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It becomes increasingly popular to perform mediation analysis for complex data from sophisticated experimental studies. In this paper, we present Granger Mediation Analysis (GMA), a new framework for causal mediation analysis of multiple…

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…

Multivariate time series (MTS) imputation is a widely studied problem in recent years. Existing methods can be divided into two main groups, including (1) deep recurrent or generative models that primarily focus on time series features, and…

It is a challenging research endeavor to infer causal relationships in multivariate observational time-series. Such data may be represented by graphs, where nodes represent time-series, and edges directed causal influence scores between…

Recently, diffusion probabilistic models have attracted attention in generative time series forecasting due to their remarkable capacity to generate high-fidelity samples. However, the effective utilization of their strong modeling ability…

To gain insight into complex systems it is a key challenge to infer nonlinear causal directional relations from observational time-series data. Specifically, estimating causal relationships between interacting components in large systems…

We consider extension of Granger causality to nonlinear bivariate time series. In this frame, if the prediction error of the first time series is reduced by including measurements from the second time series, then the second time series is…

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…

Finite order Markov models are theoretically well-studied models for dependent discrete data. Despite their generality, application in empirical work when the order is large is rare. Practitioners avoid using higher order Markov models…

Characterising cause-effect relationships in complex systems is fundamental to understanding their underlying mechanisms. Granger causality (GC) remains a widely used computational tool for identifying causal relationships in time series…

We present a new method for forecasting systems of multiple interrelated time series. The method learns the forecast models together with discovering leading indicators from within the system that serve as good predictors improving the…

We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel Granger causality to the multivariate case, here presented,…

We introduce a rigorous mathematical framework for Granger causality in extremes, designed to identify causal links from extreme events in time series. Granger causality plays a pivotal role in uncovering directional relationships among…

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…

Time series imputation is one of the most challenge problems and has broad applications in various fields like health care and the Internet of Things. Existing methods mainly aim to model the temporally latent dependencies and the…

The imputation of the Multivariate time series (MTS) is particularly challenging since the MTS typically contains irregular patterns of missing values due to various factors such as instrument failures, interference from irrelevant data,…

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…

We consider the problem of learning deep generative models from data. We formulate a method that generates an independent sample via a single feedforward pass through a multilayer perceptron, as in the recently proposed generative…

Causal discovery (CD) from time-varying data is important in neuroscience, medicine, and machine learning. Techniques for CD encompass randomized experiments, which are generally unbiased but expensive, and algorithms such as Granger…

A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used…