Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling complex interactions between the inputs. In this work, we propose a novel yet simple approach that entails exploiting the graph data structure to model the underlying relationship between variables, i.e., variables as nodes and interactions defined by edges. Then, a variational graph autoencoder is used to naturally take the interactions into account. We first provide empirical evidence of the existence of such graph structures and then suggest a joint framework of graph structure learning and latent space optimization to adaptively search for optimal graph connectivity. Experimental results demonstrate that our method shows remarkable performance, exceeding the existing approaches with significant computational efficiency for a number of synthetic and real-world tasks.
Accurate forecasting of multivariate time series is an extensively studied subject in finance, transportation, and computer science. Fully mining the correlation and causation between the variables in a multivariate time series exhibits noticeable results in improving the performance of a time series model. Recently, some models have explored the dependencies between variables through end-to-end graph structure learning without the need for predefined graphs. However, current models do not incorporate the trade-off between efficiency and flexibility and lack the guidance of domain knowledge in the design of graph structure learning algorithms. This paper alleviates the above issues by proposing Balanced Graph Structure Learning for Forecasting (BGSLF), a novel deep learning model that joins graph structure learning and forecasting. Technically, BGSLF leverages the spatial information into convolutional operations and extracts temporal dynamics using the diffusion convolutional recurrent network. The proposed framework balance the trade-off between efficiency and flexibility by introducing Multi-Graph Generation Network (MGN) and Graph Selection Module. In addition, a method named Smooth Sparse Unit (SSU) is designed to sparse the learned graph structures, which conforms to the sparse spatial correlations in the real world. Extensive experiments on four real-world datasets demonstrate that our model achieves state-of-the-art performances with minor trainable parameters. Code will be made publicly available.
In recent years, graph neural networks (GNNs) have emerged as a successful tool in a variety of graph-related applications. However, the performance of GNNs can be deteriorated when noisy connections occur in the original graph structures; besides, the dependence on explicit structures prevents GNNs from being applied to general unstructured scenarios. To address these issues, recently emerged deep graph structure learning (GSL) methods propose to jointly optimize the graph structure along with GNN under the supervision of a node classification task. Nonetheless, these methods focus on a supervised learning scenario, which leads to several problems, i.e., the reliance on labels, the bias of edge distribution, and the limitation on application tasks. In this paper, we propose a more practical GSL paradigm, unsupervised graph structure learning, where the learned graph topology is optimized by data itself without any external guidance (i.e., labels). To solve the unsupervised GSL problem, we propose a novel StrUcture Bootstrapping contrastive LearnIng fraMEwork (SUBLIME for abbreviation) with the aid of self-supervised contrastive learning. Specifically, we generate a learning target from the original data as an "anchor graph", and use a contrastive loss to maximize the agreement between the anchor graph and the learned graph. To provide persistent guidance, we design a novel bootstrapping mechanism that upgrades the anchor graph with learned structures during model learning. We also design a series of graph learners and post-processing schemes to model the structures to learn. Extensive experiments on eight benchmark datasets demonstrate the significant effectiveness of our proposed SUBLIME and high quality of the optimized graphs.
The prevalence and perniciousness of fake news has been a critical issue on the Internet, which stimulates the development of automatic fake news detection in turn. In this paper, we focus on the evidence-based fake news detection, where several evidences are utilized to probe the veracity of news (i.e., a claim). Most previous methods first employ sequential models to embed the semantic information and then capture the claim-evidence interaction based on different attention mechanisms. Despite their effectiveness, they still suffer from two main weaknesses. Firstly, due to the inherent drawbacks of sequential models, they fail to integrate the relevant information that is scattered far apart in evidences for veracity checking. Secondly, they neglect much redundant information contained in evidences that may be useless or even harmful. To solve these problems, we propose a unified Graph-based sEmantic sTructure mining framework, namely GET in short. Specifically, different from the existing work that treats claims and evidences as sequences, we model them as graph-structured data and capture the long-distance semantic dependency among dispersed relevant snippets via neighborhood propagation. After obtaining contextual semantic information, our model reduces information redundancy by performing graph structure learning. Finally, the fine-grained semantic representations are fed into the downstream claim-evidence interaction module for predictions. Comprehensive experiments have demonstrated the superiority of GET over the state-of-the-arts.
