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We study Ising models for describing data and show that autoregressive methods may be used to learn their connections, also in the case of asymmetric connections and for multi-spin interactions. For each link the linear Granger causality is…

Neurons and Cognition · Quantitative Biology 2015-05-18 Mario Pellicoro , Sebastiano Stramaglia

Federated Graph Learning (FGL) has emerged as a powerful paradigm for decentralized training of graph neural networks while preserving data privacy. However, existing FGL methods are predominantly designed for static graphs and rely on…

Machine Learning · Computer Science 2026-04-01 Yuxuan Liu , Wenchao Xu , Haozhao Wang , Zhiming He , Zhaofeng Shi , Chongyang Xu , Peichao Wang , Boyuan Zhang

Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC)…

Populations and Evolution · Quantitative Biology 2020-11-10 Frederic Barraquand , Coralie Picoche , Matteo Detto , Florian Hartig

We investigate how efficiently a known underlying sparse causality structure of a simulated multivariate linear process can be retrieved from the analysis of time-series of short lengths. Causality is quantified from conditional transfer…

Methodology · Statistics 2017-10-06 Tomaso Aste , T. Di Matteo

Cross-slice attack attribution in 6G networks faces the fundamental challenge of distinguishing genuine causal relationships from spurious correlations in shared infrastructure environments. We propose a theoretically-grounded…

Cryptography and Security · Computer Science 2025-10-08 Minh K. Quan , Pubudu N. Pathirana

Modelling time-varying and frequency-specific relationships between two brain signals is becoming an essential methodological tool to answer heoretical questions in experimental neuroscience. In this article, we propose to estimate a…

Methodology · Statistics 2018-04-16 Sezen Cekic , Didier Grandjean , Olivier Renaud

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

Machine Learning · Computer Science 2020-10-28 Feng Yin , Lishuo Pan , Xinwei He , Tianshi Chen , Sergios Theodoridis , Zhi-Quan , Luo

Time Series Analysis has been given a great amount of study in which many useful tests were developed. The phenomenal work of Engle and Granger in 1987 and Johansen in 1988 has paved the way for the most commonly used cointegration tests so…

Numerical Analysis · Mathematics 2025-09-10 Alvey Qianli Lin , Zhiwen Zhang

Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can yield significant insights into the…

Data Analysis, Statistics and Probability · Physics 2009-11-13 Hariharan Nalatore , Govindan Rangarajan , Mingzhou Ding

Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach…

Methodology · Statistics 2025-07-08 Sofia L. Vega , Rachel C. Nethery

Causal inference in multivariate time series is challenging due to the fact that the sampling rate may not be as fast as the timescale of the causal interactions. In this context, we can view our observed series as a subsampled version of…

Methodology · Statistics 2017-04-11 Alex Tank , Emily B. Fox , Ali Shojaie

Identifying the structure of a partially observed causal system is essential to various scientific fields. Recent advances have focused on constraint-based causal discovery to solve this problem, and yet in practice these methods often face…

Machine Learning · Computer Science 2026-05-04 Xinshuai Dong , Ignavier Ng , Haoyue Dai , Jiaqi Sun , Xiangchen Song , Peter Spirtes , Kun Zhang

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

This article proposes a novel causal discovery and inference method called GrIVET for a Gaussian directed acyclic graph with unmeasured confounders. GrIVET consists of an order-based causal discovery method and a likelihood-based…

Methodology · Statistics 2023-09-22 Li Chen , Chunlin Li , Xiaotong Shen , Wei Pan

In this paper we test for Granger causality in high-dimensional vector autoregressive models (VARs) to disentangle and interpret the complex causal chains linking radiative forcings and global temperatures. By allowing for high…

Econometrics · Economics 2024-06-04 Marina Friedrich , Luca Margaritella , Stephan Smeekes

Wiener and Granger have introduced an intuitive concept of causality between two variables which is based on the idea that an effect never occurs before its cause. Later, Geweke has generalized this concept to a multivariate Granger…

Unveil, model, and comprehend the causal mechanisms underpinning natural phenomena stand as fundamental endeavors across myriad scientific disciplines. Meanwhile, new knowledge emerges when discovering causal relationships from data.…

Machine Learning · Computer Science 2023-12-13 Jiaxuan Liang , Jun Wang , Guoxian Yu , Shuyin Xia , Guoyin Wang

Clustering is an unsupervised learning technique that is useful when working with a large volume of unlabeled data. Complex dynamical systems in real life often entail data streaming from a large number of sources. Although it is desirable…

Machine Learning · Computer Science 2021-05-20 Sin Yong Tan , Homagni Saha , Margarite Jacoby , Gregor P. Henze , Soumik Sarkar

Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a…

Methodology · Statistics 2010-08-13 Stefan Haufe , Guido Nolte , Klaus-Robert Mueller , Nicole Kraemer

When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…

Statistics Theory · Mathematics 2024-08-19 Nicolas-Domenic Reiter , Andreas Gerhardus , Jonas Wahl , Jakob Runge