Granger Causality Graphs Research Articles

STGC-GNNs: A GNN-based traffic prediction framework with a spatial–temporal Granger causality graph

Accurate representation of the temporal dynamics of traffic flow traveling in the road network is the key to traffic prediction, it is therefore important to model the spatial dependence of the road network. The essence of spatial dependence is to accurately describe how traffic information transmission is affected by other nodes in the road network, and the GNN-based traffic prediction model, as a benchmark for traffic prediction, has become the most common method for the ability to model spatial dependence by transmitting traffic information with the message passing mechanism. However, existing methods model a local and static spatial dependence, which cannot transmit the global-dynamic traffic information (GDTi) required for long-term prediction. The challenge is the difficulty of detecting the precise transmission of GDTi due to the uncertainty of individual transport, especially for long-term transmission. In this paper, we propose a new hypothesis: GDTi behaves macroscopically as a transmitting causal relationship (TCR) underlying traffic flow, which remains stable under dynamic changing traffic flow. We further propose spatial–temporal Granger causality (STGC) to express TCR, which models global and dynamic spatial dependence. To model global transmission, we model the causal order and causal lag of TCR’s global transmission by a spatial–temporal alignment algorithm. To capture dynamic spatial dependence, we approximate the stable TCR underlying dynamic traffic flow by a Granger causality test. The experimental results on three backbone models show that using STGC to model the spatial dependence has better results than the original model for 45 min and 1 h long-term prediction.

Exact recovery of Granger causality graphs with unconditional pairwise tests

AbstractWe study Granger Causality in the context of wide-sense stationary time series. The focus of the analysis is to understand how the underlying topological structure of the causality graph affects graph recovery by means of the pairwise testing heuristic. Our main theoretical result establishes a sufficient condition (in particular, the graph must satisfy a polytree assumption we refer to as strong causality) under which the graph can be recovered by means of unconditional and binary pairwise causality testing. Examples from the gene regulatory network literature are provided which establish that graphs which are strongly causal, or very nearly so, can be expected to arise in practice. We implement finite sample heuristics derived from our theory, and use simulation to compare our pairwise testing heuristic against LASSO-based methods. These simulations show that, for graphs which are strongly causal (or small perturbations thereof) the pairwise testing heuristic is able to more accurately recover the underlying graph. We show that the algorithm is scalable to graphs with thousands of nodes, and that, as long as structural assumptions are met, exhibits similar high-dimensional scaling properties as the LASSO. That is, performance degrades slowly while the system size increases and the number of available samples is held fixed. Finally, a proof-of-concept application example shows, by attempting to classify alcoholic individuals using only Granger causality graphs inferred from EEG measurements, that the inferred Granger causality graph topology carries identifiable features.

Multivariate Time Series Forecasting with Transfer Entropy Graph

Multivariate Time Series (MTS) forecasting is an essential problem in many fields. Accurate forecasting results can effectively help in making decisions. To date, many MTS forecasting methods have been proposed and widely applied. However, these methods assume that the predicted value of a single variable is affected by all other variables, ignoring the causal relationship among variables. To address the above issue, we propose a novel end-to-end deep learning model, termed graph neural network with neural Granger causality, namely CauGNN, in this paper. To characterize the causal information among variables, we introduce the neural Granger causality graph in our model. Each variable is regarded as a graph node, and each edge represents the casual relationship between variables. In addition, convolutional neural network filters with different perception scales are used for time series feature extraction, to generate the feature of each node. Finally, the graph neural network is adopted to tackle the forecasting problem of the graph structure generated by the MTS. Three benchmark datasets from the real world are used to evaluate the proposed CauGNN, and comprehensive experiments show that the proposed method achieves state-of-the-art results in the MTS forecasting task.

Time-varying Group Lasso Granger Causality Graph for High Dimensional Dynamic system

Feature selection is a crucial preprocessing step in data analysis and machine learning. Since causal relationships imply the underlying mechanism of a system, causality-based feature selection methods have gradually attracted great attentions. For a high dimensional system undergoing dynamic transformation, because of the non-stationarity and sample scarcity, modeling the causal structure among these features is difficult. In this paper, we propose a time-varying Granger causal networks to capture the causal relations underlying high dimensional time-varying vector autoregressive models with high order lagged dependence. A kernel reweighted group lasso method is proposed, which overcomes the limitations of sample scarcity and transforms the problem of Granger causal structural learning into a group variable selection problem. The asymptotic consistency of the proposed algorithm is proved. We apply the time-varying Granger causal networks to simulation experiments and real data in the financial market. The study demonstrates that the method provides an efficient tool to detect changes and analysis characters of causal dependency structure in network evolution.

