Multivariate Temporal Point Process Regression

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