Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for prediction, optimization, and control of diffusion dynamics. Unfortunately, in most cases the transmission rates are unknown and need to be reconstructed from the spreading data. Moreover, in realistic settings it is impossible to monitor the state of each node at every time, and thus the data is highly incomplete. We introduce an efficient dynamic message-passing algorithm, which is able to reconstruct parameters of the spreading model given only partial information on the activation times of nodes in the network. The method is generalizable to a large class of dynamic models, as well to the case of temporal graphs.

Very interesting and well written paper, which deals with an important problem when learning diffusion models: it may be impossible to observe the activity of every node of the network. For instance, if the source is Twitter, the streaming API only allows one to monitor the activity of about 4000 users over several millions. The proposed approach is elegant and well sounded. I enjoyed to review this paper that brought me new knowledge about learning in such complex situations. The proposal is maybe not too much innovative since it mostly employs already published techniques, but from my point of view the followed methodology deserves to be published in some main machine learning venue, at least for its pedagogical aspect.