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Abstract:
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Recent advancements in technologies enable the recording of neuronal calcium concentration levels on the mesoscopic scale. Calcium concentration levels can be translated into spiking histories, which allow the learning of functional connectivity among neurons, i.e. the mechanism behind thinking. The spiking histories are multivariate point processes are inherently high-dimensional due to the large number of observed neurons in the calcium imaging. We propose a framework of two-stage procedure for estimating functional connectivity from spiking histories, where the first stage employs the sure screening to reduce the dimensionality of the problem, and the second stage uses a sparse additive model to learn the connectivity. We propose our estimators based on a class of mutually-exciting point process known as the Hawkes process. The properties of the proposed procedure are established under the high-dimensional regime. Simulation studies are carried out to complement the theory. We apply the proposed procedure on calcium imaging data on the mouse visual cortex.
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