  Mastering the dynamics of social influence requires separating, in a database
of information propagation traces, the genuine causal processes from temporal
correlation, i.e., homophily and other spurious causes. However, most studies
to characterize social influence, and, in general, most data-science analyses
focus on correlations, statistical independence, or conditional independence.
Only recently, there has been a resurgence of interest in "causal data
science", e.g., grounded on causality theories. In this paper we adopt a
principled causal approach to the analysis of social influence from
information-propagation data, rooted in the theory of probabilistic causation.
  Our approach consists of two phases. In the first one, in order to avoid the
pitfalls of misinterpreting causation when the data spans a mixture of several
subtypes ("Simpson's paradox"), we partition the set of propagation traces into
groups, in such a way that each group is as less contradictory as possible in
terms of the hierarchical structure of information propagation. To achieve this
goal, we borrow the notion of "agony" and define the Agony-bounded Partitioning
problem, which we prove being hard, and for which we develop two efficient
algorithms with approximation guarantees. In the second phase, for each group
from the first phase, we apply a constrained MLE approach to ultimately learn a
minimal causal topology. Experiments on synthetic data show that our method is
able to retrieve the genuine causal arcs w.r.t. a ground-truth generative
model. Experiments on real data show that, by focusing only on the extracted
causal structures instead of the whole social graph, the effectiveness of
predicting influence spread is significantly improved.
