  While the study of a single network is well-established, technological
advances now allow for the collection of multiple networks with relative ease.
Increasingly, anywhere from several to thousands of networks can be created
from brain imaging, gene co-expression data, or microbiome measurements. And
these networks, in turn, are being looked to as potentially powerful features
to be used in modeling. However, with networks being non-Euclidean in nature,
how best to incorporate them into standard modeling tasks is not obvious. In
this paper, we propose a Bayesian modeling framework that provides a unified
approach to binary classification, anomaly detection, and survival analysis
with network inputs. We encode the networks in the kernel of a Gaussian process
prior via their pairwise differences and we discuss several choices of provably
positive definite kernel that can be plugged into our models. Although our
methods are widely applicable, we are motivated here in particular by
microbiome research (where network analysis is emerging as the standard
approach for capturing the interconnectedness of microbial taxa across both
time and space) and its potential for reducing preterm delivery and improving
personalization of prenatal care.
