Graph neural networks (GNNs) have attracted tremendous attention from the graph learning community in recent years. It has been widely adopted in various real-world applications from diverse domains, such as social networks and biological graphs. The research and applications of graph deep learning present new challenges, including the sparse nature of graph data, complicated training of GNNs, and non-standard evaluation of graph tasks. To tackle the issues, we present CogDL, a comprehensive library for graph deep learning that allows researchers and practitioners to conduct experiments, compare methods, and build applications with ease and efficiency. In CogDL, we propose a unified design for the training and evaluation of GNN models for various graph tasks, making it unique among existing graph learning libraries. By utilizing this unified trainer, CogDL can optimize the GNN training loop with several training techniques, such as mixed precision training. Moreover, we develop efficient sparse operators for CogDL, enabling it to become the most competitive graph library for efficiency. Another important CogDL feature is its focus on ease of use with the aim of facilitating open and reproducible research of graph learning. We leverage CogDL to report and maintain benchmark results on fundamental graph tasks, which can be reproduced and directly used by the community.
Graph neural networks have been widely used on modeling graph data, achieving impressive results on node classification and link prediction tasks. Yet, obtaining an accurate representation for a graph further requires a pooling function that maps a set of node representations into a compact form. A simple sum or average over all node representations considers all node features equally without consideration of their task relevance, and any structural dependencies among them. Recently proposed hierarchical graph pooling methods, on the other hand, may yield the same representation for two different graphs that are distinguished by the Weisfeiler-Lehman test, as they suboptimally preserve information from the node features. To tackle these limitations of existing graph pooling methods, we first formulate the graph pooling problem as a multiset encoding problem with auxiliary information about the graph structure, and propose a Graph Multiset Transformer (GMT) which is a multi-head attention based global pooling layer that captures the interaction between nodes according to their structural dependencies. We show that GMT satisfies both injectiveness and permutation invariance, such that it is at most as powerful as the Weisfeiler-Lehman graph isomorphism test. Moreover, our methods can be easily extended to the previous node clustering approaches for hierarchical graph pooling. Our experimental results show that GMT significantly outperforms state-of-the-art graph pooling methods on graph classification benchmarks with high memory and time efficiency, and obtains even larger performance gain on graph reconstruction and generation tasks.
Graph convolutional networks have been successfully applied in various graph-based tasks. In a typical graph convolutional layer, node features are updated by aggregating neighborhood information. Repeatedly applying graph convolutions can cause the oversmoothing issue, i.e., node features at deep layers converge to similar values. Previous studies have suggested that oversmoothing is one of the major issues that restrict the performance of graph convolutional networks. In this paper, we propose a stochastic regularization method to tackle the oversmoothing problem. In the proposed method, we stochastically scale features and gradients (SSFG) by a factor sampled from a probability distribution in the training procedure. By explicitly applying a scaling factor to break feature convergence, the oversmoothing issue is alleviated. We show that applying stochastic scaling at the gradient level is complementary to that applied at the feature level to improve the overall performance. Our method does not increase the number of trainable parameters. When used together with ReLU, our SSFG can be seen as a stochastic ReLU activation function. We experimentally validate our SSFG regularization method on three commonly used types of graph networks. Extensive experimental results on seven benchmark datasets for four graph-based tasks demonstrate that our SSFG regularization is effective in improving the overall performance of the baseline graph networks.
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent homology, encodes rich structural information regarding the multi-hop paths connecting nodes. Based on this feature, we propose a graph neural network method that outperforms state-of-the-arts on different benchmarks. As another contribution, we propose a novel algorithm to more efficiently compute the extended persistence diagrams for graphs. This algorithm can be generally applied to accelerate many other topological methods for graph learning tasks.
We consider two popular Graph Representation Learning (GRL) methods: message passing for node classification and network embedding for link prediction. For each, we pick a popular model that we: (i) linearize and (ii) and switch its training objective to Frobenius norm error minimization. These simplifications can cast the training into finding the optimal parameters in closed-form. We program in TensorFlow a functional form of Truncated Singular Value Decomposition (SVD), such that, we could decompose a dense matrix $\mathbf{M}$, without explicitly computing $\mathbf{M}$. We achieve competitive performance on popular GRL tasks while providing orders of magnitude speedup. We open-source our code at http://github.com/samihaija/tf-fsvd
We propose CRaWl, a novel neural network architecture for graph learning. Like graph neural networks, CRaWl layers update node features on a graph and thus can freely be combined or interleaved with GNN layers. Yet CRaWl operates fundamentally different from message passing graph neural networks. CRaWl layers extract and aggregate information on subgraphs appearing along random walks through a graph using 1D Convolutions. Thereby it detects long range interactions and computes non-local features. As the theoretical basis for our approach, we prove a theorem stating that the expressiveness of CRaWl is incomparable with that of the Weisfeiler Leman algorithm and hence with graph neural networks. That is, there are functions expressible by CRaWl, but not by GNNs and vice versa. This result extends to higher levels of the Weisfeiler Leman hierarchy and thus to higher-order GNNs. Empirically, we show that CRaWl matches state-of-the-art GNN architectures across a multitude of benchmark datasets for classification and regression on graphs.
Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.
The recent success of graph neural networks has significantly boosted molecular property prediction, advancing activities such as drug discovery. The existing deep neural network methods usually require large training dataset for each property, impairing their performances in cases (especially for new molecular properties) with a limited amount of experimental data, which are common in real situations. To this end, we propose Meta-MGNN, a novel model for few-shot molecular property prediction. Meta-MGNN applies molecular graph neural network to learn molecular representation and builds a meta-learning framework for model optimization. To exploit unlabeled molecular information and address task heterogeneity of different molecular properties, Meta-MGNN further incorporates molecular structure, attribute based self-supervised modules and self-attentive task weights into the former framework, strengthening the whole learning model. Extensive experiments on two public multi-property datasets demonstrate that Meta-MGNN outperforms a variety of state-of-the-art methods.
Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised embedding of graph datasets and for online graph subspace estimation and tracking.
Semi-supervised learning on graphs is a widely applicable problem in network science and machine learning. Two standard algorithms -- label propagation and graph neural networks -- both operate by repeatedly passing information along edges, the former by passing labels and the latter by passing node features, modulated by neural networks. These two types of algorithms have largely developed separately, and there is little understanding about the structure of network data that would make one of these approaches work particularly well compared to the other or when the approaches can be meaningfully combined. Here, we develop a Markov random field model for the data generation process of node attributes, based on correlations of attributes on and between vertices, that motivates and unifies these algorithmic approaches. We show that label propagation, a linearized graph convolutional network, and their combination can all be derived as conditional expectations under our model, when conditioning on different attributes. In addition, the data model highlights deficiencies in existing graph neural networks (while producing new algorithmic solutions), serves as a rigorous statistical framework for understanding graph learning issues such as over-smoothing, creates a testbed for evaluating inductive learning performance, and provides a way to sample graphs attributes that resemble empirical data. We also find that a new algorithm derived from our data generation model, which we call a Linear Graph Convolution, performs extremely well in practice on empirical data, and provide theoretical justification for why this is the case.
A scalable semi-supervised node classification method on graph-structured data, called GraphHop, is proposed in this work. The graph contains attributes of all nodes but labels of a few nodes. The classical label propagation (LP) method and the emerging graph convolutional network (GCN) are two popular semi-supervised solutions to this problem. The LP method is not effective in modeling node attributes and labels jointly or facing a slow convergence rate on large-scale graphs. GraphHop is proposed to its shortcoming. With proper initial label vector embeddings, each iteration of GraphHop contains two steps: 1) label aggregation and 2) label update. In Step 1, each node aggregates its neighbors' label vectors obtained in the previous iteration. In Step 2, a new label vector is predicted for each node based on the label of the node itself and the aggregated label information obtained in Step 1. This iterative procedure exploits the neighborhood information and enables GraphHop to perform well in an extremely small label rate setting and scale well for very large graphs. Experimental results show that GraphHop outperforms state-of-the-art graph learning methods on a wide range of tasks (e.g., multi-label and multi-class classification on citation networks, social graphs, and commodity consumption graphs) in graphs of various sizes. Our codes are publicly available on GitHub (https://github.com/TianXieUSC/GraphHop).
In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of practitioners' toolboxes. In this paper, we investigate the fundamental problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market times series data. In particular, we present natural justifications, supported by empirical evidence, for the usage of the Laplacian matrix as a model for the precision matrix of financial assets, while also establishing a direct link that reveals how Laplacian constraints are coupled to meaningful physical interpretations related to the market index factor and to conditional correlations between stocks. Those interpretations lead to a set of guidelines that practitioners should be aware of when estimating graphs in financial markets. In addition, we design numerical algorithms based on the alternating direction method of multipliers to learn undirected, weighted graphs that take into account stylized facts that are intrinsic to financial data such as heavy tails and modularity. We illustrate how to leverage the learned graphs into practical scenarios such as stock time series clustering and foreign exchange network estimation. The proposed graph learning algorithms outperform the state-of-the-art methods in an extensive set of practical experiments. Furthermore, we obtain theoretical and empirical convergence results for the proposed algorithms. Along with the developed methodologies for graph learning in financial markets, we release an R package, called fingraph, accommodating the code and data to obtain all the experimental results.
