Graph neural networks, a powerful deep learning tool to model graph-structured data, have demonstrated remarkable performance on numerous graph learning tasks. To address the data noise and data scarcity issues in deep graph learning, the research on graph data augmentation has intensified lately. However, conventional data augmentation methods can hardly handle graph-structured data which is defined in non-Euclidean space with multi-modality. In this survey, we formally formulate the problem of graph data augmentation and further review the representative techniques and their applications in different deep graph learning problems. Specifically, we first propose a taxonomy for graph data augmentation techniques and then provide a structured review by categorizing the related work based on the augmented information modalities. Moreover, we summarize the applications of graph data augmentation in two representative problems in data-centric deep graph learning: (1) reliable graph learning which focuses on enhancing the utility of input graph as well as the model capacity via graph data augmentation; and (2) low-resource graph learning which targets on enlarging the labeled training data scale through graph data augmentation. For each problem, we also provide a hierarchical problem taxonomy and review the existing literature related to graph data augmentation. Finally, we point out promising research directions and the challenges in future research.
Recently, template-based (TB) and template-free (TF) molecule graph learning methods have shown promising results to retrosynthesis. TB methods are more accurate using pre-encoded reaction templates, and TF methods are more scalable by decomposing retrosynthesis into subproblems, i.e., center identification and synthon completion. To combine both advantages of TB and TF, we suggest breaking a full-template into several semi-templates and embedding them into the two-step TF framework. Since many semi-templates are reduplicative, the template redundancy can be reduced while the essential chemical knowledge is still preserved to facilitate synthon completion. We call our method SemiRetro, introduce a new GNN layer (DRGAT) to enhance center identification, and propose a novel self-correcting module to improve semi-template classification. Experimental results show that SemiRetro significantly outperforms both existing TB and TF methods. In scalability, SemiRetro covers 98.9\% data using 150 semi-templates, while previous template-based GLN requires 11,647 templates to cover 93.3\% data. In top-1 accuracy, SemiRetro exceeds template-free G2G 4.8\% (class known) and 6.0\% (class unknown). Besides, SemiRetro has better training efficiency than existing methods.
Spectral Graph Neural Networks (GNNs) with various graph filters have received extensive affirmation due to their promising performance in graph learning problems. However, it is known that GNNs do not always perform well. Although graph filters provide theoretical foundations for model explanations, it is unclear when a spectral GNN will fail. In this paper, focusing on node classification problems, we conduct a theoretical analysis of spectral GNNs performance by investigating their prediction error. With the aid of graph indicators including homophily degree and response efficiency we proposed, we establish a comprehensive understanding of complex relationships between graph structure, node labels, and graph filters. We indicate that graph filters with low response efficiency on label difference are prone to fail. To enhance GNNs performance, we provide a provably better strategy for filter design from our theoretical analysis - using data-driven filter banks, and propose simple models for empirical validation. Experimental results show consistency with our theoretical results and support our strategy.
With the explosive growth of new graduates with research degrees every year, unprecedented challenges arise for early-career researchers to find a job at a suitable institution. This study aims to understand the behavior of academic job transition and hence recommend suitable institutions for PhD graduates. Specifically, we design a deep learning model to predict the career move of early-career researchers and provide suggestions. The design is built on top of scholarly/academic networks, which contains abundant information about scientific collaboration among scholars and institutions. We construct a heterogeneous scholarly network to facilitate the exploring of the behavior of career moves and the recommendation of institutions for scholars. We devise an unsupervised learning model called HAI (Heterogeneous graph Attention InfoMax) which aggregates attention mechanism and mutual information for institution recommendation. Moreover, we propose scholar attention and meta-path attention to discover the hidden relationships between several meta-paths. With these mechanisms, HAI provides ordered recommendations with explainability. We evaluate HAI upon a real-world dataset against baseline methods. Experimental results verify the effectiveness and efficiency of our approach.
Deep graph learning (DGL) has achieved remarkable progress in both business and scientific areas ranging from finance and e-commerce to drug and advanced material discovery. Despite the progress, applying DGL to real-world applications faces a series of reliability threats including inherent noise, distribution shift, and adversarial attacks. This survey aims to provide a comprehensive review of recent advances for improving the reliability of DGL algorithms against the above threats. In contrast to prior related surveys which mainly focus on adversarial attacks and defense, our survey covers more reliability-related aspects of DGL, i.e., inherent noise and distribution shift. Additionally, we discuss the relationships among above aspects and highlight some important issues to be explored in future research.
Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriads of graph analytic tasks and applications. In general, most GNNs depend on the homophily assumption that nodes belonging to the same class are more likely to be connected. However, as a ubiquitous graph property in numerous real-world scenarios, heterophily, i.e., nodes with different labels tend to be linked, significantly limits the performance of tailor-made homophilic GNNs. Hence, GNNs for heterophilic graphs are gaining increasing research attention to enhance graph learning with heterophily. In this paper, we provide a comprehensive review of GNNs for heterophilic graphs. Specifically, we propose a systematic taxonomy that essentially governs existing heterophilic GNN models, along with a general summary and detailed analysis. Furthermore, we discuss the correlation between graph heterophily and various graph research domains, aiming to facilitate the development of more effective GNNs across a spectrum of practical applications and learning tasks in the graph research community. In the end, we point out the potential directions to advance and stimulate more future research and applications on heterophilic graph learning with GNNs.
We propose a time-varying graph signal recovery method for estimating the true time-varying graph signal from corrupted observations by leveraging dynamic graphs. Most of the conventional methods for time-varying graph signal recovery have been proposed under the assumption that the underlying graph that houses the signals is static. However, in light of rapid advances in sensor technology, the assumption that sensor networks are time-varying like the signals is becoming a very practical problem setting. In this paper, we focus on such cases and formulate dynamic graph signal recovery as a constrained convex optimization problem that simultaneously estimates both time-varying graph signals and sparsely modeled outliers. In our formulation, we use two types of regularizations, time-varying graph Laplacian-based and temporal differencebased, and also separately modeled missing values with known positions and unknown outliers to achieve robust estimations from highly degraded data. In addition, an algorithm is developed to efficiently solve the optimization problem based on a primaldual splitting method. Extensive experiments on simulated drone remote sensing data and real-world sea surface temperature data demonstrate the advantages of the proposed method over existing methods.
Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not only for the input, but also at every layer of the network. This approach involves repeatedly mapping to and from hyperbolic space, which makes these networks complicated to implement, computationally expensive to scale, and numerically unstable to train. In this paper, we propose a simpler approach: learn a hyperbolic embedding of the input, then map once from it to Euclidean space using a mapping that encodes geometric priors by respecting the isometries of hyperbolic space, and finish with a standard Euclidean network. The key insight is to use a random feature mapping via the eigenfunctions of the Laplace operator, which we show can approximate any isometry-invariant kernel on hyperbolic space. Our method can be used together with any graph neural networks: using even a linear graph model yields significant improvements in both efficiency and performance over other hyperbolic baselines in both transductive and inductive tasks.
Lighting prediction from a single image is becoming increasingly important in many vision and augmented reality (AR) applications in which shading and shadow consistency between virtual and real objects should be guaranteed. However, this is a notoriously ill-posed problem, especially for indoor scenarios, because of the complexity of indoor luminaires and the limited information involved in 2D images. In this paper, we propose a graph learning-based framework for indoor lighting estimation. At its core is a new lighting model (dubbed DSGLight) based on depth-augmented Spherical Gaussians (SG) and a Graph Convolutional Network (GCN) that infers the new lighting representation from a single LDR image of limited field-of-view. Our lighting model builds 128 evenly distributed SGs over the indoor panorama, where each SG encoding the lighting and the depth around that node. The proposed GCN then learns the mapping from the input image to DSGLight. Compared with existing lighting models, our DSGLight encodes both direct lighting and indirect environmental lighting more faithfully and compactly. It also makes network training and inference more stable. The estimated depth distribution enables temporally stable shading and shadows under spatially-varying lighting. Through thorough experiments, we show that our method obviously outperforms existing methods both qualitatively and quantitatively.
Open-set domain adaptation (OSDA) has gained considerable attention in many visual recognition tasks. However, most existing OSDA approaches are limited due to three main reasons, including: (1) the lack of essential theoretical analysis of generalization bound, (2) the reliance on the coexistence of source and target data during adaptation, and (3) failing to accurately estimate the uncertainty of model predictions. We propose a Progressive Graph Learning (PGL) framework that decomposes the target hypothesis space into the shared and unknown subspaces, and then progressively pseudo-labels the most confident known samples from the target domain for hypothesis adaptation. Moreover, we tackle a more realistic source-free open-set domain adaptation (SF-OSDA) setting that makes no assumption about the coexistence of source and target domains, and introduce a balanced pseudo-labeling (BP-L) strategy in a two-stage framework, namely SF-PGL. Different from PGL that applies a class-agnostic constant threshold for all target samples for pseudo-labeling, the SF-PGL model uniformly selects the most confident target instances from each category at a fixed ratio. The confidence thresholds in each class are regarded as the 'uncertainty' of learning the semantic information, which are then used to weigh the classification loss in the adaptation step. We conducted unsupervised and semi-supervised OSDA and SF-OSDA experiments on the benchmark image classification and action recognition datasets. Additionally, we find that balanced pseudo-labeling plays a significant role in improving calibration, which makes the trained model less prone to over-confident or under-confident predictions on the target data. Source code is available at https://github.com/Luoyadan/SF-PGL.
