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

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 networks 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. Our methodology exploits the theory of Gaussian processes and naturally requires the use of a kernel, which we obtain by modifying the well-known Hamming distance. Moreover, kernels provide a principled way to integrate data of mixed types. We motivate and demonstrate the whole of our methodology in the area of microbiome research, where network analysis is emerging as the standard approach for capturing the interconnectedness of microbial taxa across both time and space.