Graph kernels are historically the most widely-used technique for graph classification tasks. However, these methods suffer from limited performance because of the hand-crafted combinatorial features of graphs. In recent years, graph neural networks (GNNs) have become the state-of-the-art method in downstream graph-related tasks due to their superior performance. Most GNNs are based on Message Passing Neural Network (MPNN) frameworks. However, recent studies show that MPNNs can not exceed the power of the Weisfeiler-Lehman (WL) algorithm in graph isomorphism test. To address the limitations of existing graph kernel and GNN methods, in this paper, we propose a novel GNN framework, termed \textit{Kernel Graph Neural Networks} (KerGNNs), which integrates graph kernels into the message passing process of GNNs. Inspired by convolution filters in convolutional neural networks (CNNs), KerGNNs adopt trainable hidden graphs as graph filters which are combined with subgraphs to update node embeddings using graph kernels. In addition, we show that MPNNs can be viewed as special cases of KerGNNs. We apply KerGNNs to multiple graph-related tasks and use cross-validation to make fair comparisons with benchmarks. We show that our method achieves competitive performance compared with existing state-of-the-art methods, demonstrating the potential to increase the representation ability of GNNs. We also show that the trained graph filters in KerGNNs can reveal the local graph structures of the dataset, which significantly improves the model interpretability compared with conventional GNN models.
In graph classification, attention and pooling-based graph neural networks (GNNs) prevail to extract the critical features from the input graph and support the prediction. They mostly follow the paradigm of learning to attend, which maximizes the mutual information between the attended graph and the ground-truth label. However, this paradigm makes GNN classifiers recklessly absorb all the statistical correlations between input features and labels in the training data, without distinguishing the causal and noncausal effects of features. Instead of underscoring the causal features, the attended graphs are prone to visit the noncausal features as the shortcut to predictions. Such shortcut features might easily change outside the training distribution, thereby making the GNN classifiers suffer from poor generalization. In this work, we take a causal look at the GNN modeling for graph classification. With our causal assumption, the shortcut feature serves as a confounder between the causal feature and prediction. It tricks the classifier to learn spurious correlations that facilitate the prediction in in-distribution (ID) test evaluation, while causing the performance drop in out-of-distribution (OOD) test data. To endow the classifier with better interpretation and generalization, we propose the Causal Attention Learning (CAL) strategy, which discovers the causal patterns and mitigates the confounding effect of shortcuts. Specifically, we employ attention modules to estimate the causal and shortcut features of the input graph. We then parameterize the backdoor adjustment of causal theory -- combine each causal feature with various shortcut features. It encourages the stable relationships between the causal estimation and prediction, regardless of the changes in shortcut parts and distributions. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness of CAL.
Graph representation learning has drawn increasing attention in recent years, especially for learning the low dimensional embedding at both node and graph level for classification and recommendations tasks. To enable learning the representation on the large-scale graph data in the real world, numerous research has focused on developing different sampling strategies to facilitate the training process. Herein, we propose an adaptive Graph Policy-driven Sampling model (GPS), where the influence of each node in the local neighborhood is realized through the adaptive correlation calculation. Specifically, the selections of the neighbors are guided by an adaptive policy algorithm, contributing directly to the message aggregation, node embedding updating, and graph level readout steps. We then conduct comprehensive experiments against baseline methods on graph classification tasks from various perspectives. Our proposed model outperforms the existing ones by 3%-8% on several vital benchmarks, achieving state-of-the-art performance in real-world datasets.
Subgraph recognition aims at discovering a compressed substructure of a graph that is most informative to the graph property. It can be formulated by optimizing Graph Information Bottleneck (GIB) with a mutual information estimator. However, GIB suffers from training instability and degenerated results due to its intrinsic optimization process. To tackle these issues, we reformulate the subgraph recognition problem into two steps: graph perturbation and subgraph selection, leading to a novel Variational Graph Information Bottleneck (VGIB) framework. VGIB first employs the noise injection to modulate the information flow from the input graph to the perturbed graph. Then, the perturbed graph is encouraged to be informative to the graph property. VGIB further obtains the desired subgraph by filtering out the noise in the perturbed graph. With the customized noise prior for each input, the VGIB objective is endowed with a tractable variational upper bound, leading to a superior empirical performance as well as theoretical properties. Extensive experiments on graph interpretation, explainability of Graph Neural Networks, and graph classification show that VGIB finds better subgraphs than existing methods. Code is avaliable at https://github.com/Samyu0304/VGIB
The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be represented as regular grids in the Euclidean space, extending the convolution operator to work on graphs proves more challenging, due to their irregular structure. In this paper, we propose to use graph kernels, i.e. kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain. This allows us to define an entirely structural model that does not require computing the embedding of the input graph. Our architecture allows to plug-in any type of graph kernels and has the added benefit of providing some interpretability in terms of the structural masks that are learned during the training process, similarly to what happens for convolutional masks in traditional convolutional neural networks. We perform an extensive ablation study to investigate the model hyper-parameters' impact and show that our model achieves competitive performance on standard graph classification and regression datasets.
