  In this work, we formalize the problem of causal inference over graph-based
relational time-series data where each node in the graph has one or more
time-series associated to it. We propose causal inference models for this
problem that leverage both the graph topology and time-series to accurately
estimate local causal effects of nodes. Furthermore, the relational time-series
causal inference models are able to estimate local effects for individual nodes
by exploiting local node-centric temporal dependencies and
topological/structural dependencies. We show that simpler causal models that do
not consider the graph topology are recovered as special cases of the proposed
relational time-series causal inference model. We describe the conditions under
which the resulting estimate can be used to estimate a causal effect, and
describe how the Durbin-Wu-Hausman test of specification can be used to test
for the consistency of the proposed estimator from data. Empirically, we
demonstrate the effectiveness of the causal inference models on both synthetic
data with known ground-truth and a large-scale observational relational
time-series data set collected from Wikipedia.
