  Point process modeling is gaining increasing attention, as point process type
data are emerging in numerous scientific applications. In this article,
motivated by a neuronal spike trains study, we propose a novel point process
regression model, where both the response and the predictor can be a
high-dimensional point process. We model the predictor effects through the
conditional intensities using a set of basis transferring functions in a
convolutional fashion. We organize the corresponding transferring coefficients
in the form of a three-way tensor, then impose the low-rank, sparsity, and
subgroup structures on this coefficient tensor. These structures help reduce
the dimensionality, integrate information across different individual
processes, and facilitate the interpretation. We develop a highly scalable
optimization algorithm for parameter estimation. We derive the large sample
error bound for the recovered coefficient tensor, and establish the subgroup
identification consistency, while allowing the dimension of the multivariate
point process to diverge. We demonstrate the efficacy of our method through
both simulations and a cross-area neuronal spike trains analysis in a sensory
cortex study.
