In this article, we develop a new ℓ0-based sparse Poisson graphical model with applications to gene network inference from RNA-seq gene expression count data. Assuming a pair-wise Markov property, we propose to fit a separate broken adaptive ridge-regularized log-linear Poisson regression on each node to evaluate the conditional, instead of marginal, association between two genes in the presence of all other genes. The resulting sparse gene networks are generally more accurate than those generated by the ℓ1-regularized Poisson graphical model as demonstrated by our empirical studies. A real data illustration is given on a kidney renal clear cell carcinoma micro-RNA-seq data from the Cancer Genome Atlas.
Keywords: Markov networks; Poisson graphical models; graphical models; next generation sequencing data; ℓ0 regularization.