基于点过程数据的网络估计
Network Estimation from Point Process Data
摘要：
考虑观察网络中离散事件的集合，这些事件反映了网络节点如何相互影响。这些数据在从生物神经网络、社交网络内的交互以及各种其他设置记录的尖峰序列中很常见。这种形式的数据可以被建模为自激点过程，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估计自激参数和推断基本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，这些假设由这里的新方法解决。具体来说，本文中我们（1）将饱和度引入点过程模型，既保证了稳定性，又模拟了非线性阈值效应;（2）施加一般的低维结构假设，包括稀疏性、组稀疏性和低秩性，允许在高维环境中开发边界;以及（3）通过移动平均和高阶自回归分量结合长程记忆效应。使用我们的一般框架，我们提供了一些新的理论保证高维自激点过程，反映了底层网络结构和长期记忆所发挥的作用。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。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
