Related papers: Quantifying Causal Coupling Strength: A Lag-specif…
The representations of conditional entropy and conditional mutual information are significant in explaining the unique effects among variables. While previous studies based on conditional contrastive sampling have effectively removed…
We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging…
Inferring causal relationships from observed data is an important task, yet it becomes challenging when the data is subject to various external interferences. Most of these interferences are the additional effects of external factors on…
Information transfer between time series is calculated by using the asymmetric information-theoretic measure known as transfer entropy. Geweke's autoregressive formulation of Granger causality is used to find linear transfer entropy, and…
The information shared among observables representing processes of interest is traditionally evaluated in terms of macroscale measures characterizing aggregate properties of the underlying processes and their interactions. Traditional…
We introduce a novel framework for temporal causal discovery and inference that addresses two key challenges: complex nonlinear dependencies and spurious correlations. Our approach employs a multi-layer Transformer-based time-series…
In studies of entanglement, finding out if a state is entangled and quantifying the amount of entanglement contained in a state are related but different questions. Similarly in studies of causality, finding out the causal structures…
Transfer entropy is a widely used measure for quantifying directed information flows in complex systems. While the challenges of estimating transfer entropy for continuous data are well known, it has two major shortcomings for data of…
The causal Markov condition (CMC) is a postulate that links observations to causality. It describes the conditional independences among the observations that are entailed by a causal hypothesis in terms of a directed acyclic graph. In the…
Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors…
The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer…
The crucial aspect of this demonstration is the discovery of renewal events, hidden in the computed dynamics of a multifractal metronome, which enables the replacement of the phenomenon of strong anticipation with a time delayed…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
We investigate causal inference in the asymptotic regime as the number of variables approaches infinity using an information-theoretic framework. We define structural entropy of a causal model in terms of its description complexity measured…
Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…
Efficient and accurate learning of constitutive laws is crucial for accurately predicting the mechanical behavior of materials under complex loading conditions. Accurate model calibration hinges on a delicate interplay between the…
Based on the monogamy of entanglement, we develop the technique of quantum conditioning to build an {\it additive} entanglement measure: the conditional entanglement of mutual information. Its {\it operational} meaning is elaborated to be…
In classical information theory, a causal relationship between two variables is typically modelled by assuming that, for every possible state of one of the variables, there exists a particular distribution of states of the second variable.…
In this work, conditional entropy is used to quantify the information loss induced by passing a continuous random variable through a memoryless nonlinear input-output system. We derive an expression for the information loss depending on the…
We define Persistent Mutual Information (PMI) as the Mutual (Shannon) Information between the past history of a system and its evolution significantly later in the future. This quantifies how much past observations enable long term…