Related papers: Nonparametric Identification of Kronecker Networks
Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…
Conventional topology learning methods for dynamical networks become inapplicable to processes exhibiting low-rank characteristics. To address this, we propose the low rank dynamical network model which ensures identifiability. By employing…
Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or…
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…
Graph topology inference of network processes with co-evolving and interacting time-series is crucial for network studies. Vector autoregressive models (VAR) are popular approaches for topology inference of directed graphs; however, in…
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,…
How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and…
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…
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…
A major challenge for causal inference from time-series data is the trade-off between computational feasibility and accuracy. Motivated by process motifs for lagged covariance in an autoregressive model with slow mean-reversion, we propose…
We study Granger causality in the context of wide-sense stationary time series, where our focus is on the topological aspects of the underlying causality graph. We establish sufficient conditions (in particular, we develop the notion of a…
In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model…
Learning causal relationships is a fundamental problem in science. Anchor regression has been developed to address this problem for a large class of causal graphical models, though the relationships between the variables are assumed to be…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
The ability to compare complex systems can provide new insight into the fundamental nature of the processes captured in ways that are otherwise inaccessible to observation. Here, we introduce the $n$-tangle method to directly compare two…
Complex networks provide a powerful mathematical representation of complex systems in nature and society. To understand complex networks, it is crucial to explore their internal structures, also called structural regularities. The task of…
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…
Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal DAGs with non-Gaussian and/or nonlinear structural equation models…
Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the…
We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the…