ease of application, and explainability properties. However, when it comes to graph-structured data, it is not clear how to apply them effectively, in a way that incorporates the topological information with the tabular data available on the vertices of the graph. To address this challenge, we introduce TREE-G. TREE-G modifies standard decision trees, by introducing a novel split function that is specialized for graph data. Not only does this split function incorporate the node features and the topological information, but it also uses a novel pointer mechanism that allows split nodes to use information computed in previous splits. Therefore, the split function adapts to the predictive task and the graph at hand. We analyze the theoretical properties of TREE-G and demonstrate its benefits empirically on multiple graph and vertex prediction benchmarks. In these experiments, TREE-G consistently outperforms other tree-based models and often outperforms other graph-learning algorithms such as Graph Neural Networks (GNNs) and Graph Kernels, sometimes by large margins. Moreover, TREE-Gs models and their predictions can be explained and visualized
Graph neural networks (GNNs) have gained traction over the past few years for their superior performance in numerous machine learning tasks. Graph Convolutional Neural Networks (GCN) are a common variant of GNNs that are known to have high performance in semi-supervised node classification (SSNC), and work well under the assumption of homophily. Recent literature has highlighted that GCNs can achieve strong performance on heterophilous graphs under certain "special conditions". These arguments motivate us to understand why, and how, GCNs learn to perform SSNC. We find a positive correlation between similarity of latent node embeddings of nodes within a class and the performance of a GCN. Our investigation on underlying graph structures of a dataset finds that a GCN's SSNC performance is significantly influenced by the consistency and uniqueness in neighborhood structure of nodes within a class.
Graph convolution is a recent scalable method for performing deep feature learning on attributed graphs by aggregating local node information over multiple layers. Such layers only consider attribute information of node neighbors in the forward model and do not incorporate knowledge of global network structure in the learning task. In particular, the modularity function provides a convenient source of information about the community structure of networks. In this work we investigate the effect on the quality of learned representations by the incorporation of community structure preservation objectives of networks in the graph convolutional model. We incorporate the objectives in two ways, through an explicit regularization term in the cost function in the output layer and as an additional loss term computed via an auxiliary layer. We report the effect of community structure preserving terms in the graph convolutional architectures. Experimental evaluation on two attributed bibilographic networks showed that the incorporation of the community-preserving objective improves semi-supervised node classification accuracy in the sparse label regime.
Embedding knowledge graphs into low-dimensional spaces is a popular method for applying approaches, such as link prediction or node classification, to these databases. This embedding process is very costly in terms of both computational time and space. Part of the reason for this is the optimisation of hyperparameters, which involves repeatedly sampling, by random, guided, or brute-force selection, from a large hyperparameter space and testing the resulting embeddings for their quality. However, not all hyperparameters in this search space will be equally important. In fact, with prior knowledge of the relative importance of the hyperparameters, some could be eliminated from the search altogether without significantly impacting the overall quality of the outputted embeddings. To this end, we ran a Sobol sensitivity analysis to evaluate the effects of tuning different hyperparameters on the variance of embedding quality. This was achieved by performing thousands of embedding trials, each time measuring the quality of embeddings produced by different hyperparameter configurations. We regressed the embedding quality on those hyperparameter configurations, using this model to generate Sobol sensitivity indices for each of the hyperparameters. By evaluating the correlation between Sobol indices, we find substantial variability in the hyperparameter sensitivities between knowledge graphs, with differing dataset characteristics being the probable cause of these inconsistencies. As an additional contribution of this work we identify several relations in the UMLS knowledge graph that may cause data leakage via inverse relations, and derive and present UMLS-43, a leakage-robust variant of that graph.
Following the success of convolution on non-Euclidean space, the corresponding pooling approaches have also been validated on various tasks regarding graphs. However, because of the fixed compression quota and stepwise pooling design, these hierarchical pooling methods still suffer from local structure damage and suboptimal problem. In this work, inspired by structural entropy, we propose a hierarchical pooling approach, SEP, to tackle the two issues. Specifically, without assigning the layer-specific compression quota, a global optimization algorithm is designed to generate the cluster assignment matrices for pooling at once. Then, we present an illustration of the local structure damage from previous methods in the reconstruction of ring and grid synthetic graphs. In addition to SEP, we further design two classification models, SEP-G and SEP-N for graph classification and node classification, respectively. The results show that SEP outperforms state-of-the-art graph pooling methods on graph classification benchmarks and obtains superior performance on node classifications.
