Existing graph contrastive learning methods rely on augmentation techniques based on random perturbations (e.g., randomly adding or dropping edges and nodes). Nevertheless, altering certain edges or nodes can unexpectedly change the graph characteristics, and choosing the optimal perturbing ratio for each dataset requires onerous manual tuning. In this paper, we introduce Implicit Graph Contrastive Learning (iGCL), which utilizes augmentations in the latent space learned from a Variational Graph Auto-Encoder by reconstructing graph topological structure. Importantly, instead of explicitly sampling augmentations from latent distributions, we further propose an upper bound for the expected contrastive loss to improve the efficiency of our learning algorithm. Thus, graph semantics can be preserved within the augmentations in an intelligent way without arbitrary manual design or prior human knowledge. Experimental results on both graph-level and node-level tasks show that the proposed method achieves state-of-the-art performance compared to other benchmarks, where ablation studies in the end demonstrate the effectiveness of modules in iGCL.
In this work we propose a random graph model that can produce graphs at different levels of sparsity. We analyze how sparsity affects the graph spectra, and thus the performance of graph neural networks (GNNs) in node classification on dense and sparse graphs. We compare GNNs with spectral methods known to provide consistent estimators for community detection on dense graphs, a closely related task. We show that GNNs can outperform spectral methods on sparse graphs, and illustrate these results with numerical examples on both synthetic and real graphs.
Analysis of the fairness of machine learning (ML) algorithms recently attracted many researchers' interest. Most ML methods show bias toward protected groups, which limits the applicability of ML models in many applications like crime rate prediction etc. Since the data may have missing values which, if not appropriately handled, are known to further harmfully affect fairness. Many imputation methods are proposed to deal with missing data. However, the effect of missing data imputation on fairness is not studied well. In this paper, we analyze the effect on fairness in the context of graph data (node attributes) imputation using different embedding and neural network methods. Extensive experiments on six datasets demonstrate severe fairness issues in missing data imputation under graph node classification. We also find that the choice of the imputation method affects both fairness and accuracy. Our results provide valuable insights into graph data fairness and how to handle missingness in graphs efficiently. This work also provides directions regarding theoretical studies on fairness in graph data.
Graph convolution networks (GCNs) have been enormously successful in learning representations over several graph-based machine learning tasks. Specific to learning rich node representations, most of the methods have solely relied on the homophily assumption and have shown limited performance on the heterophilous graphs. While several methods have been developed with new architectures to address heterophily, we argue that by learning graph representations across two spaces i.e., topology and feature space GCNs can address heterophily. In this work, we experimentally demonstrate the performance of the proposed GCN framework over semi-supervised node classification task on both homophilous and heterophilous graph benchmarks by learning and combining representations across the topological and the feature spaces.
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by additionally making use of graph structure based on the relational inductive bias (edge bias), rather than treating the nodes as collections of independent and identically distributed (i.i.d.) samples. Though GNNs are believed to outperform basic NNs in real-world tasks, it is found that in some cases, GNNs have little performance gain or even underperform graph-agnostic NNs. To identify these cases, based on graph signal processing and statistical hypothesis testing, we propose two measures which analyze the cases in which the edge bias in features and labels does not provide advantages. Based on the measures, a threshold value can be given to predict the potential performance advantages of graph-aware models over graph-agnostic models.
Approximate solutions to various NP-hard combinatorial optimization problems have been found by learned heuristics using complex learning models. In particular, vertex (node) classification in graphs has been a helpful method towards finding the decision boundary to distinguish vertices in an optimal set from the rest. By following this approach, we use a learning framework for a pruning process of the input graph towards reducing the runtime of the maximum clique enumeration problem. We extensively study the role of using different vertex representations on the performance of this heuristic method, using graph embedding algorithms, such as Node2vec and DeepWalk, and representations using higher-order graph features comprising local subgraph counts. Our results show that Node2Vec and DeepWalk are promising embedding methods in representing nodes towards classification purposes. We observe that using local graph features in the classification process produce more accurate results when combined with a feature elimination process. Finally, we provide tests on random graphs to show the robustness and scalability of our method.
