Semiparametric estimation for dynamic networks with shifted connecting intensities

Abstract

Neural circuits are of paramount importance in the nervous system, as they are the essential infrastructure in guiding animal behavior. However, modeling the development of neural circuits poses significant challenges due to inherent properties of the development process. First, the neural circuit development process is transient, where the course of development can only be observed once. Second, despite potentially sharing similar underlying mechanisms for development, neural circuits from different subjects possess distinct sets of neurons, which limits the sharing of information across subjects. Third, neurons have diverse, unobserved activation times, which may obscure the analysis of neural activities. In light of these challenges, this study presents a novel approach aimed at clustering neurons based on their connecting behaviors while accommodating disparities at the neuron level. To this end, we propose a dynamic stochastic block model that accommodates unknown time shifts. We establish the conditions that guarantee the identifiability of cluster memberships of nodes and representative connecting intensities across clusters. Using methods for shape invariant models, we propose computationally efficient semiparametric estimation procedures to simultaneously estimate time shifts, cluster memberships, and connecting intensities. We illustrate the performance of the proposed procedures via extensive simulation experiments. We further apply the proposed method on a motor circuit development data from zebrafish to reveal distinct roles of neurons and identify representative connecting behaviors.