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Compressed sensing is a scheme that allows for sparse signals to be acquired, transmitted and stored using far fewer measurements than done by conventional means employing Nyquist sampling theorem. Since many naturally occurring signals are…
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…
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…
Exploratory analysis of time series data can yield a better understanding of complex dynamical systems. Granger causality is a practical framework for analysing interactions in sequential data, applied in a wide range of domains. In this…
A novel approach is developed for discovering directed connectivity between specified pairs of nodes in a high-dimensional network (HDN) of brain signals. To accurately identify causal connectivity for such specified objectives, it is…
Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger…
Causal inference is one of the most fundamental problems across all domains of science. We address the problem of inferring a causal direction from two observed discrete symbolic sequences $X$ and $Y$. We present a framework which relies on…
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…
Most of the metrics used for detecting a causal relationship among multiple time series ignore the effects of practical measurement impairments, such as finite sample effects, undersampling and measurement noise. It has been shown that…
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)…
Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality…
Granger causal inference is a contentious but widespread method used in fields ranging from economics to neuroscience. The original definition addresses the notion of causality in time series by establishing functional dependence…
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.…
A widely applied approach to causal inference from a non-experimental time series $X$, often referred to as "(linear) Granger causal analysis", is to regress present on past and interpret the regression matrix $\hat{B}$ causally. However,…
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…
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer…
Identifying the causal structure of systems with multiple dynamic elements is critical to several scientific disciplines. The conventional approach is to conduct statistical tests of causality, for example with Granger Causality, between…
Granger causality has been employed to investigate causality relations between components of stationary multiple time series. We generalize this concept by developing statistical inference for local Granger causality for multivariate…
Causality in time series can be challenging to determine, especially in the presence of non-linear dependencies. Granger causality helps analyze potential relationships between variables, thereby offering a method to determine whether one…
While most classical approaches to Granger causality detection repose upon linear time series assumptions, many interactions in neuroscience and economics applications are nonlinear. We develop an approach to nonlinear Granger causality…