  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.
