To make accurate predictions, understand mechanisms, and design interventions in systems of many variables, we wish to learn causal graphs from large scale data. Unfortunately the space of all possible causal graphs is enormous so scalably and accurately searching for the best fit to the data is a challenge. In principle we could substantially decrease the search space, or learn the graph entirely, by testing the conditional independence of variables. However, deciding if two variables are adjacent in a causal graph may require an exponential number of tests. Here we build a scalable and flexible method to evaluate if two variables are adjacent in a causal graph, the Differentiable Adjacency Test (DAT). DAT replaces an exponential number of tests with a provably equivalent relaxed problem. It then solves this problem by training two neural networks. We build a graph learning method based on DAT, DAT-Graph, that can also learn from data with interventions. DAT-Graph can learn graphs of 1000 variables with state of the art accuracy. Using the graph learned by DAT-Graph, we also build models that make much more accurate predictions of the effects of interventions on large scale RNA sequencing data.
Estimating matrices in the symmetric positive-definite (SPD) cone is of interest for many applications ranging from computer vision to graph learning. While there exist various convex optimization-based estimators, they remain limited in expressivity due to their model-based approach. The success of deep learning motivates the use of learning-based approaches to estimate SPD matrices with neural networks in a data-driven fashion. However, designing effective neural architectures for SPD learning is challenging, particularly when the task requires additional structural constraints, such as element-wise sparsity. Current approaches either do not ensure that the output meets all desired properties or lack expressivity. In this paper, we introduce SpodNet, a novel and generic learning module that guarantees SPD outputs and supports additional structural constraints. Notably, it solves the challenging task of learning jointly SPD and sparse matrices. Our experiments illustrate the versatility and relevance of SpodNet layers for such applications.
Subgraph Graph Neural Networks (Subgraph GNNs) enhance the expressivity of message-passing GNNs by representing graphs as sets of subgraphs. They have shown impressive performance on several tasks, but their complexity limits applications to larger graphs. Previous approaches suggested processing only subsets of subgraphs, selected either randomly or via learnable sampling. However, they make suboptimal subgraph selections or can only cope with very small subset sizes, inevitably incurring performance degradation. This paper introduces a new Subgraph GNNs framework to address these issues. We employ a graph coarsening function to cluster nodes into super-nodes with induced connectivity. The product between the coarsened and the original graph reveals an implicit structure whereby subgraphs are associated with specific sets of nodes. By running generalized message-passing on such graph product, our method effectively implements an efficient, yet powerful Subgraph GNN. Controlling the coarsening function enables meaningful selection of any number of subgraphs while, contrary to previous methods, being fully compatible with standard training techniques. Notably, we discover that the resulting node feature tensor exhibits new, unexplored permutation symmetries. We leverage this structure, characterize the associated linear equivariant layers and incorporate them into the layers of our Subgraph GNN architecture. Extensive experiments on multiple graph learning benchmarks demonstrate that our method is significantly more flexible than previous approaches, as it can seamlessly handle any number of subgraphs, while consistently outperforming baseline approaches.
CAD (Computer-Aided Design) plays a crucial role in mechanical industry, where large numbers of similar-shaped CAD parts are often created. Efficiently reusing these parts is key to reducing design and production costs for enterprises. Retrieval systems are vital for achieving CAD reuse, but the complex shapes of CAD models are difficult to accurately describe using text or keywords, making traditional retrieval methods ineffective. While existing representation learning approaches have been developed for CAD, manually labeling similar samples in these methods is expensive. Additionally, CAD models' unique parameterized data structure presents challenges for applying existing 3D shape representation learning techniques directly. In this work, we propose GC-CAD, a self-supervised contrastive graph neural network-based method for mechanical CAD retrieval that directly models parameterized CAD raw files. GC-CAD consists of two key modules: structure-aware representation learning and contrastive graph learning framework. The method leverages graph neural networks to extract both geometric and topological information from CAD models, generating feature representations. We then introduce a simple yet effective contrastive graph learning framework approach, enabling the model to train without manual labels and generate retrieval-ready representations. Experimental results on four datasets including human evaluation demonstrate that the proposed method achieves significant accuracy improvements and up to 100 times efficiency improvement over the baseline methods.
