  Diffusion processes in networks are increasingly used to model the spread of
information and social influence. In several applications in computational
sustainability such as the spread of wildlife, infectious diseases and traffic
mobility pattern, the observed data often consists of only aggregate
information. In this work, we present new models that generalize standard
diffusion processes to such collective settings. We also present optimization
based techniques that can accurately learn the underlying dynamics of the given
contagion process, including the hidden network structure, by only observing
the time a node becomes active and the associated aggregate information.
Empirically, our technique is highly robust and accurately learns network
structure with more than 90% recall and precision. Results on real-world flu
spread data in the US confirm that our technique can also accurately model
infectious disease spread.
