title: Network inference in the presence of latent confounders: the role of instantaneous causalities.
abstract: BACKGROUND
  Detecting causal interactions in multivariate systems, in terms of Granger-causality, is of major interest in the Neurosciences. Typically, it is almost impossible to observe all components of the system. Missing certain components can lead to the appearance of spurious interactions. The aim of this study is to demonstrate the effect of this and to demonstrate that distinction between latent confounders and volume conduction is possible in some cases.
  
  
  METHODS
  Our new method uses a combination of renormalised partial directed coherence and analysis of the (partial) covariance matrix of residual noise process to detect instantaneous, spurious interactions. Sub-network analyses are performed to infer the true network structure of the underlying system.
  
  
  RESULTS
  We provide evidence that it is possible to distinguish between instantaneous interactions that occur as a result of a latent confounder and those that occur as a result of volume conduction.
  
  
  METHODS
  Our novel approach demonstrates to what extent inference of unobserved important processes as well as the distinction between latent confounders and volume conduction is possible. We suggest a combination of measures of Granger-causality and covariance selection models to achieve this numerically.
  
  
  CONCLUSIONS
  Sub-network analyses enable a much more precise and correct inference of the true underlying network structure in some cases. From this it is possible to distinguish between unobserved processes and volume conduction. Our approach is straightforwardly adaptable to various measures of Granger-causality emphasising its ubiquitous successful applicability.
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, King's College, Old Aberdeen AB24 3UE, United Kingdom. Electronic address: h.elsegai@gmail.com.
authors.forename: Heba
authors.initials: H
authors.lastname: Elsegai
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, King's College, Old Aberdeen AB24 3UE, United Kingdom. Electronic address: r01hcs14@abdn.ac.uk.
authors.forename: Helen
authors.initials: H
authors.lastname: Shiells
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, King's College, Old Aberdeen AB24 3UE, United Kingdom. Electronic address: m.thiel@abdn.ac.uk.
authors.forename: Marco
authors.initials: M
authors.lastname: Thiel
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, King's College, Old Aberdeen AB24 3UE, United Kingdom. Electronic address: b.schelter@abdn.ac.uk.
authors.forename: Björn
authors.initials: B
authors.lastname: Schelter
mesh_terms: D000465:Algorithms; D000818:Animals; D001921:Brain / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology
keywords: Granger causality; Instantaneous interactions; Latent confounders; VAR modelling; rPDC