Many improvements on GNNs can be deemed as operations on the spectrum of the underlying graph matrix, which motivates us to directly study the characteristics of the spectrum and their effects on GNN performance. By generalizing most existing GNN architectures, we show that the correlation issue caused by the $unsmooth$ spectrum becomes the obstacle to leveraging more powerful graph filters as well as developing deep architectures, which therefore restricts GNNs' performance. Inspired by this, we propose the correlation-free architecture which naturally removes the correlation issue among different channels, making it possible to utilize more sophisticated filters within each channel. The final correlation-free architecture with more powerful filters consistently boosts the performance of learning graph representations. Code is available at https://github.com/qslim/gnn-spectrum.
Graph convolutional networks (GCNs) have achieved remarkable learning ability for dealing with various graph structural data recently. In general, deep GCNs do not work well since graph convolution in conventional GCNs is a special form of Laplacian smoothing, which makes the representation of different nodes indistinguishable. In the literature, multi-scale information was employed in GCNs to enhance the expressive power of GCNs. However, over-smoothing phenomenon as a crucial issue of GCNs remains to be solved and investigated. In this paper, we propose two novel multi-scale GCN frameworks by incorporating self-attention mechanism and multi-scale information into the design of GCNs. Our methods greatly improve the computational efficiency and prediction accuracy of the GCNs model. Extensive experiments on both node classification and graph classification demonstrate the effectiveness over several state-of-the-art GCNs. Notably, the proposed two architectures can efficiently mitigate the over-smoothing problem of GCNs, and the layer of our model can even be increased to $64$.
Recently, Graph Neural Networks (GNNs) have gained popularity in a variety of real-world scenarios. Despite the great success, the architecture design of GNNs heavily relies on manual labor. Thus, automated graph neural network (AutoGNN) has attracted interest and attention from the research community, which makes significant performance improvements in recent years. However, existing AutoGNN works mainly adopt an implicit way to model and leverage the link information in the graphs, which is not well regularized to the link prediction task on graphs, and limits the performance of AutoGNN for other graph tasks. In this paper, we present a novel AutoGNN work that explicitly models the link information, abbreviated to AutoGEL. In such a way, AutoGEL can handle the link prediction task and improve the performance of AutoGNNs on the node classification and graph classification task. Specifically, AutoGEL proposes a novel search space containing various design dimensions at both intra-layer and inter-layer designs and adopts a more robust differentiable search algorithm to further improve efficiency and effectiveness. Experimental results on benchmark data sets demonstrate the superiority of AutoGEL on several tasks.
Graph Neural Networks (GNNs) have achieved unprecedented success in identifying categorical labels of graphs. However, most existing graph classification problems with GNNs follow the protocol of balanced data splitting, which misaligns with many real-world scenarios in which some classes have much fewer labels than others. Directly training GNNs under this imbalanced scenario may lead to uninformative representations of graphs in minority classes, and compromise the overall classification performance, which signifies the importance of developing effective GNNs towards handling imbalanced graph classification. Existing methods are either tailored for non-graph structured data or designed specifically for imbalanced node classification while few focus on imbalanced graph classification. To this end, we introduce a novel framework, Graph-of-Graph Neural Networks (G$^2$GNN), which alleviates the graph imbalance issue by deriving extra supervision globally from neighboring graphs and locally from stochastic augmentations of graphs. Globally, we construct a graph of graphs (GoG) based on kernel similarity and perform GoG propagation to aggregate neighboring graph representations. Locally, we employ topological augmentation via masking node features or dropping edges with self-consistency regularization to generate stochastic augmentations of each graph that improve the model generalibility. Extensive graph classification experiments conducted on seven benchmark datasets demonstrate our proposed G$^2$GNN outperforms numerous baselines by roughly 5\% in both F1-macro and F1-micro scores. The implementation of G$^2$GNN is available at https://github.com/YuWVandy/G2GNN}{https://github.com/YuWVandy/G2GNN