Self-supervised learning (especially contrastive learning) methods on heterogeneous graphs can effectively get rid of the dependence on supervisory data. Meanwhile, most existing representation learning methods embed the heterogeneous graphs into a single geometric space, either Euclidean or hyperbolic. This kind of single geometric view is usually not enough to observe the complete picture of heterogeneous graphs due to their rich semantics and complex structures. Under these observations, this paper proposes a novel self-supervised learning method, termed as Geometry Contrastive Learning (GCL), to better represent the heterogeneous graphs when supervisory data is unavailable. GCL views a heterogeneous graph from Euclidean and hyperbolic perspective simultaneously, aiming to make a strong merger of the ability of modeling rich semantics and complex structures, which is expected to bring in more benefits for downstream tasks. GCL maximizes the mutual information between two geometric views by contrasting representations at both local-local and local-global semantic levels. Extensive experiments on four benchmarks data sets show that the proposed approach outperforms the strong baselines, including both unsupervised methods and supervised methods, on three tasks, including node classification, node clustering and similarity search.
Representation learning on graphs, also called graph embedding, has demonstrated its significant impact on a series of machine learning applications such as classification, prediction and recommendation. However, existing work has largely ignored the rich information contained in the properties (or attributes) of both nodes and edges of graphs in modern applications, e.g., those represented by property graphs. To date, most existing graph embedding methods either focus on plain graphs with only the graph topology, or consider properties on nodes only. We propose PGE, a graph representation learning framework that incorporates both node and edge properties into the graph embedding procedure. PGE uses node clustering to assign biases to differentiate neighbors of a node and leverages multiple data-driven matrices to aggregate the property information of neighbors sampled based on a biased strategy. PGE adopts the popular inductive model for neighborhood aggregation. We provide detailed analyses on the efficacy of our method and validate the performance of PGE by showing how PGE achieves better embedding results than the state-of-the-art graph embedding methods on benchmark applications such as node classification and link prediction over real-world datasets.
Learning unbiased node representations under class-imbalanced graph data is challenging due to interactions between adjacent nodes. Existing studies have in common that they compensate the minor class nodes `as a group' according to their overall quantity (ignoring node connections in graph), which inevitably increase the false positive cases for major nodes. We hypothesize that the increase in these false positive cases is highly affected by the label distribution around each node and confirm it experimentally. In addition, in order to handle this issue, we propose Topology-Aware Margin (TAM) to reflect local topology on the learning objective. Our method compares the connectivity pattern of each node with the class-averaged counter-part and adaptively adjusts the margin accordingly based on that. Our method consistently exhibits superiority over the baselines on various node classification benchmark datasets with representative GNN architectures.
Node classification is of great importance among various graph mining tasks. In practice, real-world graphs generally follow the long-tail distribution, where a large number of classes only consist of limited labeled nodes. Although Graph Neural Networks (GNNs) have achieved significant improvements in node classification, their performance decreases substantially in such a few-shot scenario. The main reason can be attributed to the vast generalization gap between meta-training and meta-test due to the task variance caused by different node/class distributions in meta-tasks (i.e., node-level and class-level variance). Therefore, to effectively alleviate the impact of task variance, we propose a task-adaptive node classification framework under the few-shot learning setting. Specifically, we first accumulate meta-knowledge across classes with abundant labeled nodes. Then we transfer such knowledge to the classes with limited labeled nodes via our proposed task-adaptive modules. In particular, to accommodate the different node/class distributions among meta-tasks, we propose three essential modules to perform \emph{node-level}, \emph{class-level}, and \emph{task-level} adaptations in each meta-task, respectively. In this way, our framework can conduct adaptations to different meta-tasks and thus advance the model generalization performance on meta-test tasks. Extensive experiments on four prevalent node classification datasets demonstrate the superiority of our framework over the state-of-the-art baselines. Our code is provided at https://github.com/SongW-SW/TENT.
Graph Neural Networks (GNNs) typically operate by message-passing, where the state of a node is updated based on the information received from its neighbours. Most message-passing models act as graph convolutions, where features are mixed by a shared, linear transformation before being propagated over the edges. On node-classification tasks, graph convolutions have been shown to suffer from two limitations: poor performance on heterophilic graphs, and over-smoothing. It is common belief that both phenomena occur because such models behave as low-pass filters, meaning that the Dirichlet energy of the features decreases along the layers incurring a smoothing effect that ultimately makes features no longer distinguishable. In this work, we rigorously prove that simple graph-convolutional models can actually enhance high frequencies and even lead to an asymptotic behaviour we refer to as over-sharpening, opposite to over-smoothing. We do so by showing that linear graph convolutions with symmetric weights minimize a multi-particle energy that generalizes the Dirichlet energy; in this setting, the weight matrices induce edge-wise attraction (repulsion) through their positive (negative) eigenvalues, thereby controlling whether the features are being smoothed or sharpened. We also extend the analysis to non-linear GNNs, and demonstrate that some existing time-continuous GNNs are instead always dominated by the low frequencies. Finally, we validate our theoretical findings through ablations and real-world experiments.
