  Genome-scale gene networks contain regulatory genes called hubs that have
many interaction partners. These genes usually play an essential role in gene
regulation and cellular processes. Despite recent advancements in
high-throughput technology, inferring gene networks with hub genes from
high-dimensional data still remains a challenging problem. Novel statistical
network inference methods are needed for efficient and accurate reconstruction
of hub networks from high-dimensional data. To address this challenge we
propose DW-Lasso, a degree weighted Lasso (least absolute shrinkage and
selection operator) method which infers gene networks with hubs efficiently
under the low sample size setting. Our network reconstruction approach is
formulated as a two stage procedure: first, the degree of networks is estimated
iteratively, and second, the gene regulatory network is reconstructed using
degree information. A useful property of the proposed method is that it
naturally favors the accumulation of neighbors around hub genes and thereby
helps in accurate modeling of the high-throughput data under the assumption
that the underlying network exhibits hub structure. In a simulation study, we
demonstrate good predictive performance of the proposed method in comparison to
traditional Lasso type methods in inferring hub and scale-free graphs. We show
the effectiveness of our method in an application to microarray data of
\textit{E.coli} and RNA sequencing data of Kidney Clear Cell Carcinoma from The
Cancer Genome Atlas datasets.
