Differentially private GNNs (Graph Neural Networks) have been recently studied to provide high accuracy in various tasks on graph data while strongly protecting user privacy. In particular, a recent study proposes an algorithm to protect each user's feature vector in an attributed graph, which includes feature vectors along with node IDs and edges, with LDP (Local Differential Privacy), a strong privacy notion without a trusted third party. However, this algorithm does not protect edges (friendships) in a social graph, hence cannot protect user privacy in unattributed graphs, which include only node IDs and edges. How to provide strong privacy with high accuracy in unattributed graphs remains open. In this paper, we propose a novel LDP algorithm called the DPRR (Degree-Preserving Randomized Response) to provide LDP for edges in GNNs. Our DPRR preserves each user's degree hence a graph structure while providing edge LDP. Technically, our DPRR uses Warner's RR (Randomized Response) and strategic edge sampling, where each user's sampling probability is automatically tuned using the Laplacian mechanism to preserve the degree information under edge LDP. We also propose a privacy budget allocation method to make the noise in both Warner's RR and the Laplacian mechanism small. We focus on graph classification as a task of GNNs and evaluate the DPRR using three social graph datasets. Our experimental results show that the DPRR significantly outperforms three baselines and provides accuracy close to a non-private algorithm in all datasets with a reasonable privacy budget, e.g., epsilon=1. Finally, we introduce data poisoning attacks to our DPRR and a defense against the attacks. We evaluate them using the three social graph datasets and discuss the experimental results.
Given a graph dataset, how can we augment it for accurate graph classification? Graph augmentation is an essential strategy to improve the performance of graph-based tasks, and has been widely utilized for analyzing web and social graphs. However, previous works for graph augmentation either a) involve the target model in the process of augmentation, losing the generalizability to other tasks, or b) rely on simple heuristics that lead to unreliable results. In this work, we introduce five desired properties for effective augmentation. Then, we propose NodeSam (Node Split and Merge) and SubMix (Subgraph Mix), two model-agnostic approaches for graph augmentation that satisfy all desired properties with different motivations. NodeSam makes a balanced change of the graph structure to minimize the risk of semantic change, while SubMix mixes random subgraphs of multiple graphs to create rich soft labels combining the evidence for different classes. Our experiments on social networks and molecular graphs show that NodeSam and SubMix outperform existing approaches in graph classification.
Most methods for explaining black-box classifiers (e.g. on tabular data, images, or time series) rely on measuring the impact that removing/perturbing features has on the model output. This forces the explanation language to match the classifier's feature space. However, when dealing with graph data, in which the basic features correspond to the edges describing the graph structure, this matching between features space and explanation language might not be appropriate. Decoupling the feature space (edges) from a desired high-level explanation language (such as motifs) is thus a major challenge towards developing actionable explanations for graph classification tasks. In this paper we introduce GRAPHSHAP, a Shapley-based approach able to provide motif-based explanations for identity-aware graph classifiers, assuming no knowledge whatsoever about the model or its training data: the only requirement is that the classifier can be queried as a black-box at will. For the sake of computational efficiency we explore a progressive approximation strategy and show how a simple kernel can efficiently approximate explanation scores, thus allowing GRAPHSHAP to scale on scenarios with a large explanation space (i.e. large number of motifs). We showcase GRAPHSHAP on a real-world brain-network dataset consisting of patients affected by Autism Spectrum Disorder and a control group. Our experiments highlight how the classification provided by a black-box model can be effectively explained by few connectomics patterns.