Heterogeneous graph neural networks (GNNs) achieve strong performance on node classification tasks in a semi-supervised learning setting. However, as in the simpler homogeneous GNN case, message-passing-based heterogeneous GNNs may struggle to balance between resisting the oversmoothing that may occur in deep models, and capturing long-range dependencies of graph structured data. Moreover, the complexity of this trade-off is compounded in the heterogeneous graph case due to the disparate heterophily relationships between nodes of different types. To address these issues, we propose a novel heterogeneous GNN architecture in which layers are derived from optimization steps that descend a novel relation-aware energy function. The corresponding minimizer is fully differentiable with respect to the energy function parameters, such that bilevel optimization can be applied to effectively learn a functional form whose minimum provides optimal node representations for subsequent classification tasks. In particular, this methodology allows us to model diverse heterophily relationships between different node types while avoiding oversmoothing effects. Experimental results on 8 heterogeneous graph benchmarks demonstrates that our proposed method can achieve competitive node classification accuracy
Graph Neural Networks (GNNs) have achieved great success on a node classification task. Despite the broad interest in developing and evaluating GNNs, they have been assessed with limited benchmark datasets. As a result, the existing evaluation of GNNs lacks fine-grained analysis from various characteristics of graphs. Motivated by this, we conduct extensive experiments with a synthetic graph generator that can generate graphs having controlled characteristics for fine-grained analysis. Our empirical studies clarify the strengths and weaknesses of GNNs from four major characteristics of real-world graphs with class labels of nodes, i.e., 1) class size distributions (balanced vs. imbalanced), 2) edge connection proportions between classes (homophilic vs. heterophilic), 3) attribute values (biased vs. random), and 4) graph sizes (small vs. large). In addition, to foster future research on GNNs, we publicly release our codebase that allows users to evaluate various GNNs with various graphs. We hope this work offers interesting insights for future research.
As one of the most popular machine learning models today, graph neural networks (GNNs) have attracted intense interest recently, and so does their explainability. Users are increasingly interested in a better understanding of GNN models and their outcomes. Unfortunately, today's evaluation frameworks for GNN explainability often rely on few inadequate synthetic datasets, leading to conclusions of limited scope due to a lack of complexity in the problem instances. As GNN models are deployed to more mission-critical applications, we are in dire need for a common evaluation protocol of explainability methods of GNNs. In this paper, we propose, to our best knowledge, the first systematic evaluation framework for GNN explainability, considering explainability on three different "user needs". We propose a unique metric that combines the fidelity measures and classifies explanations based on their quality of being sufficient or necessary. We scope ourselves to node classification tasks and compare the most representative techniques in the field of input-level explainability for GNNs. For the inadequate but widely used synthetic benchmarks, surprisingly shallow techniques such as personalized PageRank have the best performance for a minimum computation time. But when the graph structure is more complex and nodes have meaningful features, gradient-based methods are the best according to our evaluation criteria. However, none dominates the others on all evaluation dimensions and there is always a trade-off. We further apply our evaluation protocol in a case study for frauds explanation on eBay transaction graphs to reflect the production environment.
Graph neural networks (GNNs) have been intensively applied to various graph-based applications. Despite their success, manually designing the well-behaved GNNs requires immense human expertise. And thus it is inefficient to discover the potentially optimal data-specific GNN architecture. This paper proposes DFG-NAS, a new neural architecture search (NAS) method that enables the automatic search of very deep and flexible GNN architectures. Unlike most existing methods that focus on micro-architectures, DFG-NAS highlights another level of design: the search for macro-architectures on how atomic propagation (\textbf{\texttt{P}}) and transformation (\textbf{\texttt{T}}) operations are integrated and organized into a GNN. To this end, DFG-NAS proposes a novel search space for \textbf{\texttt{P-T}} permutations and combinations based on message-passing dis-aggregation, defines four custom-designed macro-architecture mutations, and employs the evolutionary algorithm to conduct an efficient and effective search. Empirical studies on four node classification tasks demonstrate that DFG-NAS outperforms state-of-the-art manual designs and NAS methods of GNNs.