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While the study of a single network is well-established, technologicaladvances now allow for the collection of multiple networks with relative ease.Increasingly, anywhere from several to thousands of networks can be createdfrom brain imaging, gene co-expression data, or microbiome measurements. Andthese networks, in turn, are being looked to as potentially powerful featuresto be used in modeling. However, with networks being non-Euclidean in nature,how best to incorporate them into standard modeling tasks is not obvious. Inthis paper, we propose a Bayesian modeling framework that provides a unifiedapproach to binary classification, anomaly detection, and survival analysiswith network inputs. We encode the networks in the kernel of a Gaussian processprior via their pairwise differences and we discuss several choices of provablypositive definite kernel that can be plugged into our models. Although ourmethods are widely applicable, we are motivated here in particular bymicrobiome research (where network analysis is emerging as the standardapproach for capturing the interconnectedness of microbial taxa across bothtime and space) and its potential for reducing preterm delivery and improvingpersonalization of prenatal care.

Bayesian classification, anomaly detection, and survival analysis using network inputs with application to the microbiome