Graph Structure Learning (GSL) recently has attracted considerable attentions in its capacity of optimizing graph structure as well as learning suitable parameters of Graph Neural Networks (GNNs) simultaneously. Current GSL methods mainly learn an optimal graph structure (final view) from single or multiple information sources (basic views), however the theoretical guidance on what is the optimal graph structure is still unexplored. In essence, an optimal graph structure should only contain the information about tasks while compress redundant noise as much as possible, which is defined as "minimal sufficient structure", so as to maintain the accurancy and robustness. How to obtain such structure in a principled way? In this paper, we theoretically prove that if we optimize basic views and final view based on mutual information, and keep their performance on labels simultaneously, the final view will be a minimal sufficient structure. With this guidance, we propose a Compact GSL architecture by MI compression, named CoGSL. Specifically, two basic views are extracted from original graph as two inputs of the model, which are refinedly reestimated by a view estimator. Then, we propose an adaptive technique to fuse estimated views into the final view. Furthermore, we maintain the performance of estimated views and the final view and reduce the mutual information of every two views. To comprehensively evaluate the performance of CoGSL, we conduct extensive experiments on several datasets under clean and attacked conditions, which demonstrate the effectiveness and robustness of CoGSL.
Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.
Recently deep learning has been successfully applied to unsupervised active learning. However, current method attempts to learn a nonlinear transformation via an auto-encoder while ignoring the sample relation, leaving huge room to design more effective representation learning mechanisms for unsupervised active learning. In this paper, we propose a novel deep unsupervised Active Learning model via Learnable Graphs, named ALLG. ALLG benefits from learning optimal graph structures to acquire better sample representation and select representative samples. To make the learnt graph structure more stable and effective, we take into account $k$-nearest neighbor graph as a priori, and learn a relation propagation graph structure. We also incorporate shortcut connections among different layers, which can alleviate the well-known over-smoothing problem to some extent. To the best of our knowledge, this is the first attempt to leverage graph structure learning for unsupervised active learning. Extensive experiments performed on six datasets demonstrate the efficacy of our method.
Coupled dynamical systems are frequently observed in nature, but often not well understood in terms of their causal structure without additional domain knowledge about the system. Especially when analyzing observational time series data of dynamical systems where it is not possible to conduct controlled experiments, for example time series of climate variables, it can be challenging to determine how features causally influence each other. There are many techniques available to recover causal relationships from data, such as Granger causality, convergent cross mapping, and causal graph structure learning approaches such as PCMCI. Path signatures and their associated signed areas provide a new way to approach the analysis of causally linked dynamical systems, particularly in informing a model-free, data-driven approach to algorithmic causal discovery. With this paper, we explore the use of path signatures in causal discovery and propose the application of confidence sequences to analyze the significance of the magnitude of the signed area between two variables. These confidence sequence regions converge with greater sampling length, and in conjunction with analyzing pairwise signed areas across time-shifted versions of the time series, can help identify the presence of lag/lead causal relationships. This approach provides a new way to define the confidence of a causal link existing between two time series, and ultimately may provide a framework for hypothesis testing to define whether one time series causes another
Temporal point process as the stochastic process on continuous domain of time is commonly used to model the asynchronous event sequence featuring with occurrence timestamps. Thanks to the strong expressivity of deep neural networks, they are emerging as a promising choice for capturing the patterns in asynchronous sequences, in the context of temporal point process. In this paper, we first review recent research emphasis and difficulties in modeling asynchronous event sequences with deep temporal point process, which can be concluded into four fields: encoding of history sequence, formulation of conditional intensity function, relational discovery of events and learning approaches for optimization. We introduce most of recently proposed models by dismantling them into the four parts, and conduct experiments by remodularizing the first three parts with the same learning strategy for a fair empirical evaluation. Besides, we extend the history encoders and conditional intensity function family, and propose a Granger causality discovery framework for exploiting the relations among multi-types of events. Because the Granger causality can be represented by the Granger causality graph, discrete graph structure learning in the framework of Variational Inference is employed to reveal latent structures of the graph. Further experiments show that the proposed framework with latent graph discovery can both capture the relations and achieve an improved fitting and predicting performance.
The characterisation of the brain as a functional network in which the connections between brain regions are represented by correlation values across time series has been very popular in the last years. Although this representation has advanced our understanding of brain function, it represents a simplified model of brain connectivity that has a complex dynamic spatio-temporal nature. Oversimplification of the data may hinder the merits of applying advanced non-linear feature extraction algorithms. To this end, we propose a dynamic adaptive spatio-temporal graph convolution (DAST-GCN) model to overcome the shortcomings of pre-defined static correlation-based graph structures. The proposed approach allows end-to-end inference of dynamic connections between brain regions via layer-wise graph structure learning module while mapping brain connectivity to a phenotype in a supervised learning framework. This leverages the computational power of the model, data and targets to represent brain connectivity, and could enable the identification of potential biomarkers for the supervised target in question. We evaluate our pipeline on the UKBiobank dataset for age and gender classification tasks from resting-state functional scans and show that it outperforms currently adapted linear and non-linear methods in neuroimaging. Further, we assess the generalizability of the inferred graph structure by transferring the pre-trained graph to an independent dataset for the same task. Our results demonstrate the task-robustness of the graph against different scanning parameters and demographics.
