Network estimation via poisson autoregressive models
Network estimation via poisson autoregressive models
复制标题
通过泊松自回归模型进行网络估计
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
R. Willett
中科院分区：
文献类型：
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作者：
Benjamin Mark;Garvesh Raskutti;R. Willett
多变量泊松自回归模型是捕获自激点过程的常用方法，其中来自网络中节点的级联事件序列刺激或抑制来自其他节点的事件。这些模型可用于学习社会或生物神经网络的结构。与这些多变量网络模型相关的一个重要问题是确定不同节点如何相互影响。这个问题提出了许多技术挑战，因为节点的数量通常相对于观察到的事件的数量很大。本文解决了这些挑战，并提供了一类多元自激Poisson自回归模型的学习率。重要的是，当我们的网络稀疏时，导出的学习率适用于高维设置。我们还提供了一个真实的数据示例来支持我们的方法和主要结果。
Multivariate Poisson autoregressive models are a common way of capturing self-exciting point processes, where cascading series of events from nodes in a network either stimulate or inhibit events from other nodes. These models can be used to learn the structure of social or biological neural networks. An important problem associated with these multivariate network models is determining how different nodes influence each other. This problem presents a number of technical challenges since the number of nodes is typically large relative to the number of observed events. This paper addresses these challenges and provides learning rates for a class of multivariate self-exciting Poisson autoregressive models. Importantly, the derived learning rates apply in the high-dimensional setting when our network is sparse. We also provide a real data example to support our methodology and main results.