The prompt estimation of traffic incident impacts can guide commuters in their trip planning and improve the resilience of transportation agencies' decision-making on resilience. However, it is more challenging than node-level and graph-level forecasting tasks, as it requires extracting the anomaly subgraph or sub-time-series from dynamic graphs. In this paper, we propose DG-Trans, a novel traffic incident impact prediction framework, to foresee the impact of traffic incidents through dynamic graph learning. The proposed framework contains a dual-level spatial transformer and an importance-score-based temporal transformer, and the performance of this framework is justified by two newly constructed benchmark datasets. The dual-level spatial transformer removes unnecessary edges between nodes to isolate the affected subgraph from the other nodes. Meanwhile, the importance-score-based temporal transformer identifies abnormal changes in node features, causing the predictions to rely more on measurement changes after the incident occurs. Therefore, DG-Trans is equipped with dual abilities that extract spatiotemporal dependency and identify anomaly nodes affected by incidents while removing noise introduced by benign nodes. Extensive experiments on real-world datasets verify that DG-Trans outperforms the existing state-of-the-art methods, especially in extracting spatiotemporal dependency patterns and predicting traffic accident impacts. It offers promising potential for traffic incident management systems.
Dynamic graphs arise in various real-world applications, and it is often welcomed to model the dynamics directly in continuous time domain for its flexibility. This paper aims to design an easy-to-use pipeline (termed as EasyDGL which is also due to its implementation by DGL toolkit) composed of three key modules with both strong fitting ability and interpretability. Specifically the proposed pipeline which involves encoding, training and interpreting: i) a temporal point process (TPP) modulated attention architecture to endow the continuous-time resolution with the coupled spatiotemporal dynamics of the observed graph with edge-addition events; ii) a principled loss composed of task-agnostic TPP posterior maximization based on observed events on the graph, and a task-aware loss with a masking strategy over dynamic graph, where the covered tasks include dynamic link prediction, dynamic node classification and node traffic forecasting; iii) interpretation of the model outputs (e.g., representations and predictions) with scalable perturbation-based quantitative analysis in the graph Fourier domain, which could more comprehensively reflect the behavior of the learned model. Extensive experimental results on public benchmarks show the superior performance of our EasyDGL for time-conditioned predictive tasks, and in particular demonstrate that EasyDGL can effectively quantify the predictive power of frequency content that a model learn from the evolving graph data.
Personalized recommender systems have been widely studied and deployed to reduce information overload and satisfy users' diverse needs. However, conventional recommendation models solely conduct a one-time training-test fashion and can hardly adapt to evolving demands, considering user preference shifts and ever-increasing users and items in the real world. To tackle such challenges, the streaming recommendation is proposed and has attracted great attention recently. Among these, continual graph learning is widely regarded as a promising approach for the streaming recommendation by academia and industry. However, existing methods either rely on the historical data replay which is often not practical under increasingly strict data regulations, or can seldom solve the \textit{over-stability} issue. To overcome these difficulties, we propose a novel \textbf{D}ynamically \textbf{E}xpandable \textbf{G}raph \textbf{C}onvolution (DEGC) algorithm from a \textit{model isolation} perspective for the streaming recommendation which is orthogonal to previous methods. Based on the motivation of disentangling outdated short-term preferences from useful long-term preferences, we design a sequence of operations including graph convolution pruning, refining, and expanding to only preserve beneficial long-term preference-related parameters and extract fresh short-term preferences. Moreover, we model the temporal user preference, which is utilized as user embedding initialization, for better capturing the individual-level preference shifts. Extensive experiments on the three most representative GCN-based recommendation models and four industrial datasets demonstrate the effectiveness and robustness of our method.
We investigate the enhancement of graph neural networks' (GNNs) representation power through their ability in substructure counting. Recent advances have seen the adoption of subgraph GNNs, which partition an input graph into numerous subgraphs, subsequently applying GNNs to each to augment the graph's overall representation. Despite their ability to identify various substructures, subgraph GNNs are hindered by significant computational and memory costs. In this paper, we tackle a critical question: Is it possible for GNNs to count substructures both \textbf{efficiently} and \textbf{provably}? Our approach begins with a theoretical demonstration that the distance to rooted nodes in subgraphs is key to boosting the counting power of subgraph GNNs. To avoid the need for repetitively applying GNN across all subgraphs, we introduce precomputed structural embeddings that encapsulate this crucial distance information. Experiments validate that our proposed model retains the counting power of subgraph GNNs while achieving significantly faster performance.