Graph Neural Networks (GNNs) have become increasingly popular and achieved impressive results in many graph-based applications. However, extensive manual work and domain knowledge are required to design effective architectures, and the results of GNN models have high variance with different training setups, which limits the application of existing GNN models. In this paper, we present AutoHEnsGNN, a framework to build effective and robust models for graph tasks without any human intervention. AutoHEnsGNN won first place in the AutoGraph Challenge for KDD Cup 2020, and achieved the best rank score of five real-life datasets in the final phase. Given a task, AutoHEnsGNN first applies a fast proxy evaluation to automatically select a pool of promising GNN models. Then it builds a hierarchical ensemble framework: 1) We propose graph self-ensemble (GSE), which can reduce the variance of weight initialization and efficiently exploit the information of local and global neighborhoods; 2) Based on GSE, a weighted ensemble of different types of GNN models is used to effectively learn more discriminative node representations. To efficiently search the architectures and ensemble weights, we propose AutoHEnsGNN$_{\text{Gradient}}$, which treats the architectures and ensemble weights as architecture parameters and uses gradient-based architecture search to obtain optimal configurations, and AutoHEnsGNN$_{\text{Adaptive}}$, which can adaptively adjust the ensemble weight based on the model accuracy. Extensive experiments on node classification, graph classification, edge prediction and KDD Cup challenge demonstrate the effectiveness and generality of AutoHEnsGNN
With the great success of deep learning in various domains, graph neural networks (GNNs) also become a dominant approach to graph classification. By the help of a global readout operation that simply aggregates all node (or node-cluster) representations, existing GNN classifiers obtain a graph-level representation of an input graph and predict its class label using the representation. However, such global aggregation does not consider the structural information of each node, which results in information loss on the global structure. Particularly, it limits the discrimination power by enforcing the same weight parameters of the classifier for all the node representations; in practice, each of them contributes to target classes differently depending on its structural semantic. In this work, we propose structural semantic readout (SSRead) to summarize the node representations at the position-level, which allows to model the position-specific weight parameters for classification as well as to effectively capture the graph semantic relevant to the global structure. Given an input graph, SSRead aims to identify structurally-meaningful positions by using the semantic alignment between its nodes and structural prototypes, which encode the prototypical features of each position. The structural prototypes are optimized to minimize the alignment cost for all training graphs, while the other GNN parameters are trained to predict the class labels. Our experimental results demonstrate that SSRead significantly improves the classification performance and interpretability of GNN classifiers while being compatible with a variety of aggregation functions, GNN architectures, and learning frameworks.
We focus on graph classification using a graph neural network (GNN) model that precomputes the node features using a bank of neighborhood aggregation graph operators arranged in parallel. These GNN models have a natural advantage of reduced training and inference time due to the precomputations but are also fundamentally different from popular GNN variants that update node features through a sequential neighborhood aggregation procedure during training. We provide theoretical conditions under which a generic GNN model with parallel neighborhood aggregations (PA-GNNs, in short) are provably as powerful as the well-known Weisfeiler-Lehman (WL) graph isomorphism test in discriminating non-isomorphic graphs. Although PA-GNN models do not have an apparent relationship with the WL test, we show that the graph embeddings obtained from these two methods are injectively related. We then propose a specialized PA-GNN model, called SPIN, which obeys the developed conditions. We demonstrate via numerical experiments that the developed model achieves state-of-the-art performance on many diverse real-world datasets while maintaining the discriminative power of the WL test and the computational advantage of preprocessing graphs before the training process.
Graph Neural Network (GNN) is a powerful tool to perform standard machine learning on graphs. To have a Euclidean representation of every node in the Non-Euclidean graph-like data, GNN follows neighbourhood aggregation and combination of information recursively along the edges of the graph. Despite having many GNN variants in the literature, no model can deal with graphs having nodes with interval-valued features. This article proposes an Interval-ValuedGraph Neural Network, a novel GNN model where, for the first time, we relax the restriction of the feature space being countable. Our model is much more general than existing models as any countable set is always a subset of the universal set $R^{n}$, which is uncountable. Here, to deal with interval-valued feature vectors, we propose a new aggregation scheme of intervals and show its expressive power to capture different interval structures. We validate our theoretical findings about our model for graph classification tasks by comparing its performance with those of the state-of-the-art models on several benchmark network and synthetic datasets.
This paper studies Dropout Graph Neural Networks (DropGNNs), a new approach that aims to overcome the limitations of standard GNN frameworks. In DropGNNs, we execute multiple runs of a GNN on the input graph, with some of the nodes randomly and independently dropped in each of these runs. Then, we combine the results of these runs to obtain the final result. We prove that DropGNNs can distinguish various graph neighborhoods that cannot be separated by message passing GNNs. We derive theoretical bounds for the number of runs required to ensure a reliable distribution of dropouts, and we prove several properties regarding the expressive capabilities and limits of DropGNNs. We experimentally validate our theoretical findings on expressiveness. Furthermore, we show that DropGNNs perform competitively on established GNN benchmarks.