Graph Neural Networks (GNNs) have achieved great success among various domains. Nevertheless, most GNN methods are sensitive to the quality of graph structures. To tackle this problem, some studies exploit different graph structure learning strategies to refine the original graph structure. However, these methods only consider feature information while ignoring available label information. In this paper, we propose a novel label-informed graph structure learning framework which incorporates label information explicitly through a class transition matrix. We conduct extensive experiments on seven node classification benchmark datasets and the results show that our method outperforms or matches the state-of-the-art baselines.
Graphs are widely used to describe real-world objects and their interactions. Graph Neural Networks (GNNs) as a de facto model for analyzing graphstructured data, are highly sensitive to the quality of the given graph structures. Therefore, noisy or incomplete graphs often lead to unsatisfactory representations and prevent us from fully understanding the mechanism underlying the system. In pursuit of an optimal graph structure for downstream tasks, recent studies have sparked an effort around the central theme of Graph Structure Learning (GSL), which aims to jointly learn an optimized graph structure and corresponding graph representations. In the presented survey, we broadly review recent progress in GSL methods. Specifically, we first formulate a general pipeline of GSL and review state-of-the-art methods classified by the way of modeling graph structures, followed by applications of GSL across domains. Finally, we point out some issues in current studies and discuss future directions.
Graph neural networks (GNNs) work well when the graph structure is provided. However, this structure may not always be available in real-world applications. One solution to this problem is to infer a task-specific latent structure and then apply a GNN to the inferred graph. Unfortunately, the space of possible graph structures grows super-exponentially with the number of nodes and so the task-specific supervision may be insufficient for learning both the structure and the GNN parameters. In this work, we propose the Simultaneous Learning of Adjacency and GNN Parameters with Self-supervision, or SLAPS, a method that provides more supervision for inferring a graph structure through self-supervision. A comprehensive experimental study demonstrates that SLAPS scales to large graphs with hundreds of thousands of nodes and outperforms several models that have been proposed to learn a task-specific graph structure on established benchmarks.
Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the performance of a time series model. When using deep neural networks as forecasting models, we hypothesize that exploiting the pairwise information among multiple (multivariate) time series also improves their forecast. If an explicit graph structure is known, graph neural networks (GNNs) have been demonstrated as powerful tools to exploit the structure. In this work, we propose learning the structure simultaneously with the GNN if the graph is unknown. We cast the problem as learning a probabilistic graph model through optimizing the mean performance over the graph distribution. The distribution is parameterized by a neural network so that discrete graphs can be sampled differentiably through reparameterization. Empirical evaluations show that our method is simpler, more efficient, and better performing than a recently proposed bilevel learning approach for graph structure learning, as well as a broad array of forecasting models, either deep or non-deep learning based, and graph or non-graph based.
Soil moisture is an important component of precision agriculture as it directly impacts the growth and quality of vegetation. Forecasting soil moisture is essential to schedule the irrigation and optimize the use of water. Physics based soil moisture models need rich features and heavy computation which is not scalable. In recent literature, conventional machine learning models have been applied for this problem. These models are fast and simple, but they often fail to capture the spatio-temporal correlation that soil moisture exhibits over a region. In this work, we propose a novel graph neural network based solution that learns temporal graph structures and forecast soil moisture in an end-to-end framework. Our solution is able to handle the problem of missing ground truth soil moisture which is common in practice. We show the merit of our algorithm on real-world soil moisture data.
With the advancement of sensing technology, multivariate time series classification (MTSC) has recently received considerable attention. Existing deep learning-based MTSC techniques, which mostly rely on convolutional or recurrent neural networks, are primarily concerned with the temporal dependency of single time series. As a result, they struggle to express pairwise dependencies among multivariate variables directly. Furthermore, current spatial-temporal modeling (e.g., graph classification) methodologies based on Graph Neural Networks (GNNs) are inherently flat and cannot aggregate hub data in a hierarchical manner. To address these limitations, we propose a novel graph pooling-based framework MTPool to obtain the expressive global representation of MTS. We first convert MTS slices to graphs by utilizing interactions of variables via graph structure learning module and attain the spatial-temporal graph node features via temporal convolutional module. To get global graph-level representation, we design an "encoder-decoder" based variational graph pooling module for creating adaptive centroids for cluster assignments. Then we combine GNNs and our proposed variational graph pooling layers for joint graph representation learning and graph coarsening, after which the graph is progressively coarsened to one node. At last, a differentiable classifier takes this coarsened representation to get the final predicted class. Experiments on ten benchmark datasets exhibit MTPool outperforms state-of-the-art strategies in the MTSC task.