This paper presents our Facial Action Units (AUs) detection submission to the fifth Affective Behavior Analysis in-the-wild Competition (ABAW). Our approach consists of three main modules: (i) a pre-trained facial representation encoder which produce a strong facial representation from each input face image in the input sequence; (ii) an AU-specific feature generator that specifically learns a set of AU features from each facial representation; and (iii) a spatio-temporal graph learning module that constructs a spatio-temporal graph representation. This graph representation describes AUs contained in all frames and predicts the occurrence of each AU based on both the modeled spatial information within the corresponding face and the learned temporal dynamics among frames. The experimental results show that our approach outperformed the baseline and the spatio-temporal graph representation learning allows our model to generate the best results among all ablated systems. Our model ranks at the 4th place in the AU recognition track at the 5th ABAW Competition. Our code is publicly available at https://github.com/wzh125/ABAW-5.
Graph transformers have emerged as a promising architecture for a variety of graph learning and representation tasks. Despite their successes, though, it remains challenging to scale graph transformers to large graphs while maintaining accuracy competitive with message-passing networks. In this paper, we introduce Exphormer, a framework for building powerful and scalable graph transformers. Exphormer consists of a sparse attention mechanism based on two mechanisms: virtual global nodes and expander graphs, whose mathematical characteristics, such as spectral expansion, pseduorandomness, and sparsity, yield graph transformers with complexity only linear in the size of the graph, while allowing us to prove desirable theoretical properties of the resulting transformer models. We show that incorporating Exphormer into the recently-proposed GraphGPS framework produces models with competitive empirical results on a wide variety of graph datasets, including state-of-the-art results on three datasets. We also show that Exphormer can scale to datasets on larger graphs than shown in previous graph transformer architectures. Code can be found at \url{https://github.com/hamed1375/Exphormer}.
Heterogeneous graphs provide a compact, efficient, and scalable way to model data involving multiple disparate modalities. This makes modeling audiovisual data using heterogeneous graphs an attractive option. However, graph structure does not appear naturally in audiovisual data. Graphs for audiovisual data are constructed manually which is both difficult and sub-optimal. In this work, we address this problem by (i) proposing a parametric graph construction strategy for the intra-modal edges, and (ii) learning the crossmodal edges. To this end, we develop a new model, heterogeneous graph crossmodal network (HGCN) that learns the crossmodal edges. Our proposed model can adapt to various spatial and temporal scales owing to its parametric construction, while the learnable crossmodal edges effectively connect the relevant nodes across modalities. Experiments on a large benchmark dataset (AudioSet) show that our model is state-of-the-art (0.53 mean average precision), outperforming transformer-based models and other graph-based models.
Cellular traffic prediction is an indispensable part for intelligent telecommunication networks. Nevertheless, due to the frequent user mobility and complex network scheduling mechanisms, cellular traffic often inherits complicated spatial-temporal patterns, making the prediction incredibly challenging. Although recent advanced algorithms such as graph-based prediction approaches have been proposed, they frequently model spatial dependencies based on static or dynamic graphs and neglect the coexisting multiple spatial correlations induced by traffic generation. Meanwhile, some works lack the consideration of the diverse cellular traffic patterns, result in suboptimal prediction results. In this paper, we propose a novel deep learning network architecture, Adaptive Hybrid Spatial-Temporal Graph Neural Network (AHSTGNN), to tackle the cellular traffic prediction problem. First, we apply adaptive hybrid graph learning to learn the compound spatial correlations among cell towers. Second, we implement a Temporal Convolution Module with multi-periodic temporal data input to capture the nonlinear temporal dependencies. In addition, we introduce an extra Spatial-Temporal Adaptive Module to conquer the heterogeneity lying in cell towers. Our experiments on two real-world cellular traffic datasets show AHSTGNN outperforms the state-of-the-art by a significant margin, illustrating the superior scalability of our method for spatial-temporal cellular traffic prediction.
