Uncovering Interactions in the Frequency Domain

Abstract

Oscillatory activity plays a critical role in regulating biological processes at levels ranging from subcellular, cellular, and network to the whole organism, and often involves a large number of interacting elements. We shed light on this issue by introducing a novel approach called partial Granger causality to reliably reveal interaction patterns in multivariate data with exogenous inputs and latent variables in the frequency domain. The method is extensively tested with toy models, and successfully applied to experimental datasets, including (1) gene microarray data of HeLa cell cycle; (2) in vivo multi-electrode array (MEA) local field potentials (LFPs) recorded from the inferotemporal cortex of a sheep; and (3) in vivo LFPs recorded from distributed sites in the right hemisphere of a macaque monkey.

Unified asymptotic theory for all partial directed coherence forms

“…Contrary to PDC failure claims [17], figures 4-6 show that all PDC forms successfully infer connectivity, which is further confirmed by the time domain Wald-type Granger causality [14] p-value tests listed in figure 4.…”

“…This allows investigation of the example in reference [17] by taking a i as uniform independent random variables in the [0, 1] interval and b i = 2 and c i = 5, leading to system inputs that are no longer white.…”

A Note on Inferring Acyclic Network Structures Using Granger Causality Tests

“…The auto-regressive lag-length was fixed as (p = 2), since (15) (Brovelli et al, 2004;Seth et al 2006;Mukhopadhyay and Chatterjeee, 2007;Fujita et al, 2007;Guo et al, 2008). Interpretation of GC results across multivariate processes can especially be challenging when there are unobserved variables.…”

“…1. Recent studies have used Granger causality (Granger, 1969;Hamilton, 1994) and its extensions for modeling causal relationships from the observed multivariate time series including gene expression data (Brovelli et al, 2004;Seth et al 2006;Mukhopadhyay and Chatterjeee, 2007;Fujita et al, 2007;Guo et al, 2008). It is important to note that causal relationships inferred using GC can be either unidirectional (acyclic) or bidirectional (cyclic).…”

Find synaptic topology from spike trains

“…A basic problem is how to detect the system structure from the neural activities. In the classic statistical approaches, such as correlation analysis, cluster analysis, principal component analysis (PCA), independent component analysis (ICA) [8] and causality analysis [9], [10], the system is considered as linear and analyzed without including the biophysical properties of neurons. With the biophysical knowledge, it is more realistic and efficient to utilize a specific model to describe the data and detect the system structure.…”