Neuronal network reconstruction through causality measures

Understanding the causal connectivity within a network is crucial for unraveling its functional dynamics. However，the inferred causal connections are fundamentally influenced by the choice of causality measure employed, which may not always align with the actual structural connectivity of the network. The relationship between causal and structural connectivity, especially how different causality measures affect the inferred causal links, requires further exploration. In this talk, we examine nonlinear networks characterized by pulse signal outputs, such as spiking neural networks, using four prevalent causality measures: time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We provide a theoretical analysis of the interconnections among these measures when applied to pulse signals. Utilizing both a simulated Hodgkin–Huxley network and an empirical mouse brain network as case studies, we validate the quantitative relationships between these causality measures. Our results show a strong correspondence between the causal connectivity derived from any of these measures and the actual structural connectivity, thereby establishing a direct linkage between them. We highlight that structural connectivity in networks with output pulse signals can be reconstructed on a pairwise basis, without needing global information from all network nodes, effectively avoiding the curse of dimensionality. Our approach offers a robust and practical methodology for reconstructing networks based on pulse outputs.