Tackling unfairness in graph learning models is a challenging task, as the unfairness issues on graphs involve both attributes and topological structures. Existing work on fair graph learning simply assumes that attributes of all nodes are available for model training and then makes fair predictions. In practice, however, the attributes of some nodes might not be accessible due to missing data or privacy concerns, which makes fair graph learning even more challenging. In this paper, we propose FairAC, a fair attribute completion method, to complement missing information and learn fair node embeddings for graphs with missing attributes. FairAC adopts an attention mechanism to deal with the attribute missing problem and meanwhile, it mitigates two types of unfairness, i.e., feature unfairness from attributes and topological unfairness due to attribute completion. FairAC can work on various types of homogeneous graphs and generate fair embeddings for them and thus can be applied to most downstream tasks to improve their fairness performance. To our best knowledge, FairAC is the first method that jointly addresses the graph attribution completion and graph unfairness problems. Experimental results on benchmark datasets show that our method achieves better fairness performance with less sacrifice in accuracy, compared with the state-of-the-art methods of fair graph learning. Code is available at: https://github.com/donglgcn/FairAC.
Graph convolutional networks (GCNs) were a great step towards extending deep learning to unstructured data such as graphs. But GCNs still need a constructed graph to work with. To solve this problem, classical graphs such as $k$-nearest neighbor are usually used to initialize the GCN. Although it is computationally efficient to construct $k$-nn graphs, the constructed graph might not be very useful for learning. In a $k$-nn graph, points are restricted to have a fixed number of edges, and all edges in the graph have equal weights. We present a new way to construct the graph and initialize the GCN. It is based on random projection forest (rpForest). rpForest enables us to assign varying weights on edges indicating varying importance, which enhanced the learning. The number of trees is a hyperparameter in rpForest. We performed spectral analysis to help us setting this parameter in the right range. In the experiments, initializing the GCN using rpForest provides better results compared to $k$-nn initialization.
Graph Neural Networks (GNNs) are increasingly becoming the favorite method for graph learning. They exploit the semi-supervised nature of deep learning, and they bypass computational bottlenecks associated with traditional graph learning methods. In addition to the feature matrix $X$, GNNs need an adjacency matrix $A$ to perform feature propagation. In many cases, the adjacency matrix $A$ is missing. We introduce a graph construction scheme that constructs the adjacency matrix $A$ using unsupervised and supervised information. Unsupervised information characterizes the neighborhood around points. We used Principal Axis trees (PA-trees) as a source for unsupervised information, where we create edges between points falling onto the same leaf node. For supervised information, we used the concept of penalty and intrinsic graphs. A penalty graph connects points with different class labels, whereas an intrinsic graph connects points with the same class labels. We used the penalty and intrinsic graphs to remove or add edges to the graph constructed via PA-tree. We tested this graph construction scheme on two well-known GNNs: 1) Graph Convolutional Network (GCN) and 2) Simple Graph Convolution (SGC). The experiments show that it is better to use SGC because it is faster and delivers better or the same results as GCN. We also test the effect of oversmoothing on both GCN and SGC. We found out that the level of smoothing has to be carefully selected for SGC to avoid oversmoothing.
