A Bayesian Framework for Estimating Properties of Network Dilusions

The analysis of network connections, diusion processes and cascades
is of practical and academic interest across many disciplines. Many prob-
lems in this analysis involve evaluating properties of the diusion network.
However, these properties often involve variables that are not explicitly
observed in real world diusions, such as the network connection strengths
and the diusion paths of infections over the network. These hidden vari-
ables therefore need to be estimated for these properties to be evaluated.
In this paper, we propose and study this novel problem in a Bayesian
framework by capturing the posterior distribution of these hidden vari-
ables given the observed cascades, and computing the expectation of these
properties under this posterior distribution. We identify and characterize
interesting network diusion properties whose expectations can be com-
puted exactly and eciently, either wholly or in part. For properties that
are not `nice' in this sense, we propose a Gibbs Sampling framework for
Monte-Carlo integration. In detailed experiments using various network
diusion properties over multiple synthetic and real datasets, we demon-
strate that the proposed approach is signicantly more accurate than a
frequentist plug-in baseline. We also propose a map-reduce implementa-
tion of our framework and demonstrate that this scales easily for large
datasets.