Nonlinear Granger causality graph method for data-driven target attack in power cyber-physical systems

Owing to the deep integration of the information and communication technologies, power cyber-physical systems (CPSs) have become smart but are vulnerable to cyber attacks. To correctly assess the vulnerability of power CPSs and further study feasible countermeasures, we verify that a data-driven target attack on a nonlinear Granger causality graph (NGCG) can be constructed successfully, even if adversaries cannot acquire the configuration information of the systems. A NGCG is a unified framework for the processing and analysis of nonlinear measurement data or datasets and can be used to evaluate the significance of power nodes or lines. In addition, an algorithm including data-driven parameter estimation, noise removal and data reconstruction based on symplectic geometry is introduced to make the NGCG a parameter-free and noise-tolerant method. In particular, three new indexes on the weight analysis of the NGCG are defined to quantitatively evaluate the significance of power nodes or lines. Finally, several case studies of a nonlinear simulation model and power systems in detail verify the effectiveness and superiority of the proposed data-driven target attack. The results show the proposed target attack can select the key attack targets more accurately and lead to physical system collapse with the least number of attack steps.

Linear Dynamic Network Reconstruction from Heterogeneous Datasets

This paper addresses reconstruction of linear dynamic networks from heterogeneous datasets. Those datasets consist of measurements from linear dynamical systems in multiple experiments subjected to different experimental conditions, e.g., changes/perturbations in parameters, disturbance or noise. A main assumption is that the Boolean structures of the underlying networks are the same in all experiments. The ARMAX model is adopted to parameterize the general linear dynamic network representation “Dynamical Structure Function” (DSF), which provides the Granger Causality graph as a special case. The network identification is performed by integrating all available datasets and promote group sparsity to assure both network sparsity and the consistency of Boolean structures over datasets. In terms of solving the problem, a treatment by the iterative reweighted l1 method is used, together with its implementations via proximal methods and ADMM for large-dimensional networks.

Causal conditioning and instantaneous coupling in causality graphs

This study aims at providing the definitive links between Massey and Kramer’s directed information theory and Granger causality graphs, recently formalized by Eichler. This naturally leads to consider two concepts of causality that can occur in physical systems: dynamical causality and instantaneous coupling. Although it is well accepted that the former is assessed by conditional transfer entropy, the latter is often overlooked, even if it was clearly introduced and understood in seminal studies. In the bivariate case, we show that directed information is decomposed into the sum of transfer entropy and instantaneous information exchange. In the multivariate case, encountered for conditional graph modeling, such a decomposition does not hold anymore. We provide a new insight into the problem of instantaneous coupling and show how it affects the estimated structure of a graphical model that should provide a sparse representation of a complex system. This result is discussed and analyzed for the inference of causality graphs. Two synthetic examples are developed to illustrate the theoretical concepts. Practical issues are also briefly discussed on these examples and an extension of Leonenko’s k-nearest neighbors based entropy estimators is used to derive a nonparametric estimator of directed information.

The Relation between Granger Causality and Directed Information Theory: A Review

This report reviews the conceptual and theoretical links between Granger causality and directed information theory. We begin with a short historical tour of Granger causality, concentrating on its closeness to information theory. The definitions of Granger causality based on prediction are recalled, and the importance of the observation set is discussed. We present the definitions based on conditional independence. The notion of instantaneous coupling is included in the definitions. The concept of Granger causality graphs is discussed. We present directed information theory from the perspective of studies of causal influences between stochastic processes. Causal conditioning appears to be the cornerstone for the relation between information theory and Granger causality. In the bivariate case, the fundamental measure is the directed information, which decomposes as the sum of the transfer entropies and a term quantifying instantaneous coupling. We show the decomposition of the mutual information into the sums of the transfer entropies and the instantaneous coupling measure, a relation known for the linear Gaussian case. We study the multivariate case, showing that the useful decomposition is blurred by instantaneous coupling. The links are further developed by studying how measures based on directed information theory naturally emerge from Granger causality inference frameworks as hypothesis testing.

On directed information theory and Granger causality graphs

Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory includes measures such as the transfer entropy, and that it is the adequate information theoretic framework needed for neuroscience applications, such as connectivity inference problems.

Learning Granger causality graphs for multivariate nonlinear time series

An information theory method is proposed to test the Granger causality and contemporaneous conditional independence in Granger causality graph models. In the graphs, the vertex set denotes the component series of the multivariate time series, and the directed edges denote causal dependence, while the undirected edges reflect the instantaneous dependence. The presence of the edges is measured by a statistics based on conditional mutual information and tested by a permutation procedure. Furthermore, for the existed relations, a statistics based on the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity. The significance of the nonlinear test statistics is determined by a bootstrap method based on surrogate data. We investigate the finite sample behavior of the procedure through simulation time series with different dependence structures, including linear and nonlinear relations.