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Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…

Disordered Systems and Neural Networks · Physics 2009-11-13 Daniele Marinazzo , Mario Pellicoro , Sebastiano Stramaglia

The key to traffic prediction is to accurately depict the temporal dynamics of traffic flow traveling in a road network, so it is important to model the spatial dependence of the road network. The essence of spatial dependence is to…

Machine Learning · Computer Science 2023-06-28 Silu He , Qinyao Luo , Ronghua Du , Ling Zhao , Haifeng Li

The problem of estimating high-dimensional network models arises naturally in the analysis of many physical, biological and socio-economic systems. Examples include stock price fluctuations in financial markets and gene regulatory networks…

Methodology · Statistics 2013-10-09 Sumanta Basu , Ali Shojaie , George Michailidis

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…

Statistics Theory · Mathematics 2011-07-18 Michael Eichler

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks…

Computation · Statistics 2020-01-08 Elsa Siggiridou , Christos Koutlis , Alkiviadis Tsimpiris , Dimitris Kugiumtzis

Granger causal modeling is an emerging topic that can uncover Granger causal relationship behind multivariate time series data. In many real-world systems, it is common to encounter a large amount of multivariate time series data collected…

Machine Learning · Computer Science 2021-02-11 Yunfei Chu , Xiaowei Wang , Jianxin Ma , Kunyang Jia , Jingren Zhou , Hongxia Yang

Inferring causal relationships in observational time series data is an important task when interventions cannot be performed. Granger causality is a popular framework to infer potential causal mechanisms between different time series. The…

Machine Learning · Computer Science 2022-07-22 Zexuan Yin , Paolo Barucca

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…

Machine Learning · Computer Science 2024-12-25 Haitao Lin , Cheng Tan , Lirong Wu , Zhangyang Gao , Zicheng Liu , Stan. Z. Li

Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multivariate data sets in a format amenable for human…

Signal Processing · Electrical Eng. & Systems 2020-11-16 Bakht Zaman , Luis Miguel Lopez Ramos , Daniel Romero , Baltasar Beferull-Lozano

Granger causality is widely used for causal structure discovery in complex systems from multivariate time series data. Traditional Granger causality tests based on linear models often fail to detect even mild non-linear causal…

Machine Learning · Computer Science 2025-10-23 Ziyi Zhang , Shaogang Ren , Xiaoning Qian , Nick Duffield

Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such…

Chaotic Dynamics · Physics 2009-11-10 Yonghong Chen , Govindan Rangarajan , Jianfeng Feng , Mingzhou Ding

Inferring causal relations from time series measurements is an ill-posed mathematical problem, where typically an infinite number of potential solutions can reproduce the given data. We explore in depth a strategy to disambiguate between…

Dynamical Systems · Mathematics 2020-11-04 George Stepaniants , Bingni W. Brunton , J. Nathan Kutz

This paper explores the potential of the transformer models for learning Granger causality in networks with complex nonlinear dynamics at every node, as in neurobiological and biophysical networks. Our study primarily focuses on a…

Machine Learning · Computer Science 2025-10-21 Ziyu Lu , Anika Tabassum , Shruti Kulkarni , Lu Mi , J. Nathan Kutz , Eric Shea-Brown , Seung-Hwan Lim

The concept of Granger causality is increasingly being applied for the characterization of directional interactions in different applications. A multivariate framework for estimating Granger causality is essential in order to account for…

Methodology · Statistics 2020-11-04 Angeliki Papana , Elsa Siggiridou , Dimitris Kugiumtzis

Complex dynamical systems are prevalent in many scientific disciplines. In the analysis of such systems two aspects are of particular interest: 1) the temporal patterns along which they evolve and 2) the underlying causal mechanisms.…

Methodology · Statistics 2022-05-31 Nicolas-Domenic Reiter , Andreas Gerhardus , Jakob Runge

Causal discovery algorithms based on probabilistic graphical models have emerged in geoscience applications for the identification and visualization of dynamical processes. The key idea is to learn the structure of a graphical model from…

Machine Learning · Computer Science 2015-12-29 Imme Ebert-Uphoff , Yi Deng

The present study explores the intricacies of causal relationship extraction, a vital component in the pursuit of causality knowledge. Causality is frequently intertwined with temporal elements, as the progression from cause to effect is…

Computation and Language · Computer Science 2023-04-24 Xiaosong Yuan , Ke Chen , Wanli Zuo , Yijia Zhang

Introduced more than a half century ago, Granger causality has become a popular tool for analyzing time series data in many application domains, from economics and finance to genomics and neuroscience. Despite this popularity, the validity…

Methodology · Statistics 2021-05-10 Ali Shojaie , Emily B. Fox

Understanding causal relationships in time series is fundamental to many domains, including neuroscience, economics, and behavioral science. Granger causality is one of the well-known techniques for inferring causality in time series.…

Artificial Intelligence · Computer Science 2025-08-04 Chakattrai Sookkongwaree , Tattep Lakmuang , Chainarong Amornbunchornvej

Accurate flight delay prediction is crucial for the secure and effective operation of the air traffic system. Recent advances in modeling inter-airport relationships present a promising approach for investigating flight delay prediction…

Computational Engineering, Finance, and Science · Computer Science 2024-07-23 Qihui Zhu , Shenwen Chen , Tong Guo , Yisheng Lv , Wenbo Du