UCSC-SOE-18-16: High Dimensional Bayesian Network Classification with Low Rank and Sparse Shrinkage Priors

Sharmistha Guha and Abel Rodriguez
12/17/2018 09:32 AM
This article proposes a novel Bayesian classification framework for networks with labeled nodes. While literature on statistical modeling of network data typically involves analysis of a single network, the recent emergence of complex datasets in several biological applications, including brain imaging studies, presents a pressing need to devise a network classifier for every individual.
This article considers one such application from a brain connectome study, where the overarching goal is to classify subjects into two separate groups based on their brain network data, along with identifying influential regions of interest (ROIs) (referred to as nodes). Existing approaches either treat all edge weights as a long vector or summarize the network information with a few summary measures. Both these approaches ignore the full network structure, may lead to less desirable inference in small samples and are not designed to identify significant network nodes. We propose a novel binary logistic regression framework with the network as the predictor and a binary response, the network predictor coefficient being modeled using an additive structure having a low-rank and a sparse component. The framework is able to accurately detect both nodes and edges in the network influencing the classification. Our framework is implemented using an efficient Markov Chain Monte Carlo algorithm.
Theoretically, we show asymptotically optimal classification for the proposed framework when the number of network edges grows faster than the sample size. The framework is empirically validated by extensive simulation studies and analysis of a brain connectome data.