Recently, transformers have shown promising performance in learning graph representations. However, there are still some challenges when applying transformers to real-world scenarios due to the fact that deep transformers are hard to train from scratch and the quadratic memory consumption w.r.t. the number of nodes. In this paper, we propose Graph Masked Autoencoders (GMAEs), a self-supervised transformer-based model for learning graph representations. To address the above two challenges, we adopt the masking mechanism and the asymmetric encoder-decoder design. Specifically, GMAE takes partially masked graphs as input, and reconstructs the features of the masked nodes. The encoder and decoder are asymmetric, where the encoder is a deep transformer and the decoder is a shallow transformer. The masking mechanism and the asymmetric design make GMAE a memory-efficient model compared with conventional transformers. We show that, when serving as a conventional self-supervised graph representation model, GMAE achieves state-of-the-art performance on both the graph classification task and the node classification task under common downstream evaluation protocols. We also show that, compared with training in an end-to-end manner from scratch, we can achieve comparable performance after pre-training and fine-tuning using GMAE while simplifying the training process.
This work develops \emph{mixup for graph data}. Mixup has shown superiority in improving the generalization and robustness of neural networks by interpolating features and labels between two random samples. Traditionally, Mixup can work on regular, grid-like, and Euclidean data such as image or tabular data. However, it is challenging to directly adopt Mixup to augment graph data because different graphs typically: 1) have different numbers of nodes; 2) are not readily aligned; and 3) have unique typologies in non-Euclidean space. To this end, we propose $\mathcal{G}$-Mixup to augment graphs for graph classification by interpolating the generator (i.e., graphon) of different classes of graphs. Specifically, we first use graphs within the same class to estimate a graphon. Then, instead of directly manipulating graphs, we interpolate graphons of different classes in the Euclidean space to get mixed graphons, where the synthetic graphs are generated through sampling based on the mixed graphons. Extensive experiments show that $\mathcal{G}$-Mixup substantially improves the generalization and robustness of GNNs.
The growing importance of understanding and addressing algorithmic bias in artificial intelligence (AI) has led to a surge in research on AI fairness, which often assumes that the underlying data is independent and identically distributed (IID). However, real-world data frequently exists in non-IID graph structures that capture connections among individual units. To effectively mitigate bias in AI systems, it is essential to bridge the gap between traditional fairness literature, designed for IID data, and the prevalence of non-IID graph data. This survey reviews recent advancements in fairness amidst non-IID graph data, including the newly introduced fair graph generation and the commonly studied fair graph classification. In addition, available datasets and evaluation metrics for future research are identified, the limitations of existing work are highlighted, and promising future directions are proposed.
In several machine learning tasks for graph structured data, the graphs under consideration may be composed of a varying number of nodes. Therefore, it is necessary to design pooling methods that aggregate the graph representations of varying size to representations of fixed size which can be used in downstream tasks, such as graph classification. Existing graph pooling methods offer no guarantee with regards to the similarity of a graph representation and its pooled version. In this work, we address this limitation by proposing FlowPool, a pooling method that optimally preserves the statistics of a graph representation to its pooled counterpart by minimising their Wasserstein distance. This is achieved by performing a Wasserstein gradient flow with respect to the pooled graph representation. Our method relies on a versatile implementation which can take into account the geometry of the representation space through any ground cost and computes the gradient of the Wasserstein distance with automatic differentiation. We propose the differentiation of the Wasserstein flow layer using an implicit differentiation scheme. Therefore, our pooling method is amenable to automatic differentiation and can be integrated in end-to-end deep learning architectures. Further, FlowPool is invariant to permutations and can therefore be combined with permutation equivariant feature extraction layers in GNNs in order to obtain predictions that are independent of the ordering of the nodes. Experimental results demonstrate that our method leads to an increase in performance compared to existing pooling methods when evaluated on graph classification.
Graph Neural Networks (GNNs) have established themselves as the state-of-the-art models for many machine learning applications such as the analysis of social networks, protein interactions and molecules. Several among these datasets contain privacy-sensitive data. Machine learning with differential privacy is a promising technique to allow deriving insight from sensitive data while offering formal guarantees of privacy protection. However, the differentially private training of GNNs has so far remained under-explored due to the challenges presented by the intrinsic structural connectivity of graphs. In this work, we introduce differential privacy for graph-level classification, one of the key applications of machine learning on graphs. Our method is applicable to deep learning on multi-graph datasets and relies on differentially private stochastic gradient descent (DP-SGD). We show results on a variety of synthetic and public datasets and evaluate the impact of different GNN architectures and training hyperparameters on model performance for differentially private graph classification. Finally, we apply explainability techniques to assess whether similar representations are learned in the private and non-private settings and establish robust baselines for future work in this area.