Heterogeneous graphs are pervasive in practical scenarios, where each graph consists of multiple types of nodes and edges. Representation learning on heterogeneous graphs aims to obtain low-dimensional node representations that could preserve both node attributes and relation information. However, most of the existing graph convolution approaches were designed for homogeneous graphs, and therefore cannot handle heterogeneous graphs. Some recent methods designed for heterogeneous graphs are also faced with several issues, including the insufficient utilization of heterogeneous properties, structural information loss, and lack of interpretability. In this paper, we propose HGConv, a novel Heterogeneous Graph Convolution approach, to learn comprehensive node representations on heterogeneous graphs with a hybrid micro/macro level convolutional operation. Different from existing methods, HGConv could perform convolutions on the intrinsic structure of heterogeneous graphs directly at both micro and macro levels: A micro-level convolution to learn the importance of nodes within the same relation, and a macro-level convolution to distinguish the subtle difference across different relations. The hybrid strategy enables HGConv to fully leverage heterogeneous information with proper interpretability. Moreover, a weighted residual connection is designed to aggregate both inherent attributes and neighbor information of the focal node adaptively. Extensive experiments on various tasks demonstrate not only the superiority of HGConv over existing methods, but also the intuitive interpretability of our approach for graph analysis.
The ability to segment teeth precisely from digitized 3D dental models is an essential task in computer-aided orthodontic surgical planning. To date, deep learning based methods have been popularly used to handle this task. State-of-the-art methods directly concatenate the raw attributes of 3D inputs, namely coordinates and normal vectors of mesh cells, to train a single-stream network for fully-automated tooth segmentation. This, however, has the drawback of ignoring the different geometric meanings provided by those raw attributes. This issue might possibly confuse the network in learning discriminative geometric features and result in many isolated false predictions on the dental model. Against this issue, we propose a two-stream graph convolutional network (TSGCNet) to learn multi-view geometric information from different geometric attributes. Our TSGCNet adopts two graph-learning streams, designed in an input-aware fashion, to extract more discriminative high-level geometric representations from coordinates and normal vectors, respectively. These feature representations learned from the designed two different streams are further fused to integrate the multi-view complementary information for the cell-wise dense prediction task. We evaluate our proposed TSGCNet on a real-patient dataset of dental models acquired by 3D intraoral scanners, and experimental results demonstrate that our method significantly outperforms state-of-the-art methods for 3D shape segmentation.
Bayesian Optimization (BO) has shown significant success in tackling expensive low-dimensional black-box optimization problems. Many optimization problems of interest are high-dimensional, and scaling BO to such settings remains an important challenge. In this paper, we consider generalized additive models in which low-dimensional functions with overlapping subsets of variables are composed to model a high-dimensional target function. Our goal is to lower the computational resources required and facilitate faster model learning by reducing the model complexity while retaining the sample-efficiency of existing methods. Specifically, we constrain the underlying dependency graphs to tree structures in order to facilitate both the structure learning and optimization of the acquisition function. For the former, we propose a hybrid graph learning algorithm based on Gibbs sampling and mutation. In addition, we propose a novel zooming-based algorithm that permits generalized additive models to be employed more efficiently in the case of continuous domains. We demonstrate and discuss the efficacy of our approach via a range of experiments on synthetic functions and real-world datasets.
For graph learning tasks, many existing methods utilize a message-passing mechanism where vertex features are updated iteratively by aggregation of neighbor information. This strategy provides an efficient means for graph features extraction, but obtained features after many iterations might contain too much information from other vertices, and tend to be similar to each other. This makes their representations less expressive. Learning graphs using paths, on the other hand, can be less adversely affected by this problem because it does not involve all vertex neighbors. However, most of them can only compare paths with the same length, which might engender information loss. To resolve this difficulty, we propose a new Graph Kernel based on a Longest Common Subsequence (LCS) similarity. Moreover, we found that the widely-used R-convolution framework is unsuitable for path-based Graph Kernel because a huge number of comparisons between dissimilar paths might deteriorate graph distances calculation. Therefore, we propose a novel metric space by exploiting the proposed LCS-based similarity, and compute a new Wasserstein-based graph distance in this metric space, which emphasizes more the comparison between similar paths. Furthermore, to reduce the computational cost, we propose an adjacent point merging operation to sparsify point clouds in the metric space.
