Multivariate Temporal Point Process Regression

TL;DR

This paper introduces a novel high-dimensional multivariate point process regression model that incorporates low-rank, sparsity, and subgroup structures, with scalable estimation and theoretical guarantees, demonstrated on neuronal spike train data.

Contribution

It proposes a new tensor-based regression framework for multivariate point processes with structured regularization, scalable algorithms, and theoretical error bounds.

Findings

Effective in simulations

Successfully applied to neuronal spike train data

Provides theoretical guarantees for estimation accuracy

Abstract

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.