Most graph neural network models learn embeddings of nodes in static attributed graphs for predictive analysis. Recent attempts have been made to learn temporal proximity of the nodes. We find that real dynamic attributed graphs exhibit complex co-evolution of node attributes and graph structure. Learning node embeddings for forecasting change of node attributes and birth and death of links over time remains an open problem. In this work, we present a novel framework called CoEvoGNN for modeling dynamic attributed graph sequence. It preserves the impact of earlier graphs on the current graph by embedding generation through the sequence. It has a temporal self-attention mechanism to model long-range dependencies in the evolution. Moreover, CoEvoGNN optimizes model parameters jointly on two dynamic tasks, attribute inference and link prediction over time. So the model can capture the co-evolutionary patterns of attribute change and link formation. This framework can adapt to any graph neural algorithms so we implemented and investigated three methods based on it: CoEvoGCN, CoEvoGAT, and CoEvoSAGE. Experiments demonstrate the framework (and its methods) outperform strong baselines on predicting an entire unseen graph snapshot of personal attributes and interpersonal links in dynamic social graphs and financial graphs.
We study the problem of node classification on graphs with few-shot novel labels, which has two distinctive properties: (1) There are novel labels to emerge in the graph; (2) The novel labels have only a few representative nodes for training a classifier. The study of this problem is instructive and corresponds to many applications such as recommendations for newly formed groups with only a few users in online social networks. To cope with this problem, we propose a novel Meta Transformed Network Embedding framework (MetaTNE), which consists of three modules: (1) A \emph{structural module} provides each node a latent representation according to the graph structure. (2) A \emph{meta-learning module} captures the relationships between the graph structure and the node labels as prior knowledge in a meta-learning manner. Additionally, we introduce an \emph{embedding transformation function} that remedies the deficiency of the straightforward use of meta-learning. Inherently, the meta-learned prior knowledge can be used to facilitate the learning of few-shot novel labels. (3) An \emph{optimization module} employs a simple yet effective scheduling strategy to train the above two modules with a balance between graph structure learning and meta-learning. Experiments on four real-world datasets show that MetaTNE brings a huge improvement over the state-of-the-art methods.
Graph Neural Networks (GNNs) are powerful tools in representation learning for graphs. However, recent studies show that GNNs are vulnerable to carefully-crafted perturbations, called adversarial attacks. Adversarial attacks can easily fool GNNs in making predictions for downstream tasks. The vulnerability to adversarial attacks has raised increasing concerns for applying GNNs in safety-critical applications. Therefore, developing robust algorithms to defend adversarial attacks is of great significance. A natural idea to defend adversarial attacks is to clean the perturbed graph. It is evident that real-world graphs share some intrinsic properties. For example, many real-world graphs are low-rank and sparse, and the features of two adjacent nodes tend to be similar. In fact, we find that adversarial attacks are likely to violate these graph properties. Therefore, in this paper, we explore these properties to defend adversarial attacks on graphs. In particular, we propose a general framework Pro-GNN, which can jointly learn a structural graph and a robust graph neural network model from the perturbed graph guided by these properties. Extensive experiments on real-world graphs demonstrate that the proposed framework achieves significantly better performance compared with the state-of-the-art defense methods, even when the graph is heavily perturbed. We release the implementation of Pro-GNN to our DeepRobust repository for adversarial attacks and defenses (footnote: https://github.com/DSE-MSU/DeepRobust). The specific experimental settings to reproduce our results can be found in https://github.com/ChandlerBang/Pro-GNN.
Visual dialog is a task of answering a sequence of questions grounded in an image using the previous dialog history as context. In this paper, we study how to address two fundamental challenges for this task: (1) reasoning over underlying semantic structures among dialog rounds and (2) identifying several appropriate answers to the given question. To address these challenges, we propose a Sparse Graph Learning (SGL) method to formulate visual dialog as a graph structure learning task. SGL infers inherently sparse dialog structures by incorporating binary and score edges and leveraging a new structural loss function. Next, we introduce a Knowledge Transfer (KT) method that extracts the answer predictions from the teacher model and uses them as pseudo labels. We propose KT to remedy the shortcomings of single ground-truth labels, which severely limit the ability of a model to obtain multiple reasonable answers. As a result, our proposed model significantly improves reasoning capability compared to baseline methods and outperforms the state-of-the-art approaches on the VisDial v1.0 dataset. The source code is available at https://github.com/gicheonkang/SGLKT-VisDial.