For weakly supervised anomaly detection, most existing work is limited to the problem of inadequate video representation due to the inability of modeling long-term contextual information. To solve this, we propose a novel weakly supervised adaptive graph convolutional network (WAGCN) to model the complex contextual relationship among video segments. By which, we fully consider the influence of other video segments on the current one when generating the anomaly probability score for each segment. Firstly, we combine the temporal consistency as well as feature similarity of video segments to construct a global graph, which makes full use of the association information among spatial-temporal features of anomalous events in videos. Secondly, we propose a graph learning layer in order to break the limitation of setting topology manually, which can extract graph adjacency matrix based on data adaptively and effectively. Extensive experiments on two public datasets (i.e., UCF-Crime dataset and ShanghaiTech dataset) demonstrate the effectiveness of our approach which achieves state-of-the-art performance.
Despite recent success in using the invariance principle for out-of-distribution (OOD) generalization on Euclidean data (e.g., images), studies on graph data are still limited. Different from images, the complex nature of graphs poses unique challenges to adopting the invariance principle. In particular, distribution shifts on graphs can appear in a variety of forms such as attributes and structures, making it difficult to identify the invariance. Moreover, domain or environment partitions, which are often required by OOD methods on Euclidean data, could be highly expensive to obtain for graphs. To bridge this gap, we propose a new framework, called Causality Inspired Invariant Graph LeArning (CIGA), to capture the invariance of graphs for guaranteed OOD generalization under various distribution shifts. Specifically, we characterize potential distribution shifts on graphs with causal models, concluding that OOD generalization on graphs is achievable when models focus only on subgraphs containing the most information about the causes of labels. Accordingly, we propose an information-theoretic objective to extract the desired subgraphs that maximally preserve the invariant intra-class information. Learning with these subgraphs is immune to distribution shifts. Extensive experiments on 16 synthetic or real-world datasets, including a challenging setting -- DrugOOD, from AI-aided drug discovery, validate the superior OOD performance of CIGA.
The performance of graph representation learning is affected by the quality of graph input. While existing research usually pursues a globally smoothed graph embedding, we believe the rarely observed anomalies are as well harmful to an accurate prediction. This work establishes a graph learning scheme that automatically detects (locally) corrupted feature attributes and recovers robust embedding for prediction tasks. The detection operation leverages a graph autoencoder, which does not make any assumptions about the distribution of the local corruptions. It pinpoints the positions of the anomalous node attributes in an unbiased mask matrix, where robust estimations are recovered with sparsity promoting regularizer. The optimizer approaches a new embedding that is sparse in the framelet domain and conditionally close to input observations. Extensive experiments are provided to validate our proposed model can recover a robust graph representation from black-box poisoning and achieve excellent performance.
Designing spectral convolutional networks is a challenging problem in graph learning. ChebNet, one of the early attempts, approximates the spectral graph convolutions using Chebyshev polynomials. GCN simplifies ChebNet by utilizing only the first two Chebyshev polynomials while still outperforming it on real-world datasets. GPR-GNN and BernNet demonstrate that the Monomial and Bernstein bases also outperform the Chebyshev basis in terms of learning the spectral graph convolutions. Such conclusions are counter-intuitive in the field of approximation theory, where it is established that the Chebyshev polynomial achieves the optimum convergent rate for approximating a function. In this paper, we revisit the problem of approximating the spectral graph convolutions with Chebyshev polynomials. We show that ChebNet's inferior performance is primarily due to illegal coefficients learnt by ChebNet approximating analytic filter functions, which leads to over-fitting. We then propose ChebNetII, a new GNN model based on Chebyshev interpolation, which enhances the original Chebyshev polynomial approximation while reducing the Runge phenomenon. We conducted an extensive experimental study to demonstrate that ChebNetII can learn arbitrary graph convolutions and achieve superior performance in both full- and semi-supervised node classification tasks. Most notably, we scale ChebNetII to a billion graph ogbn-papers100M, showing that spectral-based GNNs have superior performance. Our code is available at https://github.com/ivam-he/ChebNetII.