In the realm of personalized recommender systems, the challenge of adapting to evolving user preferences and the continuous influx of new users and items is paramount. Conventional models, typically reliant on a static training-test approach, struggle to keep pace with these dynamic demands. Streaming recommendation, particularly through continual graph learning, has emerged as a novel solution. However, existing methods in this area either rely on historical data replay, which is increasingly impractical due to stringent data privacy regulations; or are inability to effectively address the over-stability issue; or depend on model-isolation and expansion strategies. To tackle these difficulties, we present GPT4Rec, a Graph Prompt Tuning method for streaming Recommendation. Given the evolving user-item interaction graph, GPT4Rec first disentangles the graph patterns into multiple views. After isolating specific interaction patterns and relationships in different views, GPT4Rec utilizes lightweight graph prompts to efficiently guide the model across varying interaction patterns within the user-item graph. Firstly, node-level prompts are employed to instruct the model to adapt to changes in the attributes or properties of individual nodes within the graph. Secondly, structure-level prompts guide the model in adapting to broader patterns of connectivity and relationships within the graph. Finally, view-level prompts are innovatively designed to facilitate the aggregation of information from multiple disentangled views. These prompt designs allow GPT4Rec to synthesize a comprehensive understanding of the graph, ensuring that all vital aspects of the user-item interactions are considered and effectively integrated. Experiments on four diverse real-world datasets demonstrate the effectiveness and efficiency of our proposal.
Link prediction is a fundamental task in graph learning, inherently shaped by the topology of the graph. While traditional heuristics are grounded in graph topology, they encounter challenges in generalizing across diverse graphs. Recent research efforts have aimed to leverage the potential of heuristics, yet a unified formulation accommodating both local and global heuristics remains undiscovered. Drawing insights from the fact that both local and global heuristics can be represented by adjacency matrix multiplications, we propose a unified matrix formulation to accommodate and generalize various heuristics. We further propose the Heuristic Learning Graph Neural Network (HL-GNN) to efficiently implement the formulation. HL-GNN adopts intra-layer propagation and inter-layer connections, allowing it to reach a depth of around 20 layers with lower time complexity than GCN. Extensive experiments on the Planetoid, Amazon, and OGB datasets underscore the effectiveness and efficiency of HL-GNN. It outperforms existing methods by a large margin in prediction performance. Additionally, HL-GNN is several orders of magnitude faster than heuristic-inspired methods while requiring only a few trainable parameters. The case study further demonstrates that the generalized heuristics and learned weights are highly interpretable.
Graph neural networks (GNNs) have become instrumental in diverse real-world applications, offering powerful graph learning capabilities for tasks such as social networks and medical data analysis. Despite their successes, GNNs are vulnerable to adversarial attacks, including membership inference attacks (MIA), which threaten privacy by identifying whether a record was part of the model's training data. While existing research has explored MIA in GNNs under graph inductive learning settings, the more common and challenging graph transductive learning setting remains understudied in this context. This paper addresses this gap and proposes an effective two-stage defense, Graph Transductive Defense (GTD), tailored to graph transductive learning characteristics. The gist of our approach is a combination of a train-test alternate training schedule and flattening strategy, which successfully reduces the difference between the training and testing loss distributions. Extensive empirical results demonstrate the superior performance of our method (a decrease in attack AUROC by $9.42\%$ and an increase in utility performance by $18.08\%$ on average compared to LBP), highlighting its potential for seamless integration into various classification models with minimal overhead.
COVID-19 as a global pandemic causes a massive disruption to social stability that threatens human life and the economy. Policymakers and all elements of society must deliver measurable actions based on the pandemic's severity to minimize the detrimental impact of COVID-19. A proper forecasting system is arguably important to provide an early signal of the risk of COVID-19 infection so that the authorities are ready to protect the people from the worst. However, making a good forecasting model for infection risks in different cities or regions is not an easy task, because it has a lot of influential factors that are difficult to be identified manually. To address the current limitations, we propose a deep graph learning model, called PANDORA, to predict the infection risks of COVID-19, by considering all essential factors and integrating them into a geographical network. The framework uses geographical position relations and transportation frequency as higher-order structural properties formulated by higher-order network structures (i.e., network motifs). Moreover, four significant node attributes (i.e., multiple features of a particular area, including climate, medical condition, economy, and human mobility) are also considered. We propose three different aggregators to better aggregate node attributes and structural features, namely, Hadamard, Summation, and Connection. Experimental results over real data show that PANDORA outperforms the baseline method with higher accuracy and faster convergence speed, no matter which aggregator is chosen. We believe that PANDORA using deep graph learning provides a promising approach to get superior performance in infection risk level forecasting and help humans battle the COVID-19 crisis.
