  Recent years have seen a lot of progress in algorithms for learning
parameters of spreading dynamics from both full and partial data. Some of the
remaining challenges include model selection under the scenarios of unknown
network structure, noisy data, missing observations in time, as well as an
efficient incorporation of prior information to minimize the number of samples
required for an accurate learning. Here, we introduce a universal learning
method based on scalable dynamic message-passing technique that addresses these
challenges often encountered in real data. The algorithm leverages available
prior knowledge on the model and on the data, and reconstructs both network
structure and parameters of a spreading model. We show that a linear
computational complexity of the method with the key model parameters makes the
algorithm scalable to large network instances.
