  When dealing with spreading processes on networks it can be of the utmost
importance to test the reliability of data and identify potential unobserved
spreading paths. In this paper we address these problems and propose methods
for hidden layer identification and reconstruction. We also explore the
interplay between difficulty of the task and the structure of the multilayer
network describing the whole system where the spreading process occurs. Our
methods stem from an exact expression for the likelihood of a cascade in the
Susceptible-Infected model on an arbitrary graph. We then show that by
imploring statistical properties of unimodal distributions and simple
heuristics describing joint likelihood of a series of cascades one can obtain
an estimate of both existence of a hidden layer and its content with success
rates far exceeding those of a null model. We conduct our analyses on both
synthetic and real-world networks providing evidence for the viability of the
approach presented.

Physics and Society;Statistical Mechanics;Social and Information Networks;Data Analysis, Statistics and Probability