Contemporary graph learning algorithms are not well-defined for large molecules since they do not consider the hierarchical interactions among the atoms, which are essential to determine the molecular properties of macromolecules. In this work, we propose Multiresolution Graph Transformers (MGT), the first graph transformer architecture that can learn to represent large molecules at multiple scales. MGT can learn to produce representations for the atoms and group them into meaningful functional groups or repeating units. We also introduce Wavelet Positional Encoding (WavePE), a new positional encoding method that can guarantee localization in both spectral and spatial domains. Our proposed model achieves competitive results on two macromolecule datasets consisting of polymers and peptides, and one drug-like molecule dataset. Importantly, our model outperforms other state-of-the-art methods and achieves chemical accuracy in estimating molecular properties (e.g., GAP, HOMO and LUMO) calculated by Density Functional Theory (DFT) in the polymers dataset. Furthermore, the visualizations, including clustering results on macromolecules and low-dimensional spaces of their representations, demonstrate the capability of our methodology in learning to represent long-range and hierarchical structures. Our PyTorch implementation is publicly available at https://github.com/HySonLab/Multires-Graph-Transformer
(Directed) graphs with node attributes are a common type of data in various applications and there is a vast literature on developing metrics and efficient algorithms for comparing them. Recently, in the graph learning and optimization communities, a range of new approaches have been developed for comparing graphs with node attributes, leveraging ideas such as the Optimal Transport (OT) and the Weisfeiler-Lehman (WL) graph isomorphism test. Two state-of-the-art representatives are the OTC distance proposed in (O'Connor et al., 2022) and the WL distance in (Chen et al., 2022). Interestingly, while these two distances are developed based on different ideas, we observe that they both view graphs as Markov chains, and are deeply connected. Indeed, in this paper, we propose a unified framework to generate distances for Markov chains (thus including (directed) graphs with node attributes), which we call the Optimal Transport Markov (OTM) distances, that encompass both the OTC and the WL distances. We further introduce a special one-parameter family of distances within our OTM framework, called the discounted WL distance. We show that the discounted WL distance has nice theoretical properties and can address several limitations of the existing OTC and WL distances. Furthermore, contrary to the OTC and the WL distances, our new discounted WL distance can be differentiated after a entropy-regularization similar to the Sinkhorn distance, making it suitable to use in learning frameworks, e.g., as the reconstruction loss in a graph generative model.
The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood estimation (MLE) of the precision matrix, subject to Laplacian structural constraints, with a sparsity-inducing penalty term. This paper aims to solve this learning problem accurately and efficiently. First, since the commonly used $\ell_1$-norm penalty is inappropriate in this setting and may lead to a complete graph, we employ the nonconvex minimax concave penalty (MCP), which promotes sparse solutions with lower estimation bias. Second, as opposed to existing first-order methods for this problem, we develop a second-order proximal Newton approach to obtain an efficient solver, utilizing several algorithmic features, such as using Conjugate Gradients, preconditioning, and splitting to active/free sets. Numerical experiments demonstrate the advantages of the proposed method in terms of both computational complexity and graph learning accuracy compared to existing methods.
Company financial risk is ubiquitous and early risk assessment for listed companies can avoid considerable losses. Traditional methods mainly focus on the financial statements of companies and lack the complex relationships among them. However, the financial statements are often biased and lagged, making it difficult to identify risks accurately and timely. To address the challenges, we redefine the problem as \textbf{company financial risk assessment on tribe-style graph} by taking each listed company and its shareholders as a tribe and leveraging financial news to build inter-tribe connections. Such tribe-style graphs present different patterns to distinguish risky companies from normal ones. However, most nodes in the tribe-style graph lack attributes, making it difficult to directly adopt existing graph learning methods (e.g., Graph Neural Networks(GNNs)). In this paper, we propose a novel Hierarchical Graph Neural Network (TH-GNN) for Tribe-style graphs via two levels, with the first level to encode the structure pattern of the tribes with contrastive learning, and the second level to diffuse information based on the inter-tribe relations, achieving effective and efficient risk assessment. Extensive experiments on the real-world company dataset show that our method achieves significant improvements on financial risk assessment over previous competing methods. Also, the extensive ablation studies and visualization comprehensively show the effectiveness of our method.
User interaction data in recommender systems is a form of dyadic relation that reflects the preferences of users with items. Learning the representations of these two discrete sets of objects, users and items, is critical for recommendation. Recent multimodal recommendation models leveraging multimodal features (e.g., images and text descriptions) have been demonstrated to be effective in improving recommendation accuracy. However, state-of-the-art models enhance the dyadic relations between users and items by considering either user-user or item-item relations, leaving the high-order relations of the other side (i.e., users or items) unexplored. Furthermore, we experimentally reveal that the current multimodality fusion methods in the state-of-the-art models may degrade their recommendation performance. That is, without tainting the model architectures, these models can achieve even better recommendation accuracy with uni-modal information. On top of the finding, we propose a model that enhances the dyadic relations by learning Dual RepresentAtions of both users and items via constructing homogeneous Graphs for multimOdal recommeNdation. We name our model as DRAGON. Specifically, DRAGON constructs the user-user graph based on the commonly interacted items and the item-item graph from item multimodal features. It then utilizes graph learning on both the user-item heterogeneous graph and the homogeneous graphs (user-user and item-item) to obtain the dual representations of users and items. To capture information from each modality, DRAGON employs a simple yet effective fusion method, attentive concatenation, to derive the representations of users and items. Extensive experiments on three public datasets and seven baselines show that DRAGON can outperform the strongest baseline by 22.03% on average. Various ablation studies are conducted on DRAGON to validate its effectiveness.