Kernels on discrete structures evaluate pairwise similarities between objects which capture semantics and inherent topology information. Existing kernels on discrete structures are only developed by topology information(such as adjacency matrix of graphs), without considering original attributes of objects. This paper proposes a two-phase paradigm to aggregate comprehensive information on discrete structures leading to a Discount Markov Diffusion Learnable Kernel (DMDLK). Specifically, based on the underlying projection of DMDLK, we design a Simple Hypergraph Kernel Convolution (SHKC) for hidden representation of vertices. SHKC can adjust diffusion steps rather than stacking convolution layers to aggregate information from long-range neighborhoods which prevents over-smoothing issues of existing hypergraph convolutions. Moreover, we utilize the uniform stability bound theorem in transductive learning to analyze critical factors for the effectiveness and generalization ability of SHKC from a theoretical perspective. The experimental results on several benchmark datasets for node classification tasks verified the superior performance of SHKC over state-of-the-art methods.
Heterogeneous graph neural network has unleashed great potential on graph representation learning and shown superior performance on downstream tasks such as node classification and clustering. Existing heterogeneous graph learning networks are primarily designed to either rely on pre-defined meta-paths or use attention mechanisms for type-specific attentive message propagation on different nodes/edges, incurring many customization efforts and computational costs. To this end, we design a relation-centered Pooling and Convolution for Heterogeneous Graph learning Network, namely PC-HGN, to enable relation-specific sampling and cross-relation convolutions, from which the structural heterogeneity of the graph can be better encoded into the embedding space through the adaptive training process. We evaluate the performance of the proposed model by comparing with state-of-the-art graph learning models on three different real-world datasets, and the results show that PC-HGN consistently outperforms all the baseline and improves the performance maximumly up by 17.8%.
Graph Echo State Networks (GESN) have already demonstrated their efficacy and efficiency in graph classification tasks. However, semi-supervised node classification brought out the problem of over-smoothing in end-to-end trained deep models, which causes a bias towards high homophily graphs. We evaluate for the first time GESN on node classification tasks with different degrees of homophily, analyzing also the impact of the reservoir radius. Our experiments show that reservoir models are able to achieve better or comparable accuracy with respect to fully trained deep models that implement ad hoc variations in the architectural bias, with a gain in terms of efficiency.
Models for image segmentation, node classification and many other tasks map a single input to multiple labels. By perturbing this single shared input (e.g. the image) an adversary can manipulate several predictions (e.g. misclassify several pixels). Collective robustness certification is the task of provably bounding the number of robust predictions under this threat model. The only dedicated method that goes beyond certifying each output independently is limited to strictly local models, where each prediction is associated with a small receptive field. We propose a more general collective robustness certificate for all types of models. We further show that this approach is beneficial for the larger class of softly local models, where each output is dependent on the entire input but assigns different levels of importance to different input regions (e.g. based on their proximity in the image). The certificate is based on our novel localized randomized smoothing approach, where the random perturbation strength for different input regions is proportional to their importance for the outputs. Localized smoothing Pareto-dominates existing certificates on both image segmentation and node classification tasks, simultaneously offering higher accuracy and stronger certificates.
This paper introduces a novel Framelet Graph approach based on p-Laplacian GNN. The proposed two models, named p-Laplacian undecimated framelet graph convolution (pL-UFG) and generalized p-Laplacian undecimated framelet graph convolution (pL-fUFG) inherit the nature of p-Laplacian with the expressive power of multi-resolution decomposition of graph signals. The empirical study highlights the excellent performance of the pL-UFG and pL-fUFG in different graph learning tasks including node classification and signal denoising.