Graph-structured datasets usually have irregular graph sizes and connectivities, rendering the use of recent data augmentation techniques, such as Mixup, difficult. To tackle this challenge, we present the first Mixup-like graph augmentation method at the graph-level called Graph Transplant, which mixes irregular graphs in data space. To be well defined on various scales of the graph, our method identifies the sub-structure as a mix unit that can preserve the local information. Since the mixup-based methods without special consideration of the context are prone to generate noisy samples, our method explicitly employs the node saliency information to select meaningful subgraphs and adaptively determine the labels. We extensively validate our method with diverse GNN architectures on multiple graph classification benchmark datasets from a wide range of graph domains of different sizes. Experimental results show the consistent superiority of our method over other basic data augmentation baselines. We also demonstrate that Graph Transplant enhances the performance in terms of robustness and model calibration.
Graph representation learning methods generate numerical vector representations for the nodes in a network, thereby enabling their use in standard machine learning models. These methods aim to preserve relational information, such that nodes that are similar in the graph are found close to one another in the representation space. Similarity can be based largely on one of two notions: connectivity or structural role. In tasks where node structural role is important, connectivity based methods show poor performance. Recent work has begun to focus on scalability of learning methods to massive graphs of millions to billions of nodes and edges. Many unsupervised node representation learning algorithms are incapable of scaling to large graphs, and are unable to generate node representations for unseen nodes. In this work, we propose Inferential SIR-GN, a model which is pre-trained on random graphs, then computes node representations rapidly, including for very large networks. We demonstrate that the model is able to capture node's structural role information, and show excellent performance at node and graph classification tasks, on unseen networks. Additionally, we observe the scalability of Inferential SIR-GN is comparable to the fastest current approaches for massive graphs.
Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop a theoretical framework for graph classification problems in the partial observation setting (i.e., subgraph samplings). Equipped with insights from graph limit theory, we propose a new graph classification model that works on a randomly sampled subgraph and a novel topology to characterize the representability of the model. Our theoretical framework contributes a theoretical validation of mini-batch learning on graphs and leads to new learning-theoretic results on generalization bounds as well as size-generalizability without assumptions on the input.
Unsupervised graph representation learning is critical to a wide range of applications where labels may be scarce or expensive to procure. Contrastive learning (CL) is an increasingly popular paradigm for such settings and the state-of-the-art in unsupervised visual representation learning. Recent work attributes the success of visual CL to use of task-relevant augmentations and large, diverse datasets. Interestingly, graph CL frameworks report strong performance despite using orders of magnitude smaller datasets and employing domain-agnostic graph augmentations (DAGAs). Motivated by this discrepancy, we probe the quality of representations learnt by popular graph CL frameworks using DAGAs. We find that DAGAs can destroy task-relevant information and harm the model's ability to learn discriminative representations. On small benchmark datasets, we show the inductive bias of graph neural networks can significantly compensate for this weak discriminability. Based on our findings, we propose several sanity checks that enable practitioners to quickly assess the quality of their model's learned representations. We further propose a broad strategy for designing task-aware augmentations that are amenable to graph CL and demonstrate its efficacy on two large-scale, complex graph applications. For example, in graph-based document classification, we show task-aware augmentations improve accuracy up to 20%.
Graph neural networks, a popular class of models effective in a wide range of graph-based learning tasks, have been shown to be vulnerable to adversarial attacks. While the majority of the literature focuses on such vulnerability in node-level classification tasks, little effort has been dedicated to analysing adversarial attacks on graph-level classification, an important problem with numerous real-life applications such as biochemistry and social network analysis. The few existing methods often require unrealistic setups, such as access to internal information of the victim models, or an impractically-large number of queries. We present a novel Bayesian optimisation-based attack method for graph classification models. Our method is black-box, query-efficient and parsimonious with respect to the perturbation applied. We empirically validate the effectiveness and flexibility of the proposed method on a wide range of graph classification tasks involving varying graph properties, constraints and modes of attack. Finally, we analyse common interpretable patterns behind the adversarial samples produced, which may shed further light on the adversarial robustness of graph classification models.
Discovering distinct features and their relations from data can help us uncover valuable knowledge crucial for various tasks, e.g., classification. In neuroimaging, these features could help to understand, classify, and possibly prevent brain disorders. Model introspection of highly performant overparameterized deep learning (DL) models could help find these features and relations. However, to achieve high-performance level DL models require numerous labeled training samples ($n$) rarely available in many fields. This paper presents a pre-training method involving graph convolutional/neural networks (GCNs/GNNs), based on maximizing mutual information between two high-level embeddings of an input sample. Many of the recently proposed pre-training methods pre-train one of many possible networks of an architecture. Since almost every DL model is an ensemble of multiple networks, we take our high-level embeddings from two different networks of a model --a convolutional and a graph network--. The learned high-level graph latent representations help increase performance for downstream graph classification tasks and bypass the need for a high number of labeled data samples. We apply our method to a neuroimaging dataset for classifying subjects into healthy control (HC) and schizophrenia (SZ) groups. Our experiments show that the pre-trained model significantly outperforms the non-pre-trained model and requires $50\%$ less data for similar performance.