Extensive research efforts have been put into characterizing and constructing maximally separating multiset and graph neural networks. However, recent empirical evidence suggests the notion of separation itself doesn't capture several interesting phenomena. On the one hand, the quality of this separation may be very weak, to the extent that the embeddings of "separable" objects might even be considered identical when using fixed finite precision. On the other hand, architectures which aren't capable of separation in theory, somehow achieve separation when taking the network to be wide enough. In this work, we address both of these issues, by proposing a novel pair-wise separation quality analysis framework which is based on an adaptation of Lipschitz and \Holder{} stability to parametric functions. The proposed framework, which we name \emph{\Holder{} in expectation}, allows for separation quality analysis, without restricting the analysis to embeddings that can separate all the input space simultaneously. We prove that common sum-based models are lower-\Holder{} in expectation, with an exponent that decays rapidly with the network's depth . Our analysis leads to adversarial examples of graphs which can be separated by three 1-WL iterations, but cannot be separated in practice by standard maximally powerful Message Passing Neural Networks (MPNNs). To remedy this, we propose two novel MPNNs with improved separation quality, one of which is lower Lipschitz in expectation. We show these MPNNs can easily classify our adversarial examples, and compare favorably with standard MPNNs on standard graph learning tasks.
Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still lacking. Previous GNN generalization bounds ignore the underlying graph structures, often leading to bounds that increase with the number of nodes -- a behavior contrary to the one experienced in practice. In this paper, we take a manifold perspective to establish the statistical generalization theory of GNNs on graphs sampled from a manifold in the spectral domain. As demonstrated empirically, we prove that the generalization bounds of GNNs decrease linearly with the size of the graphs in the logarithmic scale, and increase linearly with the spectral continuity constants of the filter functions. Notably, our theory explains both node-level and graph-level tasks. Our result has two implications: i) guaranteeing the generalization of GNNs to unseen data over manifolds; ii) providing insights into the practical design of GNNs, i.e., restrictions on the discriminability of GNNs are necessary to obtain a better generalization performance. We demonstrate our generalization bounds of GNNs using synthetic and multiple real-world datasets.
We introduce Graph Kolmogorov-Arnold Networks (GKAN), an innovative neural network architecture that extends the principles of the recently proposed Kolmogorov-Arnold Networks (KAN) to graph-structured data. By adopting the unique characteristics of KANs, notably the use of learnable univariate functions instead of fixed linear weights, we develop a powerful model for graph-based learning tasks. Unlike traditional Graph Convolutional Networks (GCNs) that rely on a fixed convolutional architecture, GKANs implement learnable spline-based functions between layers, transforming the way information is processed across the graph structure. We present two different ways to incorporate KAN layers into GKAN: architecture 1 -- where the learnable functions are applied to input features after aggregation and architecture 2 -- where the learnable functions are applied to input features before aggregation. We evaluate GKAN empirically using a semi-supervised graph learning task on a real-world dataset (Cora). We find that architecture generally performs better. We find that GKANs achieve higher accuracy in semi-supervised learning tasks on graphs compared to the traditional GCN model. For example, when considering 100 features, GCN provides an accuracy of 53.5 while a GKAN with a comparable number of parameters gives an accuracy of 61.76; with 200 features, GCN provides an accuracy of 61.24 while a GKAN with a comparable number of parameters gives an accuracy of 67.66. We also present results on the impact of various parameters such as the number of hidden nodes, grid-size, and the polynomial-degree of the spline on the performance of GKAN.
In recommendation systems, high-quality user embeddings can capture subtle preferences, enable precise similarity calculations, and adapt to changing preferences over time to maintain relevance. The effectiveness of recommendation systems depends on the quality of user embedding. We propose to asynchronously learn high fidelity user embeddings for billions of users each day from sequence based multimodal user activities through a Transformer-like large scale feature learning module. The async learned user representations embeddings (ALURE) are further converted to user similarity graphs through graph learning and then combined with user realtime activities to retrieval highly related ads candidates for the ads delivery system. Our method shows significant gains in both offline and online experiments.
