Statistical Learning of Neuronal Functional Connectivity

Abstract

Identifying the network structure of a neuron ensemble beyond the standard measure of pairwise correlations is critical for understanding how information is transferred within such a neural population. However, the spike train data pose significant challenges to conventional statistical methods due to not only the complexity, massive size, and large scale, but also high dimensionality. In this article, we propose a novel “structural information enhanced” (SIE) regularization method for estimating the conditional intensities under the generalized linear model (GLM) framework to better capture the functional connectivity among neurons. We study the consistency of parameter estimation of the proposed method. A new “accelerated full gradient update” algorithm is developed to efficiently handle the complex penalty in the SIE-GLM for large sparse datasets applicable to spike train data. Simulation results indicate that our proposed method outperforms existing approaches. An application of the proposed method to a real spike train dataset, obtained from the prelimbic region of the prefrontal cortex of adult male rats when performing a T-maze based delayed-alternation task of working memory, provides some insight into the neuronal network in that region.