Granger causality (GC), originated in economics, is a statistical tool to reveal linear causal relationship between random variables. It has been used in neuroscience to show the effective connectivity between neurons in a network. However, the neural dynamics is highly nonlinear, which making linear regression based methods, Granger causality in this case, problematic and the results of Granger causality is essentially uninterpretable. Nevertheless, our work show that GC can successfully reconstruct neuronal network by using either voltage trace or spike train of the neurons. And in sparse network, spatially local measurement can still give useful information of the local network. As a byproduct of our mathematical analysis, a fast GC algorithm is also developed.
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