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Counterfactual learning has become promising for understanding and modeling causality in complex and dynamic systems. This paper presents a novel method for counterfactual learning in the context of multivariate time series analysis and…

Machine Learning · Computer Science 2026-03-03 Gianlucca Zuin , Adriano Veloso

Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this…

Methodology · Statistics 2023-07-19 Proloy Das , Behtash Babadi

This paper considers joint learning of multiple sparse Granger graphical models to discover underlying common and differential Granger causality (GC) structures across multiple time series. This can be applied to drawing group-level brain…

Machine Learning · Computer Science 2021-05-25 Parinthorn Manomaisaowapak , Jitkomut Songsiri

EEG-based emotion recognition holds significant promise for objective diagnosis of mood disorders. Graph neural networks (GNNs) have emerged as the dominant paradigm for modeling inter-channel dependencies in EEG, yet existing approaches…

Machine Learning · Computer Science 2026-05-26 Ziyi Wang , Dongyang Kuang

Granger causality analysis, as one of the most popular time series causality methods, has been widely used in the economics, neuroscience. However, unobserved confounders is a fundamental problem in the observational studies, which is still…

Machine Learning · Computer Science 2019-09-10 Yuan Meng

It is often useful in multivariate time series analysis to determine statistical causal relations between different time series. Granger causality is a fundamental measure for this purpose. Yet the traditional pairwise approach to Granger…

Neurons and Cognition · Quantitative Biology 2007-05-23 Yonghong Chen , Steven L. Bressler , Mingzhou Ding

Temporal causal analysis means understanding the underlying causes behind observed variables over time. Deep learning based methods such as transformers are increasingly used to capture temporal dynamics and causal relationships beyond mere…

Machine Learning · Computer Science 2024-11-21 Riya Mahesh , Rahul Vashisht , Chandrashekar Lakshminarayanan

The literature manifests that schizophrenia is associated with alterations in brain network connectivity. We investigate whether large-scale Extended Granger Causality (lsXGC) can capture such alterations using resting-state fMRI data. Our…

Neurons and Cognition · Quantitative Biology 2021-01-27 Axel Wismüller , M. Ali Vosoughi

When a dynamical system can be modeled as a sequence of observations, Granger causality is a powerful approach for detecting predictive interactions between its variables. However, traditional Granger causal inference has limited utility in…

Machine Learning · Computer Science 2022-10-20 Rohit Singh , Alexander P. Wu , Bonnie Berger

Exogenous variables offer valuable supplementary information for predicting future endogenous variables. Forecasting with exogenous variables needs to consider both past-to-future dependencies (i.e., temporal correlations) and the influence…

Machine Learning · Computer Science 2026-05-04 Zhengyu Li , Xiangfei Qiu , Yuhan Zhu , Xingjian Wu , Jilin Hu , Chenjuan Guo , Bin Yang

Granger causality (GC) is often considered not an actual form of causality. Still, it is arguably the most widely used method to assess the predictability of a time series from another one. Granger causality has been widely used in many…

Machine Learning · Computer Science 2023-07-21 Víctor Elvira , Émilie Chouzenoux , Jordi Cerdà , Gustau Camps-Valls

Multivariate time series anomaly detection has numerous real-world applications and is being extensively studied. Modeling pairwise correlations between variables is crucial. Existing methods employ learnable graph structures and graph…

Machine Learning · Computer Science 2025-01-24 Zehao Liu , Mengzhou Gao , Pengfei Jiao

Wahl et al. (2016, 2017) introduced the idea of Granger causality (GC) maps for Langevin systems: dynamics are localised linearly at each point in phase space as vector Ornstein-Uhlenbeck (VOU) processes, for which GCs may in principle be…

Mathematical Physics · Physics 2026-01-13 Lionel Barnett , Benjamin Wahl , Nadine Spychala , Anil K. Seth

Dependence between nodes in a network is an important concept that pervades many areas including finance, politics, sociology, genomics and the brain sciences. One way to characterize dependence between components of a multivariate time…

Machine Learning · Statistics 2024-08-08 Malik Shahid Sultan , Samuel Horvath , Hernando Ombao

Linear regression model (LRM) based on mean square error (MSE) criterion is widely used in Granger causality analysis (GCA), which is the most commonly used method to detect the causality between a pair of time series. However, when signals…

Methodology · Statistics 2019-02-20 Badong Chen , Rongjin Ma , Siyu Yu , Shaoyi Du , Jing Qin

Granger causality is well established within the neurosciences for inference of directed functional connectivity from neurophysiological data. These data usually consist of time series which subsample a continuous-time biophysiological…

Applications · Statistics 2016-09-08 Lionel Barnett , Anil K. Seth

Causal interactions in time series networks can be dynamic and nonlinear, making it difficult to identify them using conventional linear causality estimations. We propose a novel approach, called Threshold Autoregressive Modeling for…

Applications · Statistics 2025-09-19 Sipan Aslan , Hernando Ombao

Identifying causal interactions in complex dynamical systems is a fundamental challenge across the computational sciences. Existing functional connectivity methods capture correlations but not causation. While addressing directionality,…

Neurons and Cognition · Quantitative Biology 2026-03-10 Rahul Biswas , SuryaNarayana Sripada , Somabha Mukherjee , Reza Abbasi-Asl

Causal discovery from time-series data has been a central task in machine learning. Recently, Granger causality inference is gaining momentum due to its good explainability and high compatibility with emerging deep neural networks. However,…

Machine Learning · Computer Science 2023-02-16 Yuxiao Cheng , Runzhao Yang , Tingxiong Xiao , Zongren Li , Jinli Suo , Kunlun He , Qionghai Dai

Causal discovery in time-series is a fundamental problem in the machine learning community, enabling causal reasoning and decision-making in complex scenarios. Recently, researchers successfully discover causality by combining neural…

Machine Learning · Computer Science 2023-08-17 Yuxiao Cheng , Lianglong Li , Tingxiong Xiao , Zongren Li , Qin Zhong , Jinli Suo , Kunlun He