With the continuous extension of the Industrial Internet, cyber incidents caused by software vulnerabilities have been increasing in recent years. However, software vulnerabilities detection is still heavily relying on code review done by experts, and how to automatedly detect software vulnerabilities is an open problem so far. In this paper, we propose a novel solution named GraphEye to identify whether a function of C/C++ code has vulnerabilities, which can greatly alleviate the burden of code auditors. GraphEye is originated from the observation that the code property graph of a non-vulnerable function naturally differs from the code property graph of a vulnerable function with the same functionality. Hence, detecting vulnerable functions is attributed to the graph classification problem.GraphEye is comprised of VecCPG and GcGAT. VecCPG is a vectorization for the code property graph, which is proposed to characterize the key syntax and semantic features of the corresponding source code. GcGAT is a deep learning model based on the graph attention graph, which is proposed to solve the graph classification problem according to VecCPG. Finally, GraphEye is verified by the SARD Stack-based Buffer Overflow, Divide-Zero, Null Pointer Deference, Buffer Error, and Resource Error datasets, the corresponding F1 scores are 95.6%, 95.6%,96.1%,92.6%, and 96.1% respectively, which validate the effectiveness of the proposed solution.
Graph Neural Network (GNN) is an emerging technique for graph-based learning tasks such as node classification. In this work, we reveal the vulnerability of GNN to the imbalance of node labels. Traditional solutions for imbalanced classification (e.g. resampling) are ineffective in node classification without considering the graph structure. Worse still, they may even bring overfitting or underfitting results due to lack of sufficient prior knowledge. To solve these problems, we propose a novel graph neural network framework with curriculum learning (GNN-CL) consisting of two modules. For one thing, we hope to acquire certain reliable interpolation nodes and edges through the novel graph-based oversampling based on smoothness and homophily. For another, we combine graph classification loss and metric learning loss which adjust the distance between different nodes associated with minority class in feature space. Inspired by curriculum learning, we dynamically adjust the weights of different modules during training process to achieve better ability of generalization and discrimination. The proposed framework is evaluated via several widely used graph datasets, showing that our proposed model consistently outperforms the existing state-of-the-art methods.
Graph neural networks (GNNs) build on the success of deep learning models by extending them for use in graph spaces. Transfer learning has proven extremely successful for traditional deep learning problems: resulting in faster training and improved performance. Despite the increasing interest in GNNs and their use cases, there is little research on their transferability. This research demonstrates that transfer learning is effective with GNNs, and describes how source tasks and the choice of GNN impact the ability to learn generalisable knowledge. We perform experiments using real-world and synthetic data within the contexts of node classification and graph classification. To this end, we also provide a general methodology for transfer learning experimentation and present a novel algorithm for generating synthetic graph classification tasks. We compare the performance of GCN, GraphSAGE and GIN across both the synthetic and real-world datasets. Our results demonstrate empirically that GNNs with inductive operations yield statistically significantly improved transfer. Further we show that similarity in community structure between source and target tasks support statistically significant improvements in transfer over and above the use of only the node attributes.
Message passing neural networks (MPNN) have seen a steep rise in popularity since their introduction as generalizations of convolutional neural networks to graph-structured data, and are now considered state-of-the-art tools for solving a large variety of graph-focused problems. We study the generalization error of MPNNs in graph classification and regression. We assume that graphs of different classes are sampled from different random graph models. We show that, when training a MPNN on a dataset sampled from such a distribution, the generalization gap increases in the complexity of the MPNN, and decreases, not only with respect to the number of training samples, but also with the average number of nodes in the graphs. This shows how a MPNN with high complexity can generalize from a small dataset of graphs, as long as the graphs are large. The generalization bound is derived from a uniform convergence result, that shows that any MPNN, applied on a graph, approximates the MPNN applied on the geometric model that the graph discretizes.
