Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant processes may not be observed in practice. Naive estimation approaches that ignore these hidden variables can generate misleading results because of the unadjusted confounding. To plug this gap, we propose a deconfounding procedure to estimate high-dimensional point process networks with only a subset of the nodes being observed. Our method allows flexible connections between the observed and unobserved processes. It also allows the number of unobserved processes to be unknown and potentially larger than the number of observed nodes. Theoretical analyses and numerical studies highlight the advantages of the proposed method in identifying causal interactions among the observed processes.
翻译:由于技术进步导致近乎连续的时间观测,新兴的多点进程数据为因果关系发现提供了新的机会,然而,实现这一目标的一个主要障碍是,在实践中可能无法观察到许多相关进程。忽视这些隐藏变量的预测方法可能会由于未调整的混乱而产生误导性结果。为了弥合这一差距,我们建议采用一个分解程序来估计高维点进程网络,只有一组节点被观测到。我们的方法允许在被观测到和未观测到的进程中建立灵活的联系。它还允许未知的未观测进程数量,而且可能大于所观测到的节点数量。理论分析和数字研究强调了拟议方法在确定被观测到的进程之间的因果关系方面的优势。