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Multivariate Temporal Point Process Regression
Journal of the American Statistical Association ( IF 3.7 ) Pub Date : 2021-09-01 , DOI: 10.1080/01621459.2021.1955690
Xiwei Tang 1 , Lexin Li 2
Affiliation  

Abstract

Point process modeling is gaining increasing attention, as point process type data are emerging in a large variety of 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.



中文翻译:

多元时间点过程回归

摘要

随着点过程类型数据在各种科学应用中的出现,点过程建模越来越受到关注。在本文中,受神经元尖峰训练研究的启发,我们提出了一种新颖的点过程回归模型,其中响应和预测变量都可以是高维点过程。我们以卷积方式使用一组基础传递函数通过条件强度对预测器效应进行建模。我们以三向张量的形式组织相应的传递系数,然后对该系数张量施加低秩、稀疏和子群结构。这些结构有助于降低维度、整合不同个体过程中的信息并促进解释。我们开发了一种高度可扩展的参数估计优化算法。我们推导出恢复系数张量的大样本误差界,并建立子组识别一致性,同时允许多元点过程的维数发散。我们通过感觉皮层研究中的模拟和跨区域神经元尖峰序列分析证明了我们方法的有效性。

更新日期:2021-09-01
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