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We develop a multivariate functional autoregressive model (MFAR), which captures the cross-correlation among multiple functional time series and thus improves forecast accuracy. We estimate the parameters under the Bayesian dynamic linear…

Emergent behavior in complex systems arises from nonlinear interactions among components, yet the intricate nature of self-organization often obscures the underlying causal relationships, long regarded as the "holy grail" of complexity…

Robust characterization of dynamic causal interactions in multivariate biomedical signals is essential for advancing computational and algorithmic methods in biomedical imaging. Conventional approaches, such as Dynamic Bayesian Networks…

Causal processes in biomedicine may contain cycles, evolve over time or differ between populations. However, many graphical models cannot accommodate these conditions. We propose to model causation using a mixture of directed cyclic graphs…

Identifying causal relations among multi-variate time series is one of the most important elements towards understanding the complex mechanisms underlying the dynamic system. It provides critical tools for forecasting, simulations and…

We present a new framework for learning Granger causality networks for multivariate categorical time series, based on the mixture transition distribution (MTD) model. Traditionally, MTD is plagued by a nonconvex objective,…

With the advancement of neural networks, diverse methods for neural Granger causality have emerged, which demonstrate proficiency in handling complex data, and nonlinear relationships. However, the existing framework of neural Granger…

Data-based inference of directed interactions in complex dynamical systems is a problem common to many disciplines of science. In this work, we study networks of spatially separate dynamical entities, which could represent physical systems…

Deep generative models have shown tremendous capability in data density estimation and data generation from finite samples. While these models have shown impressive performance by learning correlations among features in the data, some…

Multivariate time series (MTS) forecasting is an essential problem in many fields. Accurate forecasting results can effectively help decision-making. To date, many MTS forecasting methods have been proposed and widely applied. However,…

Discovering causal relations from observational time series without making the stationary assumption is a significant challenge. In practice, this challenge is common in many areas, such as retail sales, transportation systems, and medical…

In recent years, causal modelling has been used widely to improve generalization and to provide interpretability in machine learning models. To determine cause-effect relationships in the absence of a randomized trial, we can model causal…

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…

Cause-effect analysis is crucial to understand the underlying mechanism of a system. We propose to exploit model invariance through interventions on the predictors to infer causality in nonlinear multivariate systems of time series. We…

Causal inference from observational data following the restricted structural causal model (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or nonlinearity.…

Granger-Geweke causality (GGC) is a powerful and popular method for identifying directed functional (`causal') connectivity in neuroscience. In a recent paper, Stokes and Purdon [1] raise several concerns about its use. They make two…

Physicists are starting to work in areas where noisy signal analysis is required. In these fields, such as Economics, Neuroscience, and Physics, the notion of causality should be interpreted as a statistical measure. We introduce to the lay…

This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and…

That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and…

Causal inference from observational data following the restricted structural causal models (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or…