Network Estimation From Point Process Data
Network Estimation From Point Process Data
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DOI：
10.1109/tit.2018.2875766
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发表时间：
2018-02
影响因子：
2.5
通讯作者：
Benjamin Mark;Garvesh Raskutti;R. Willett
中科院分区：
文献类型：
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作者：
Benjamin Mark;Garvesh Raskutti;R. Willett
考虑观察网络中反映网络节点如何相互影响的一组离散事件。这样的数据在从生物神经网络、社会网络内的相互作用和各种其他设置中记录的棘波序列中是常见的。这种形式的数据可以建模为自激发点过程，其中未来事件的可能性取决于过去的事件。本文讨论了从自激点过程数据中估计自激参数和推断潜在功能网络结构的问题。过去在这一领域的工作受到强有力的假设的限制，这里的新方法解决了这些假设。具体地说，在本文中，我们1)在点过程模型中加入饱和度，它既确保了稳定性，又模拟了非线性阈值效应；2)施加了一般的低维结构假设，包括稀疏性、组稀疏性和低秩性，允许在高维环境中建立界限；3)通过移动平均和高阶自回归分量来引入长期记忆效应。利用我们的一般框架，我们为高维自激点过程提供了一些新的理论保证，这些过程反映了潜在的网络结构和长时记忆所起的作用。我们还提供了模拟和真实数据的例子来支持我们的方法和主要结果。
Consider observing a collection of discrete events within a network that reflect how network nodes influence one another. Such data are common in spike trains recorded from biological neural networks, interactions within a social network, and a variety of other settings. Data of this form may be modeled as self-exciting point processes, in which the likelihood of future events depends on the past events. This paper addresses the problem of estimating self-excitation parameters and inferring the underlying functional network structure from self-exciting point process data. Past work in this area was limited by strong assumptions which are addressed by the novel approach here. Specifically, in this paper we 1) incorporate saturation in a point process model which both ensures stability and models non-linear thresholding effects; 2) impose general low-dimensional structural assumptions that include sparsity, group sparsity, and low-rankness that allows bounds to be developed in the high-dimensional setting; and 3) incorporate long-range memory effects through moving average and higher-order auto-regressive components. Using our general framework, we provide a number of novel theoretical guarantees for high-dimensional self-exciting point processes that reflect the role played by the underlying network structure and long-term memory. We also provide simulations and real data examples to support our methodology and main results.