  We consider the problem of estimating social influence, the effect that a
person's behavior has on the future behavior of their peers. The key challenge
is that shared behavior between friends could be equally explained by influence
or by two other confounding factors: 1) latent traits that caused people to
both become friends and engage in the behavior, and 2) latent preferences for
the behavior. This paper addresses the challenges of estimating social
influence with three contributions. First, we formalize social influence as a
causal effect, one which requires inferences about hypothetical interventions.
Second, we develop Poisson Influence Factorization (PIF), a method for
estimating social influence from observational data. PIF fits probabilistic
factor models to networks and behavior data to infer variables that serve as
substitutes for the confounding latent traits. Third, we develop assumptions
under which PIF recovers estimates of social influence. We empirically study
PIF with semi-synthetic and real data from Last.fm, and conduct a sensitivity
analysis. We find that PIF estimates social influence most accurately compared
to related methods and remains robust under some violations of its assumptions.
