Inferring directed networks using a rank-based connectivity measure

Abstract

Inferring the topology of a network using the knowledge of the signals of each of the interacting units is key to understanding real-world systems. One way to address this problem is using datadriven methods like cross-correlation or mutual information. However, these measures lack the ability to distinguish the direction of coupling. Here, we use a rank-based nonlinear interdependence measure originally developed for pairs of signals. This measure not only allows one to measure the strength but also the direction of the coupling. Our results for a system of coupled Lorenz dynamics show that we are able to consistently infer the underlying network for a subrange of the coupling strength and link density. Furthermore, we report that the addition of dynamical noise can benefit the reconstruction. Finally, we show an application to multichannel electroencephalographic recordings from an epilepsy patient.

Seizure Onset Zone Lateralization Using a Non-linear Analysis of Micro vs. Macro Electroencephalographic Recordings During Seizure-Free Stages of the Sleep-Wake Cycle From Epilepsy Patients

“…Our particular type of analysis can therefore be useful in the SOZ lateralization of patients undergoing invasive seizure monitoring. Some of these techniques are used for the characterization of seizure activity, the so-called ictal activity (9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22), while others are used for the analysis of the seizure-free interval . The characterization of the seizure-free interval, often referred to as interictal interval, can reveal aspects of brain dynamics that may help in the localization of the SOZ without the need to wait for seizures to occur.…”

Using machine learning to assess short term causal dependence and infer network links

“…Many past approaches have, for example, been based upon the concepts of prediction impact, [3,4] correlation, [7,8,9] information transfer, [10,11] and direct physical perturbations [12,13] . Other previous works have investigated the inference of network links from time series of node states assuming some prior knowledge of the form of the network system and using that knowledge in a fitting procedure to determine links [9,14,15,16,17] . In addition, some recent papers address network link inference from data via techniques based on delay coordinate embedding, [15] random forest methods, [18] network embedding algorithms [19] and feature ranking [20] .…”

“…Other previous works have investigated the inference of network links from time series of node states assuming some prior knowledge of the form of the network system and using that knowledge in a fitting procedure to determine links [9,14,15,16,17] . In addition, some recent papers address network link inference from data via techniques based on delay coordinate embedding, [15] random forest methods, [18] network embedding algorithms [19] and feature ranking [20] . In this paper, we introduce a technique that makes the use of an ML training process in performing predictive and interpretive tasks and attempts to use it to extract information about causal dependences.…”

“…We will show that this ML-based technique offers a unique and potentially highly effective approach to determining causal dependences. Furthermore, the presence of dynamical noise (either naturally present or intentionally injected) can very greatly improve the ability to infer causality, [14,15] while, in contrast, observational noise degrades inference.…”

Reconstructing Network Structures from Partial Measurements

“…They are therefore of little use in large networks. Lighter, probabilistic approaches identify likely coupling edges between pairs of agents from statistical properties of the corresponding pairs of trajectories [24][25][26][27][28][29]. A different and rather efficient approach extracts the network topology from the n(n − 1)/2 two-point correlators of pairs of agent trajectories in systems subjected to white [30][31][32] or correlated noise [33,34].…”