Quantitative relations among causality measures with applications to nonlinear pulse-output network reconstruction

• DOI: 10.48550/arxiv.2110.09521
• Publication Date: 2021-01-01
• Authors: Zhong-qi K. Tian; Kai Chen; Songting Li; David W. McLaughlin; Douglas Zhou
• Keywords: Causality; Causal model

The causal connectivity of a network is often inferred to understand the function. It arguably acknowledged that relies on causality measure one applies, and it may differ from network's underlying structural connectivity. However, interpretation remains be fully clarified, in particular, how depends measures relates Here, we focus nonlinear networks with pulse signals as measured output, $e.g.$, neural spike address above issues based four intensively utilized measures, $i.e.$, time-delayed correlation, mutual information, Granger causality, transfer entropy. We theoretically show these are related another when applied signals. Taking simulated Hodgkin-Huxley real mouse brain two illustrative examples, further verify quantitative relations among demonstrate by any well coincides connectivity, therefore establishing direct link between stress can reconstructed pairwisely without conditioning global information all other nodes network, thus circumventing curse dimensionality. Our framework provides practical effective approach for pulse-output reconstruction.