Intrinsic interpretability of graph neural networks (GNNs) is to find a small subset of the input graph's features -- rationale -- which guides the model prediction. Unfortunately, the leading rationalization models often rely on data biases, especially shortcut features, to compose rationales and make predictions without probing the critical and causal patterns. Moreover, such data biases easily change outside the training distribution. As a result, these models suffer from a huge drop in interpretability and predictive performance on out-of-distribution data. In this work, we propose a new strategy of discovering invariant rationale (DIR) to construct intrinsically interpretable GNNs. It conducts interventions on the training distribution to create multiple interventional distributions. Then it approaches the causal rationales that are invariant across different distributions while filtering out the spurious patterns that are unstable. Experiments on both synthetic and real-world datasets validate the superiority of our DIR in terms of interpretability and generalization ability on graph classification over the leading baselines. Code and datasets are available at https://github.com/Wuyxin/DIR-GNN.
Prior studies using graph neural networks (GNNs) for image classification have focused on graphs generated from a regular grid of pixels or similar-sized superpixels. In the latter, a single target number of superpixels is defined for an entire dataset irrespective of differences across images and their intrinsic multiscale structure. On the contrary, this study investigates image classification using graphs generated from an image-specific number of multiscale superpixels. We propose WaveMesh, a new wavelet-based superpixeling algorithm, where the number and sizes of superpixels in an image are systematically computed based on its content. WaveMesh superpixel graphs are structurally different from similar-sized superpixel graphs. We use SplineCNN, a state-of-the-art network for image graph classification, to compare WaveMesh and similar-sized superpixels. Using SplineCNN, we perform extensive experiments on three benchmark datasets under three local-pooling settings: 1) no pooling, 2) GraclusPool, and 3) WavePool, a novel spatially heterogeneous pooling scheme tailored to WaveMesh superpixels. Our experiments demonstrate that SplineCNN learns from multiscale WaveMesh superpixels on-par with similar-sized superpixels. In all WaveMesh experiments, GraclusPool performs poorer than no pooling / WavePool, indicating that poor choice of pooling can result in inferior performance while learning from multiscale superpixels.
We propose a novel positional encoding for learning graph on Transformer architecture. Existing approaches either linearize a graph to encode absolute position in the sequence of nodes, or encode relative position with another node using bias terms. The former loses preciseness of relative position from linearization, while the latter loses a tight integration of node-edge and node-topology interaction. To overcome the weakness of the previous approaches, our method encodes a graph without linearization and considers both node-topology and node-edge interaction. We name our method Graph Relative Positional Encoding dedicated to graph representation learning. Experiments conducted on various graph datasets show that the proposed method outperforms previous approaches significantly. Our code is publicly available at https://github.com/lenscloth/GRPE.
Global pooling is one of the most significant operations in many machine learning models and tasks, whose implementation, however, is often empirical in practice. In this study, we develop a novel and solid global pooling framework through the lens of optimal transport. We demonstrate that most existing global pooling methods are equivalent to solving some specializations of an unbalanced optimal transport (UOT) problem. Making the parameters of the UOT problem learnable, we unify various global pooling methods in the same framework, and accordingly, propose a generalized global pooling layer called UOT-Pooling (UOTP) for neural networks. Besides implementing the UOTP layer based on the classic Sinkhorn-scaling algorithm, we design a new model architecture based on the Bregman ADMM algorithm, which has better numerical stability and can reproduce existing pooling layers more effectively. We test our UOTP layers in several application scenarios, including multi-instance learning, graph classification, and image classification. Our UOTP layers can either imitate conventional global pooling layers or learn some new pooling mechanisms leading to better performance.