Following a fast initial breakthrough in graph based learning, Graph Neural Networks (GNNs) have reached a widespread application in many science and engineering fields, prompting the need for methods to understand their decision process. GNN explainers have started to emerge in recent years, with a multitude of methods both novel or adapted from other domains. To sort out this plethora of alternative approaches, several studies have benchmarked the performance of different explainers in terms of various explainability metrics. However, these earlier works make no attempts at providing insights into why different GNN architectures are more or less explainable, or which explainer should be preferred in a given setting. In this survey, we fill these gaps by devising a systematic experimental study, which tests ten explainers on eight representative architectures trained on six carefully designed graph and node classification datasets. With our results we provide key insights on the choice and applicability of GNN explainers, we isolate key components that make them usable and successful and provide recommendations on how to avoid common interpretation pitfalls. We conclude by highlighting open questions and directions of possible future research.
Current graph neural networks (GNNs) that tackle node classification on graphs tend to only focus on nodewise scores and are solely evaluated by nodewise metrics. This limits uncertainty estimation on graphs since nodewise marginals do not fully characterize the joint distribution given the graph structure. In this work, we propose novel edgewise metrics, namely the edgewise expected calibration error (ECE) and the agree/disagree ECEs, which provide criteria for uncertainty estimation on graphs beyond the nodewise setting. Our experiments demonstrate that the proposed edgewise metrics can complement the nodewise results and yield additional insights. Moreover, we show that GNN models which consider the structured prediction problem on graphs tend to have better uncertainty estimations, which illustrates the benefit of going beyond the nodewise setting.
Graph Neural Networks (GNNs) are vulnerable to data poisoning attacks, which will generate a poisoned graph as the input to the GNN models. We present FocusedCleaner as a poisoned graph sanitizer to effectively identify the poison injected by attackers. Specifically, FocusedCleaner provides a sanitation framework consisting of two modules: bi-level structural learning and victim node detection. In particular, the structural learning module will reverse the attack process to steadily sanitize the graph while the detection module provides ``the focus" -- a narrowed and more accurate search region -- to structural learning. These two modules will operate in iterations and reinforce each other to sanitize a poisoned graph step by step. As an important application, we show that the adversarial robustness of GNNs trained over the sanitized graph for the node classification task is significantly improved. Extensive experiments demonstrate that FocusedCleaner outperforms the state-of-the-art baselines both on poisoned graph sanitation and improving robustness.
Link prediction tasks focus on predicting possible future connections. Most existing researches measure the likelihood of links by different similarity scores on node pairs and predict links between nodes. However, the similarity-based approaches have some challenges in information loss on nodes and generalization ability on similarity indexes. To address the above issues, we propose a Line Graph Contrastive Learning(LGCL) method to obtain rich information with multiple perspectives. LGCL obtains a subgraph view by h-hop subgraph sampling with target node pairs. After transforming the sampled subgraph into a line graph, the link prediction task is converted into a node classification task, which graph convolution progress can learn edge embeddings from graphs more effectively. Then we design a novel cross-scale contrastive learning framework on the line graph and the subgraph to maximize the mutual information of them, so that fuses the structure and feature information. The experimental results demonstrate that the proposed LGCL outperforms the state-of-the-art methods and has better performance on generalization and robustness.
The current success of Graph Neural Networks (GNNs) usually relies on loading the entire attributed graph for processing, which may not be satisfied with limited memory resources, especially when the attributed graph is large. This paper pioneers to propose a Binary Graph Convolutional Network (Bi-GCN), which binarizes both the network parameters and input node attributes and exploits binary operations instead of floating-point matrix multiplications for network compression and acceleration. Meanwhile, we also propose a new gradient approximation based back-propagation method to properly train our Bi-GCN. According to the theoretical analysis, our Bi-GCN can reduce the memory consumption by an average of ~31x for both the network parameters and input data, and accelerate the inference speed by an average of ~51x, on three citation networks, i.e., Cora, PubMed, and CiteSeer. Besides, we introduce a general approach to generalize our binarization method to other variants of GNNs, and achieve similar efficiencies. Although the proposed Bi-GCN and Bi-GNNs are simple yet efficient, these compressed networks may also possess a potential capacity problem, i.e., they may not have enough storage capacity to learn adequate representations for specific tasks. To tackle this capacity problem, an Entropy Cover Hypothesis is proposed to predict the lower bound of the width of Bi-GNN hidden layers. Extensive experiments have demonstrated that our Bi-GCN and Bi-GNNs can give comparable performances to the corresponding full-precision baselines on seven node classification datasets and verified the effectiveness of our Entropy Cover Hypothesis for solving the capacity problem.