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the principle of majorization-minimization (MM), wherein we first obtain a tight surrogate function for the graph learning objective and then solve the resultant surrogate problem which has a simple closed form solution. The proposed algorithm does not require tuning of any hyperparameter and it has the desirable feature of eliminating the inactive variables in the course of the iterations - which can help speeding up the algorithm. The numerical simulations conducted using both synthetic and real world (brain-network) data show that the proposed algorithm converges faster, in terms of the average number of iterations, than several existing methods in the literature.
Learning the similarity between structured data, especially the graphs, is one of the essential problems. Besides the approach like graph kernels, Gromov-Wasserstein (GW) distance recently draws big attention due to its flexibility to capture both topological and feature characteristics, as well as handling the permutation invariance. However, structured data are widely distributed for different data mining and machine learning applications. With privacy concerns, accessing the decentralized data is limited to either individual clients or different silos. To tackle these issues, we propose a privacy-preserving framework to analyze the GW discrepancy of node embedding learned locally from graph neural networks in a federated flavor, and then explicitly place local differential privacy (LDP) based on Multi-bit Encoder to protect sensitive information. Our experiments show that, with strong privacy protections guaranteed by the $\varepsilon$-LDP algorithm, the proposed framework not only preserves privacy in graph learning but also presents a noised structural metric under GW distance, resulting in comparable and even better performance in classification and clustering tasks. Moreover, we reason the rationale behind the LDP-based GW distance analytically and empirically.
Recently, flat-minima optimizers, which seek to find parameters in low-loss neighborhoods, have been shown to improve a neural network's generalization performance over stochastic and adaptive gradient-based optimizers. Two methods have received significant attention due to their scalability: 1. Stochastic Weight Averaging (SWA), and 2. Sharpness-Aware Minimization (SAM). However, there has been limited investigation into their properties and no systematic benchmarking of them across different domains. We fill this gap here by comparing the loss surfaces of the models trained with each method and through broad benchmarking across computer vision, natural language processing, and graph representation learning tasks. We discover several surprising findings from these results, which we hope will help researchers further improve deep learning optimizers, and practitioners identify the right optimizer for their problem.
Interpretable graph learning is in need as many scientific applications depend on learning models to collect insights from graph-structured data. Previous works mostly focused on using post-hoc approaches to interpret pre-trained models (graph neural networks in particular). They argue against inherently interpretable models because the good interpretability of these models is often at the cost of their prediction accuracy. However, those post-hoc methods often fail to provide stable interpretation and may extract features that are spuriously correlated with the task. In this work, we address these issues by proposing Graph Stochastic Attention (GSAT). Derived from the information bottleneck principle, GSAT injects stochasticity to the attention weights to block the information from task-irrelevant graph components while learning stochasticity-reduced attention to select task-relevant subgraphs for interpretation. The selected subgraphs provably do not contain patterns that are spuriously correlated with the task under some assumptions. Extensive experiments on eight datasets show that GSAT outperforms the state-of-the-art methods by up to 20%$\uparrow$ in interpretation AUC and 5%$\uparrow$ in prediction accuracy. Our code is available at https://github.com/Graph-COM/GSAT.
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and can be a serious bottleneck for the learning pipeline. Inspired by recent success in neural algorithmic reasoning, we propose a novel graph neural network to estimate extended persistence diagrams (EPDs) on graphs efficiently. Our model is built on algorithmic insights, and benefits from better supervision and closer alignment with the EPD computation algorithm. We validate our method with convincing empirical results on approximating EPDs and downstream graph representation learning tasks. Our method is also efficient; on large and dense graphs, we accelerate the computation by nearly 100 times.
Higher-order features bring significant accuracy gains in semantic dependency parsing. However, modeling higher-order features with exact inference is NP-hard. Graph neural networks (GNNs) have been demonstrated to be an effective tool for solving NP-hard problems with approximate inference in many graph learning tasks. Inspired by the success of GNNs, we investigate building a higher-order semantic dependency parser by applying GNNs. Instead of explicitly extracting higher-order features from intermediate parsing graphs, GNNs aggregate higher-order information concisely by stacking multiple GNN layers. Experimental results show that our model outperforms the previous state-of-the-art parser on the SemEval 2015 Task 18 English datasets.