Anomaly detection (such as telecom fraud detection and medical image detection) has attracted the increasing attention of people. The complex interaction between multiple entities widely exists in the network, which can reflect specific human behavior patterns. Such patterns can be modeled by higher-order network structures, thus benefiting anomaly detection on attributed networks. However, due to the lack of an effective mechanism in most existing graph learning methods, these complex interaction patterns fail to be applied in detecting anomalies, hindering the progress of anomaly detection to some extent. In order to address the aforementioned issue, we present a higher-order structure based anomaly detection (GUIDE) method. We exploit attribute autoencoder and structure autoencoder to reconstruct node attributes and higher-order structures, respectively. Moreover, we design a graph attention layer to evaluate the significance of neighbors to nodes through their higher-order structure differences. Finally, we leverage node attribute and higher-order structure reconstruction errors to find anomalies. Extensive experiments on five real-world datasets (i.e., ACM, Citation, Cora, DBLP, and Pubmed) are implemented to verify the effectiveness of GUIDE. Experimental results in terms of ROC-AUC, PR-AUC, and Recall@K show that GUIDE significantly outperforms the state-of-art methods.
Dynamic link prediction is an important problem considered by many recent works proposing various approaches for learning temporal edge patterns. To assess their efficacy, models are evaluated on publicly available benchmark datasets involving continuous-time and discrete-time temporal graphs. However, as we show in this work, the suitability of common batch-oriented evaluation depends on the datasets' characteristics, which can cause two issues: First, for continuous-time temporal graphs, fixed-size batches create time windows with different durations, resulting in an inconsistent dynamic link prediction task. Second, for discrete-time temporal graphs, the sequence of batches can additionally introduce temporal dependencies that are not present in the data. In this work, we empirically show that this common evaluation approach leads to skewed model performance and hinders the fair comparison of methods. We mitigate this problem by reformulating dynamic link prediction as a link forecasting task that better accounts for temporal information present in the data. We provide implementations of our new evaluation method for commonly used graph learning frameworks.
Multitude of deep learning models have been proposed for node classification in graphs. However, they tend to perform poorly under labeled-data scarcity. Although Few-shot learning for graphs has been introduced to overcome this problem, the existing models are not easily adaptable for generic graph learning frameworks like Graph Neural Networks (GNNs). Our work proposes an Uncertainty Estimator framework that can be applied on top of any generic GNN backbone network (which are typically designed for supervised/semi-supervised node classification) to improve the node classification performance. A neural network is used to model the Uncertainty Estimator as a probability distribution rather than probabilistic discrete scalar values. We train these models under the classic episodic learning paradigm in the $n$-way, $k$-shot fashion, in an end-to-end setting. Our work demonstrates that implementation of the uncertainty estimator on a GNN backbone network improves the classification accuracy under Few-shot setting without any meta-learning specific architecture. We conduct experiments on multiple datasets under different Few-shot settings and different GNN-based backbone networks. Our method outperforms the baselines, which demonstrates the efficacy of the Uncertainty Estimator for Few-shot node classification on graphs with a GNN.
Graph signal processing represents an important advancement in the field of data analysis, extending conventional signal processing methodologies to complex networks and thereby facilitating the exploration of informative patterns and structures across various domains. However, acquiring the underlying graphs for specific applications remains a challenging task. While graph inference based on smooth graph signal representation has become one of the state-of-the-art methods, these approaches usually overlook the unique properties of networks, which are generally derived from domain-specific knowledge. Overlooking this information could make the approaches less interpretable and less effective overall. In this study, we propose a new graph inference method that leverages available domain knowledge. The proposed methodology is evaluated on the task of denoising and imputing missing sensor data, utilizing graph signal reconstruction techniques. The results demonstrate that incorporating domain knowledge into the graph inference process can improve graph signal reconstruction in district heating networks. Our code is available at \href{https://github.com/Keiv4n/IGL}{github.com/Keiv4n/IGL}.