Graph few-shot learning is of great importance among various graph learning tasks. Under the few-shot scenario, models are often required to conduct classification given limited labeled samples. Existing graph few-shot learning methods typically leverage Graph Neural Networks (GNNs) and perform classification across a series of meta-tasks. Nevertheless, these methods generally rely on the original graph (i.e., the graph that the meta-task is sampled from) to learn node representations. Consequently, the graph structure used in each meta-task is identical. Since the class sets are different across meta-tasks, node representations should be learned in a task-specific manner to promote classification performance. Therefore, to adaptively learn node representations across meta-tasks, we propose a novel framework that learns a task-specific structure for each meta-task. To handle the variety of nodes across meta-tasks, we extract relevant nodes and learn task-specific structures based on node influence and mutual information. In this way, we can learn node representations with the task-specific structure tailored for each meta-task. We further conduct extensive experiments on five node classification datasets under both single- and multiple-graph settings to validate the superiority of our framework over the state-of-the-art baselines. Our code is provided at https://github.com/SongW-SW/GLITTER.
Contrastive learning has emerged as a powerful tool for graph representation learning. However, most contrastive learning methods learn features of graphs with fixed coarse-grained scale, which might underestimate either local or global information. To capture more hierarchical and richer representation, we propose a novel Hierarchical Contrastive Learning (HCL) framework that explicitly learns graph representation in a hierarchical manner. Specifically, HCL includes two key components: a novel adaptive Learning to Pool (L2Pool) method to construct more reasonable multi-scale graph topology for more comprehensive contrastive objective, a novel multi-channel pseudo-siamese network to further enable more expressive learning of mutual information within each scale. Comprehensive experimental results show HCL achieves competitive performance on 12 datasets involving node classification, node clustering and graph classification. In addition, the visualization of learned representation reveals that HCL successfully captures meaningful characteristics of graphs.
Spectral Graph Convolutional Networks (spectral GCNNs), a powerful tool for analyzing and processing graph data, typically apply frequency filtering via Fourier transform to obtain representations with selective information. Although research shows that spectral GCNNs can be enhanced by framelet-based filtering, the massive majority of such research only considers undirected graphs. In this paper, we introduce Framelet-MagNet, a magnetic framelet-based spectral GCNN for directed graphs (digraphs). The model applies the framelet transform to digraph signals to form a more sophisticated representation for filtering. Digraph framelets are constructed with the complex-valued magnetic Laplacian, simultaneously leading to signal processing in both real and complex domains. We empirically validate the predictive power of Framelet-MagNet over a range of state-of-the-art models in node classification, link prediction, and denoising.
Graph attention networks estimate the relational importance of node neighbors to aggregate relevant information over local neighborhoods for a prediction task. However, the inferred attentions are vulnerable to spurious correlations and connectivity in the training data, hampering the generalizability of the model. We introduce CAR, a general-purpose regularization framework for graph attention networks. Embodying a causal inference approach, CAR aligns the attention mechanism with the causal effects of active interventions on graph connectivity in a scalable manner. CAR is compatible with a variety of graph attention architectures, and we show that it systematically improves generalizability on various node classification tasks. Our ablation studies indicate that CAR hones in on the aspects of graph structure most pertinent to the prediction (e.g., homophily), and does so more effectively than alternative approaches. Finally, we also show that CAR enhances interpretability of attention weights by accentuating node-neighbor relations that point to causal hypotheses. For social media network-sized graphs, a CAR-guided graph rewiring approach could allow us to combine the scalability of graph convolutional methods with the higher performance of graph attention.