Graph-assisted inverse regression for count data and its application to sequencing data

Multivariate count data, such as sequencing reads in genomics, are often connected to a clinical phenotype of interest. We develop a flexible framework for dimension reduction in regression, with predictors that are correlated counts, by modelling the conditional distribution of the predictors, given the response, using a pairwise Poisson graphical model. This new framework, called Network-based Inverse Regression for Counts (NIRC), allows us to derive a sufficient reduction of the predictors, while adjusting for the dependence structure among them. We propose a regularized criterion for estimating both the reduction structure and the network structure. The estimation algorithm can be implemented efficiently on a parallel computer. We also introduce an adaptive version and a sparse variant of the proposed procedure. The methods are evaluated on simulated data, and are applied to a gut microbiome sequencing data set. Supplemental materials for the article are available online.