Related papers: On directed information theory and Granger causali…
We present a unified mathematical derivation of the asymptotic behaviour of three of the main forms of \textit{directed transfer function} (DTF) complementing recent partial directed coherence (PDC) results \cite{Baccala2013}. Based on…
Transfer Entropy and Directed Information are information-theoretic measures of the directional dependency between stochastic processes. Following the definitions of Schreiber and Massey in discrete time, we define and evaluate these…
Recent research has explored the increasingly important role of social media by examining the dynamics of individual and group behavior, characterizing patterns of information diffusion, and identifying influential individuals. In this…
Sharing spectrum with a communicating incumbent user (IU) network requires avoiding interference to IU receivers. But since receivers are passive when in the receive mode and cannot be detected, the network topology can be used to predict…
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…
The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional…
Extracting causal connections can advance interpretable AI and machine learning. Granger causality (GC) is a robust statistical method for estimating directed influences (DC) between signals. While GC has been widely applied to analysing…
Probabilistic graphical models are a fundamental tool in statistics, machine learning, signal processing, and control. When such a model is defined on a directed acyclic graph (DAG), one can assign a partial ordering to the events occurring…
In this paper, we study a hypothesis test to determine the underlying directed graph structure of nodes in a network, where the nodes represent random processes and the direction of the links indicate a causal relationship between said…
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…
We develop a theoretical framework for defining and identifying flows of information in computational systems. Here, a computational system is assumed to be a directed graph, with "clocked" nodes that send transmissions to each other along…
A notion of directed information between two continuous-time processes is proposed. A key component in the definition is taking an infimum over all possible partitions of the time interval, which plays a role no less significant than the…
There is a recent trend to leverage the power of graph neural networks (GNNs) for brain-network based psychiatric diagnosis, which,in turn, also motivates an urgent need for psychiatrists to fully understand the decision behavior of the…
Granger causality, commonly used for inferring causal structures from time series data, has been adopted in widespread applications across various fields due to its intuitive explainability and high compatibility with emerging deep neural…
Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs,…
While correlation measures are used to discern statistical relationships between observed variables in almost all branches of data-driven scientific inquiry, what we are really interested in is the existence of causal dependence. Designing…
Traditionally, statistical and causal inference on human subjects rely on the assumption that individuals are independently affected by treatments or exposures. However, recently there has been increasing interest in settings, such as…
Transient phenomena play a key role in coordinating brain activity at multiple scales, however,their underlying mechanisms remain largely unknown. A key challenge for neural data science is thus to characterize the network interactions at…
The broad abundance of time series data, which is in sharp contrast to limited knowledge of the underlying network dynamic processes that produce such observations, calls for a rigorous and efficient method of causal network inference. Here…
Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer…