The aim of this toy model is to illustrate the difference between estimating undirected connectivity with partial correlation (based on the zero-lag covariance matrix Q0) and directed connectivity based on time-shifted covariances of the observed activity (Q1 in addition to Q0). It also shows that the mean activity (X) is very similar for all configurations, i.e., hardly informative about the original network parameters.
The script generates activity using multivariate Ornstein-Uhelnbeck (MOU) process for 4 network configurations. The 4 networks differ by the connectivity C and the input covariance matrix Σ (left of the plotted figure). The observed activity is also downsampled before calculating the observables: mean activity X and covariance matrices Q0 and Q1 (center of the figure). The network estimates for partial correlation (PC) and the MOU estimation ('est') are located on the right of the figure. Compare the estimates with the original network parameters.
Refs:
- en.wikipedia.org/wiki/Partial_correlation
- en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process
- Gilson et al. (2016) PLoS Comput Biol doi.org/10.1371/journal.pcbi.1004762
This script compares the efficiency of conditional Granger causality analysis and a novel non-parametric testing method for MVAR in a network with linear feedback in discrete time (same as MVAR, which is canonical to both estimation methods). It examines the true-detection rates and false-alarm rates for network with random size, density, etc.
Ref:
- Gilson, Tauste Campo, Chen, Thiele, Deco (2017) Net Neurosci doi.org/10.1162/NETN_a_00019
This script calculates the (dynamic) communicability for a small network of 4 nodes, reproducing parts of Fig. 2 and 3 in the paper in reference. For the dynamic network (multivariate Ornstein-Uhlenbeck here), dynamic communicability quantifies the interactions between nodes over time (via the Green function).
Ref:
- Gilson M, Kouvaris NE, Deco G, Zamora-López G (2018) Phys Rev E doi: 10.1103/PhysRevE.97.052301