Organ segmentation in CT volumes is an important pre-processing step in many computer assisted intervention and diagnosis methods. In recent years, convolutional neural networks have dominated the state of the art in this task. However, since this problem presents a challenging environment due to high variability in the organ's shape and similarity between tissues, the generation of false negative and false positive regions in the output segmentation is a common issue. Recent works have shown that the uncertainty analysis of the model can provide us with useful information about potential errors in the segmentation. In this context, we proposed a segmentation refinement method based on uncertainty analysis and graph convolutional networks. We employ the uncertainty levels of the convolutional network in a particular input volume to formulate a semi-supervised graph learning problem that is solved by training a graph convolutional network. To test our method we refine the initial output of a 2D U-Net. We validate our framework with the NIH pancreas dataset and the spleen dataset of the medical segmentation decathlon. We show that our method outperforms the state-of-the-art CRF refinement method by improving the dice score by 1% for the pancreas and 2% for spleen, with respect to the original U-Net's prediction. Finally, we perform a sensitivity analysis on the parameters of our proposal and discuss the applicability to other CNN architectures, the results, and current limitations of the model for future work in this research direction. For reproducibility purposes, we make our code publicly available at https://github.com/rodsom22/gcn_refinement.
Planning - the ability to analyze the structure of a problem in the large and decompose it into interrelated subproblems - is a hallmark of human intelligence. While deep reinforcement learning (RL) has shown great promise for solving relatively straightforward control tasks, it remains an open problem how to best incorporate planning into existing deep RL paradigms to handle increasingly complex environments. One prominent framework, Model-Based RL, learns a world model and plans using step-by-step virtual rollouts. This type of world model quickly diverges from reality when the planning horizon increases, thus struggling at long-horizon planning. How can we learn world models that endow agents with the ability to do temporally extended reasoning? In this work, we propose to learn graph-structured world models composed of sparse, multi-step transitions. We devise a novel algorithm to learn latent landmarks that are scattered (in terms of reachability) across the goal space as the nodes on the graph. In this same graph, the edges are the reachability estimates distilled from Q-functions. On a variety of high-dimensional continuous control tasks ranging from robotic manipulation to navigation, we demonstrate that our method, named L3P, significantly outperforms prior work, and is oftentimes the only method capable of leveraging both the robustness of model-free RL and generalization of graph-search algorithms. We believe our work is an important step towards scalable planning in reinforcement learning.
Graphs with complete node attributes have been widely explored recently. While in practice, there is a graph where attributes of only partial nodes could be available and those of the others might be entirely missing. This attribute-missing graph is related to numerous real-world applications and there are limited studies investigating the corresponding learning problems. Existing graph learning methods including the popular GNN cannot provide satisfied learning performance since they are not specified for attribute-missing graphs. Thereby, designing a new GNN for these graphs is a burning issue to the graph learning community. In this paper, we make a shared-latent space assumption on graphs and develop a novel distribution matching based GNN called structure-attribute transformer (SAT) for attribute-missing graphs. SAT leverages structures and attributes in a decoupled scheme and achieves the joint distribution modeling of structures and attributes by distribution matching techniques. It could not only perform the link prediction task but also the newly introduced node attribute completion task. Furthermore, practical measures are introduced to quantify the performance of node attribute completion. Extensive experiments on seven real-world datasets indicate SAT shows better performance than other methods on both link prediction and node attribute completion tasks. Codes and data are available online: https://github.com/xuChenSJTU/SAT-master-online
Representation learning on user-item graph for recommendation has evolved from using single ID or interaction history to exploiting higher-order neighbors. This leads to the success of graph convolution networks (GCNs) for recommendation such as PinSage and LightGCN. Despite effectiveness, we argue that they suffer from two limitations: (1) high-degree nodes exert larger impact on the representation learning, deteriorating the recommendations of low-degree (long-tail) items; and (2) representations are vulnerable to noisy interactions, as the neighborhood aggregation scheme further enlarges the impact of observed edges. In this work, we explore self-supervised learning on user-item graph, so as to improve the accuracy and robustness of GCNs for recommendation. The idea is to supplement the classical supervised task of recommendation with an auxiliary self-supervised task, which reinforces node representation learning via self-discrimination. Specifically, we generate multiple views of a node, maximizing the agreement between different views of the same node compared to that of other nodes. We devise three operators to generate the views -- node dropout, edge dropout, and random walk -- that change the graph structure in different manners. We term this new learning paradigm as \textit{Self-supervised Graph Learning} (SGL), implementing it on the state-of-the-art model LightGCN. Through theoretical analyses, we find that SGL has the ability of automatically mining hard negatives. Empirical studies on three benchmark datasets demonstrate the effectiveness of SGL, which improves the recommendation accuracy, especially on long-tail items, and the robustness against interaction noises. Our implementations are available at \url{https://github.com/wujcan/SGL}.