Graph Transformer (GT) recently has emerged as a new paradigm of graph learning algorithms, outperforming the previously popular Message Passing Neural Network (MPNN) on multiple benchmarks. Previous work (Kim et al., 2022) shows that with proper position embedding, GT can approximate MPNN arbitrarily well, implying that GT is at least as powerful as MPNN. In this paper, we study the inverse connection and show that MPNN with virtual node (VN), a commonly used heuristic with little theoretical understanding, is powerful enough to arbitrarily approximate the self-attention layer of GT. In particular, we first show that if we consider one type of linear transformer, the so-called Performer/Linear Transformer (Choromanski et al., 2020; Katharopoulos et al., 2020), then MPNN + VN with only O(1) depth and O(1) width can approximate a self-attention layer in Performer/Linear Transformer. Next, via a connection between MPNN + VN and DeepSets, we prove the MPNN + VN with O(n^d) width and O(1) depth can approximate the self-attention layer arbitrarily well, where d is the input feature dimension. Lastly, under some assumptions, we provide an explicit construction of MPNN + VN with O(1) width and O(n) depth approximating the self-attention layer in GT arbitrarily well. On the empirical side, we demonstrate that 1) MPNN + VN is a surprisingly strong baseline, outperforming GT on the recently proposed Long Range Graph Benchmark (LRGB) dataset, 2) our MPNN + VN improves over early implementation on a wide range of OGB datasets and 3) MPNN + VN outperforms Linear Transformer and MPNN on the climate modeling task.
Link prediction on graphs is a fundamental problem. Subgraph representation learning approaches (SGRLs), by transforming link prediction to graph classification on the subgraphs around the links, have achieved state-of-the-art performance in link prediction. However, SGRLs are computationally expensive, and not scalable to large-scale graphs due to expensive subgraph-level operations. To unlock the scalability of SGRLs, we propose a new class of SGRLs, that we call Scalable Simplified SGRL (S3GRL). Aimed at faster training and inference, S3GRL simplifies the message passing and aggregation operations in each link's subgraph. S3GRL, as a scalability framework, accommodates various subgraph sampling strategies and diffusion operators to emulate computationally-expensive SGRLs. We propose multiple instances of S3GRL and empirically study them on small to large-scale graphs. Our extensive experiments demonstrate that the proposed S3GRL models scale up SGRLs without significant performance compromise (even with considerable gains in some cases), while offering substantially lower computational footprints (e.g., multi-fold inference and training speedup).
We study the causal bandit problem when the causal graph is unknown and develop an efficient algorithm for finding the parent node of the reward node using atomic interventions. We derive the exact equation for the expected number of interventions performed by the algorithm and show that under certain graphical conditions it could perform either logarithmically fast or, under more general assumptions, slower but still sublinearly in the number of variables. We formally show that our algorithm is optimal as it meets the universal lower bound we establish for any algorithm that performs atomic interventions. Finally, we extend our algorithm to the case when the reward node has multiple parents. Using this algorithm together with a standard algorithm from bandit literature leads to improved regret bounds.
Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we investigate whether GNNs can exploit the graph structure from the perspective of the expressive power of GNNs. In our analysis, we consider graph generation processes that are controlled by hidden (or latent) node features, which contain all information about the graph structure. A typical example of this framework is kNN graphs constructed from the hidden features. In our main results, we show that GNNs can recover the hidden node features from the input graph alone, even when all node features, including the hidden features themselves and any indirect hints, are unavailable. GNNs can further use the recovered node features for downstream tasks. These results show that GNNs can fully exploit the graph structure by themselves, and in effect, GNNs can use both the hidden and explicit node features for downstream tasks. In the experiments, we confirm the validity of our results by showing that GNNs can accurately recover the hidden features using a GNN architecture built based on our theoretical analysis.