Multivariate Temporal Point Process Regression
Multivariate Temporal Point Process Regression
复制标题
DOI：
10.1080/01621459.2021.1955690
复制
发表时间：
2021-08-29
影响因子：
3.7
通讯作者：
Li，Lexin
中科院分区：
文献类型：
--
作者：
Tang，Xiwei;Li，Lexin
随着点过程类型数据在各种科学应用中的出现，点过程建模正受到越来越多的关注。在这篇文章中，基于神经元锋电位序列的研究，我们提出了一个新的点过程回归模型，其中响应和预测都可以是一个高维的点过程。我们通过条件强度使用一组卷积方式的基传递函数来建模预测器效应。我们将相应的传递系数以三向张量的形式组织起来，然后在这个系数张量上施加低秩、稀疏性和子群结构。这些结构有助于降低维度，整合不同过程的信息，并促进解释。我们开发了一个高度可扩展的参数估计优化算法。我们推导出恢复的系数张量的大样本误差界，并建立子群识别的一致性，同时允许多维点过程的维数发散。我们证明了我们的方法的有效性，通过模拟和跨区域的神经元锋电位序列分析在感觉皮层的研究。
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.