Graph neural networks are powerful architectures for structured datasets. However, current methods struggle to represent long-range dependencies. Scaling the depth or width of GNNs is insufficient to broaden receptive fields as larger GNNs encounter optimization instabilities such as vanishing gradients and representation oversmoothing, while pooling-based approaches have yet to become as universally useful as in computer vision. In this work, we propose the use of Transformer-based self-attention to learn long-range pairwise relationships, with a novel "readout" mechanism to obtain a global graph embedding. Inspired by recent computer vision results that find position-invariant attention performant in learning long-range relationships, our method, which we call GraphTrans, applies a permutation-invariant Transformer module after a standard GNN module. This simple architecture leads to state-of-the-art results on several graph classification tasks, outperforming methods that explicitly encode graph structure. Our results suggest that purely-learning-based approaches without graph structure may be suitable for learning high-level, long-range relationships on graphs. Code for GraphTrans is available at https://github.com/ucbrise/graphtrans.
We study the problem of few-shot graph classification across domains with nonequivalent feature spaces by introducing three new cross-domain benchmarks constructed from publicly available datasets. We also propose an attention-based graph encoder that uses three congruent views of graphs, one contextual and two topological views, to learn representations of task-specific information for fast adaptation, and task-agnostic information for knowledge transfer. We run exhaustive experiments to evaluate the performance of contrastive and meta-learning strategies. We show that when coupled with metric-based meta-learning frameworks, the proposed encoder achieves the best average meta-test classification accuracy across all benchmarks. The source code and data will be released here: https://github.com/kavehhassani/metagrl
Controversial content refers to any content that attracts both positive and negative feedback. Its automatic identification, especially on social media, is a challenging task as it should be done on a large number of continuously evolving posts, covering a large variety of topics. Most of the existing approaches rely on the graph structure of a topic-discussion and/or the content of messages. This paper proposes a controversy detection approach based on both graph structure of a discussion and text features. Our proposed approach relies on Graph Neural Network (gnn) to encode the graph representation (including its texts) in an embedding vector before performing a graph classification task. The latter will classify the post as controversial or not. Two controversy detection strategies are proposed. The first one is based on a hierarchical graph representation learning. Graph user nodes are embedded hierarchically and iteratively to compute the whole graph embedding vector. The second one is based on the attention mechanism, which allows each user node to give more or less importance to its neighbors when computing node embeddings. We conduct experiments to evaluate our approach using different real-world datasets. Conducted experiments show the positive impact of combining textual features and structural information in terms of performance.
Graphs can model complicated interactions between entities, which naturally emerge in many important applications. These applications can often be cast into standard graph learning tasks, in which a crucial step is to learn low-dimensional graph representations. Graph neural networks (GNNs) are currently the most popular model in graph embedding approaches. However, standard GNNs in the neighborhood aggregation paradigm suffer from limited discriminative power in distinguishing \emph{high-order} graph structures as opposed to \emph{low-order} structures. To capture high-order structures, researchers have resorted to motifs and developed motif-based GNNs. However, existing motif-based GNNs still often suffer from less discriminative power on high-order structures. To overcome the above limitations, we propose Motif Graph Neural Network (MGNN), a novel framework to better capture high-order structures, hinging on our proposed motif redundancy minimization operator and injective motif combination. First, MGNN produces a set of node representations w.r.t. each motif. The next phase is our proposed redundancy minimization among motifs which compares the motifs with each other and distills the features unique to each motif. Finally, MGNN performs the updating of node representations by combining multiple representations from different motifs. In particular, to enhance the discriminative power, MGNN utilizes an injective function to combine the representations w.r.t. different motifs. We further show that our proposed architecture increases the expressive power of GNNs with a theoretical analysis. We demonstrate that MGNN outperforms state-of-the-art methods on seven public benchmarks on both node classification and graph classification tasks.