Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes
This work addresses a key obstacle in causal discovery for multivariate point process data, which is incremental as it builds on existing methods by handling hidden variables more flexibly.
The paper tackles the problem of causal discovery in high-dimensional point process networks when some nodes are hidden, which can lead to misleading results due to unadjusted confounding. It proposes a deconfounding procedure that allows flexible connections and an unknown number of hidden nodes, with theoretical and numerical studies showing advantages in identifying causal interactions among observed processes.
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.