Embedded topic models are able to learn interpretable topics even with large and heavy-tailed vocabularies. However, they generally hold the Euclidean embedding space assumption, leading to a basic limitation in capturing hierarchical relations. To this end, we present a novel framework that introduces hyperbolic embeddings to represent words and topics. With the tree-likeness property of hyperbolic space, the underlying semantic hierarchy among words and topics can be better exploited to mine more interpretable topics. Furthermore, due to the superiority of hyperbolic geometry in representing hierarchical data, tree-structure knowledge can also be naturally injected to guide the learning of a topic hierarchy. Therefore, we further develop a regularization term based on the idea of contrastive learning to inject prior structural knowledge efficiently. Experiments on both topic taxonomy discovery and document representation demonstrate that the proposed framework achieves improved performance against existing embedded topic models.
Multivariate time-series forecasting is a critical task for many applications, and graph time-series network is widely studied due to its capability to capture the spatial-temporal correlation simultaneously. However, most existing works focus more on learning with the explicit prior graph structure, while ignoring potential information from the implicit graph structure, yielding incomplete structure modeling. Some recent works attempt to learn the intrinsic or implicit graph structure directly while lacking a way to combine explicit prior structure with implicit structure together. In this paper, we propose Regularized Graph Structure Learning (RGSL) model to incorporate both explicit prior structure and implicit structure together, and learn the forecasting deep networks along with the graph structure. RGSL consists of two innovative modules. First, we derive an implicit dense similarity matrix through node embedding, and learn the sparse graph structure using the Regularized Graph Generation (RGG) based on the Gumbel Softmax trick. Second, we propose a Laplacian Matrix Mixed-up Module (LM3) to fuse the explicit graph and implicit graph together. We conduct experiments on three real-word datasets. Results show that the proposed RGSL model outperforms existing graph forecasting algorithms with a notable margin, while learning meaningful graph structure simultaneously. Our code and models are made publicly available at https://github.com/alipay/RGSL.git.
The prevalence and perniciousness of fake news have been a critical issue on the Internet, which stimulates the development of automatic fake news detection in turn. In this paper, we focus on 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 attention mechanisms. Despite their effectiveness, they still suffer from three weaknesses. Firstly, sequential models fail to integrate the relevant information that is scattered far apart in evidences. Secondly, they underestimate much redundant information in evidences may be useless or harmful. Thirdly, insufficient data utilization limits the separability and reliability of representations captured by the model. To solve these problems, we propose a unified Graph-based sEmantic structure mining framework with ConTRAstive Learning, namely GETRAL in short. Specifically, we first model claims and evidences as graph-structured data to capture the long-distance semantic dependency. Consequently, we reduce information redundancy by performing graph structure learning. Then the fine-grained semantic representations are fed into the claim-evidence interaction module for predictions. Finally, an adversarial contrastive learning module is applied to make full use of data and strengthen representation learning. Comprehensive experiments have demonstrated the superiority of GETRAL over the state-of-the-arts and validated the efficacy of semantic mining with graph structure and contrastive learning.
Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to construct a graph among images is to treat each image as a node and assign pairwise image similarities as weights to corresponding edges. It is well known that pairwise similarities between images are sensitive to the noise in feature representations, leading to unreliable graph structures. We address this problem from the viewpoint of statistical tests. By viewing the feature vector of each node as an independent sample, the decision of whether creating an edge between two nodes based on their similarity in feature representation can be thought as a ${\it single}$ statistical test. To improve the robustness in the decision of creating an edge, multiple samples are drawn and integrated by ${\it multiple}$ statistical tests to generate a more reliable similarity measure, consequentially more reliable graph structure. The corresponding elegant matrix form named $\mathcal{B}\textbf{-Attention}$ is designed for efficiency. The effectiveness of multiple tests for graph structure learning is verified both theoretically and empirically on multiple clustering and ReID benchmark datasets. Source codes are available at https://github.com/Thomas-wyh/B-Attention.
