  We study the problem of learning influence functions under incomplete
observations of node activations. Incomplete observations are a major concern
as most (online and real-world) social networks are not fully observable. We
establish both proper and improper PAC learnability of influence functions
under randomly missing observations. Proper PAC learnability under the
Discrete-Time Linear Threshold (DLT) and Discrete-Time Independent Cascade
(DIC) models is established by reducing incomplete observations to complete
observations in a modified graph. Our improper PAC learnability result applies
for the DLT and DIC models as well as the Continuous-Time Independent Cascade
(CIC) model. It is based on a parametrization in terms of reachability
features, and also gives rise to an efficient and practical heuristic.
Experiments on synthetic and real-world datasets demonstrate the ability of our
method to compensate even for a fairly large fraction of missing observations.
