title: Causal inference in neuronal time-series using adaptive decomposition.
abstract: BACKGROUND
  The assessment of directed functional connectivity from neuronal data is increasingly common in neuroscience by applying measures based in the Granger causality (GC) framework. Although initially these consisted in simple analyses based on directionality strengths, current methods aim to discriminate causal effects both in time and frequency domain.
  
  
  METHODS
  We study the effect of adaptive data analysis on the GC framework by combining empirical mode decomposition (EMD) and causal analysis of neuronal signals. EMD decomposes data into simple amplitude and phase modulated oscillatory modes, the intrinsic mode functions (IMFs), from which it is possible to compute their instantaneous frequencies (IFs). Hence, we propose a method where causality is estimated between IMFs with comparable IFs, in a static or time-varying procedure, and then attributed to the frequencies corresponding to the IF of the driving IMF for improved frequency localization.
  
  
  RESULTS
  We apply a thorough simulation framework involving all possible combinations of EMD algorithms with causality metrics and realistically simulated datasets. Results show that synchrosqueezing wavelet transform and noise-assisted multivariate EMD, paired with generalized partial directed coherence or with Geweke's GC, provide the highest sensitivity and specificity results.
  
  
  METHODS
  Compared to standard causal analysis, the output of selected representative instances of this methodology result in the fulfillment of performance criteria in a well-known benchmark with real animal epicranial recordings and improved frequency resolution for simulated neural data.
  
  
  CONCLUSIONS
  This study presents empirical evidence that adaptive data analysis is a fruitful addition to the existing causal framework.
authors.affiliation: Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, Campo Grande, 1749-016 Lisboa, Portugal. Electronic address: jprodrigues@fc.ul.pt.
authors.forename: João
authors.initials: J
authors.lastname: Rodrigues
authors.affiliation: Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, Campo Grande, 1749-016 Lisboa, Portugal. Electronic address: aandrade@fc.ul.pt.
authors.forename: Alexandre
authors.initials: A
authors.lastname: Andrade
mesh_terms: D000465:Algorithms; D000818:Animals; D001921:Brain / Q000502:physiology*; D058256:Brain Waves / Q000502:physiology*; D003198:Computer Simulation; D004569:Electroencephalography; D005583:Fourier Analysis; D006801:Humans; D015999:Multivariate Analysis; D016571:Neural Networks, Computer; D012815:Signal Processing, Computer-Assisted; D013997:Time Factors
keywords: Directed functional connectivity; Empirical mode decomposition; Granger causality; Time series analysis; Time-frequency analysis