Graph neural networks (GNNs) have demonstrated success in learning representations of brain graphs derived from functional magnetic resonance imaging (fMRI) data. However, existing GNN methods assume brain graphs are static over time and the graph adjacency matrix is known prior to model training. These assumptions contradict evidence that brain graphs are time-varying with a connectivity structure that depends on the choice of functional connectivity measure. Incorrectly representing fMRI data with noisy brain graphs can adversely affect GNN performance. To address this, we propose DynDepNet, a novel method for learning the optimal time-varying dependency structure of fMRI data induced by downstream prediction tasks. Experiments on real-world fMRI datasets, for the task of sex classification, demonstrate that DynDepNet achieves state-of-the-art results, outperforming the best baseline in terms of accuracy by approximately 8 and 6 percentage points, respectively. Furthermore, analysis of the learned dynamic graphs reveals prediction-related brain regions consistent with existing neuroscience literature.
Topology-imbalance is a graph-specific imbalance problem caused by the uneven topology positions of labeled nodes, which significantly damages the performance of GNNs. What topology-imbalance means and how to measure its impact on graph learning remain under-explored. In this paper, we provide a new understanding of topology-imbalance from a global view of the supervision information distribution in terms of under-reaching and over-squashing, which motivates two quantitative metrics as measurements. In light of our analysis, we propose a novel position-aware graph structure learning framework named PASTEL, which directly optimizes the information propagation path and solves the topology-imbalance issue in essence. Our key insight is to enhance the connectivity of nodes within the same class for more supervision information, thereby relieving the under-reaching and over-squashing phenomena. Specifically, we design an anchor-based position encoding mechanism, which better incorporates relative topology position and enhances the intra-class inductive bias by maximizing the label influence. We further propose a class-wise conflict measure as the edge weights, which benefits the separation of different node classes. Extensive experiments demonstrate the superior potential and adaptability of PASTEL in enhancing GNNs' power in different data annotation scenarios.
Multivariate time series anomaly detection has been extensively studied under the semi-supervised setting, where a training dataset with all normal instances is required. However, preparing such a dataset is very laborious since each single data instance should be fully guaranteed to be normal. It is, therefore, desired to explore multivariate time series anomaly detection methods based on the dataset without any label knowledge. In this paper, we propose MTGFlow, an unsupervised anomaly detection approach for multivariate time series anomaly detection via dynamic graph and entity-aware normalizing flow, leaning only on a widely accepted hypothesis that abnormal instances exhibit sparse densities than the normal. However, the complex interdependencies among entities and the diverse inherent characteristics of each entity pose significant challenges on the density estimation, let alone to detect anomalies based on the estimated possibility distribution. To tackle these problems, we propose to learn the mutual and dynamic relations among entities via a graph structure learning model, which helps to model accurate distribution of multivariate time series. Moreover, taking account of distinct characteristics of the individual entities, an entity-aware normalizing flow is developed to describe each entity into a parameterized normal distribution, thereby producing fine-grained density estimation. Incorporating these two strategies, MTGFlow achieves superior anomaly detection performance. Experiments on five public datasets with seven baselines are conducted, MTGFlow outperforms the SOTA methods by up to 5.0 AUROC\%. Codes will be released at https://github.com/zqhang/Detecting-Multivariate-Time-Series-Anomalies-with-Zero-Known-Label.
With the development of graph kernels and graph representation learning, many superior methods have been proposed to handle scalability and oversmoothing issues on graph structure learning. However, most of those strategies are designed based on practical experience rather than theoretical analysis. In this paper, we use a particular dummy node connecting to all existing vertices without affecting original vertex and edge properties. We further prove that such the dummy node can help build an efficient monomorphic edge-to-vertex transform and an epimorphic inverse to recover the original graph back. It also indicates that adding dummy nodes can preserve local and global structures for better graph representation learning. We extend graph kernels and graph neural networks with dummy nodes and conduct experiments on graph classification and subgraph isomorphism matching tasks. Empirical results demonstrate that taking graphs with dummy nodes as input significantly boosts graph structure learning, and using their edge-to-vertex graphs can also achieve similar results. We also discuss the gain of expressive power from the dummy in neural networks.
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.
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.
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) 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.
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.