We build interpretable and lightweight transformer-like neural networks by unrolling iterative optimization algorithms that minimize graph smoothness priors -- the quadratic graph Laplacian regularizer (GLR) and the $\ell_1$-norm graph total variation (GTV) -- subject to an interpolation constraint. The crucial insight is that a normalized signal-dependent graph learning module amounts to a variant of the basic self-attention mechanism in conventional transformers. Unlike "black-box" transformers that require learning of large key, query and value matrices to compute scaled dot products as affinities and subsequent output embeddings, resulting in huge parameter sets, our unrolled networks employ shallow CNNs to learn low-dimensional features per node to establish pairwise Mahalanobis distances and construct sparse similarity graphs. At each layer, given a learned graph, the target interpolated signal is simply a low-pass filtered output derived from the minimization of an assumed graph smoothness prior, leading to a dramatic reduction in parameter count. Experiments for two image interpolation applications verify the restoration performance, parameter efficiency and robustness to covariate shift of our graph-based unrolled networks compared to conventional transformers.
Exploring the complex structure of the human brain is crucial for understanding its functionality and diagnosing brain disorders. Thanks to advancements in neuroimaging technology, a novel approach has emerged that involves modeling the human brain as a graph-structured pattern, with different brain regions represented as nodes and the functional relationships among these regions as edges. Moreover, graph neural networks (GNNs) have demonstrated a significant advantage in mining graph-structured data. Developing GNNs to learn brain graph representations for brain disorder analysis has recently gained increasing attention. However, there is a lack of systematic survey work summarizing current research methods in this domain. In this paper, we aim to bridge this gap by reviewing brain graph learning works that utilize GNNs. We first introduce the process of brain graph modeling based on common neuroimaging data. Subsequently, we systematically categorize current works based on the type of brain graph generated and the targeted research problems. To make this research accessible to a broader range of interested researchers, we provide an overview of representative methods and commonly used datasets, along with their implementation sources. Finally, we present our insights on future research directions. The repository of this survey is available at \url{https://github.com/XuexiongLuoMQ/Awesome-Brain-Graph-Learning-with-GNNs}.
Previous graph-based approaches in Aspect based Sentiment Analysis(ABSA) have demonstrated impressive performance by utilizing graph neural networks and attention mechanisms to learn structures of static dependency trees and dynamic latent trees. However, incorporating both semantic and syntactic information simultaneously within complex global structures can introduce irrelevant contexts and syntactic dependencies during the process of graph structure learning, potentially resulting in inaccurate predictions. In order to address the issues above, we propose S$^2$GSL, incorporating Segment to Syntactic enhanced Graph Structure Learning for ABSA. Specifically,S$^2$GSL is featured with a segment-aware semantic graph learning and a syntax-based latent graph learning enabling the removal of irrelevant contexts and dependencies, respectively. We further propose a self-adaptive aggregation network that facilitates the fusion of two graph learning branches, thereby achieving complementarity across diverse structures. Experimental results on four benchmarks demonstrate the effectiveness of our framework.
Accurate traffic flow forecasting is a crucial research topic in transportation management. However, it is a challenging problem due to rapidly changing traffic conditions, high nonlinearity of traffic flow, and complex spatial and temporal correlations of road networks. Most existing studies either try to capture the spatial dependencies between roads using the same semantic graph over different time steps, or assume all sensors on the roads are equally likely to be connected regardless of the distance between them. However, we observe that the spatial dependencies between roads indeed change over time, and two distant roads are not likely to be helpful to each other when predicting the traffic flow, both of which limit the performance of existing studies. In this paper, we propose Temporal Graph Learning Recurrent Neural Network (TGLRN) to address these problems. More precisely, to effectively model the nature of time series, we leverage Recurrent Neural Networks (RNNs) to dynamically construct a graph at each time step, thereby capturing the time-evolving spatial dependencies between roads (i.e., microscopic view). Simultaneously, we provide the Adaptive Structure Information to the model, ensuring that close and consecutive sensors are considered to be more important for predicting the traffic flow (i.e., macroscopic view). Furthermore, to endow TGLRN with robustness, we introduce an edge sampling strategy when constructing the graph at each time step, which eventually leads to further improvements on the model performance. Experimental results on four commonly used real-world benchmark datasets show the effectiveness of TGLRN.