Related papers: Kernel method for nonlinear Granger causality

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.…

In this paper, we propose a new Granger causality measure which is robust against the confounding influence of latent common inputs. This measure is inspired by partial Granger causality in the literature, and its variant. Using numerical…

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…

Although nonstationary data are more common in the real world, most existing causal discovery methods do not take nonstationarity into consideration. In this letter, we propose a kernel embedding-based approach, ENCI, for nonstationary…

We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal. Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more…

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…

Granger causality is a widely-used criterion for analyzing interactions in large-scale networks. As most physical interactions are inherently nonlinear, we consider the problem of inferring the existence of pairwise Granger causality…

An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved.…

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…

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…

Temporal point process as the stochastic process on continuous domain of time is commonly used to model the asynchronous event sequence featuring with occurrence timestamps. Thanks to the strong expressivity of deep neural networks, they…

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…

Inferring a cause from its effect using observed time series data is a major challenge in natural and social sciences. Assuming the effect is generated by the cause trough a linear system, we propose a new approach based on the hypothesis…

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience.…

Causal discovery from time-series data has been a central task in machine learning. Recently, Granger causality inference is gaining momentum due to its good explainability and high compatibility with emerging deep neural networks. However,…

Identifying causality behind complex systems plays a significant role in different domains, such as decision making, policy implementations, and management recommendations. However, existing causality studies on temporal event sequences…

This paper explores the potential of the transformer models for learning Granger causality in networks with complex nonlinear dynamics at every node, as in neurobiological and biophysical networks. Our study primarily focuses on a…

Many scientific problems require identifying a small set of covariates that are associated with a target response and estimating their effects. Often, these effects are nonlinear and include interactions, so linear and additive methods can…

Causality defines the relationship between cause and effect. In multivariate time series field, this notion allows to characterize the links between several time series considering temporal lags. These phenomena are particularly important…