Inferring gene regulatory relationships with a high‐dimensional robust approach

Gene expression (GE) levels have important biological and clinical implications. They are regulated by copy number alterations (CNAs). Modeling the regulatory relationships between GEs and CNAs facilitates understanding disease biology and can also have values in translational medicine. The expression level of a gene can be regulated by its cis‐acting as well as trans‐acting CNAs, and the set of trans‐acting CNAs is usually not known, which poses a high‐dimensional selection and estimation problem. Most of the existing studies share a common limitation in that they cannot accommodate long‐tailed distributions or contamination of GE data. In this study, we develop a high‐dimensional robust regression approach to infer the regulatory relationships between GEs and CNAs. A high‐dimensional regression model is used to accommodate the effects of both cis‐acting and trans‐acting CNAs. A density power divergence loss function is used to accommodate long‐tailed GE distributions and contamination. Penalization is adopted for regularized estimation and selection of relevant CNAs. The proposed approach is effectively realized using a coordinate descent algorithm. Simulation shows that it has competitive performance compared to the nonrobust benchmark and the robust LAD (least absolute deviation) approach. We analyze TCGA (The Cancer Genome Atlas) data on cutaneous melanoma and study GE‐CNA regulations in the RAP (regulation of apoptosis) pathway, which further demonstrates the satisfactory performance of the proposed approach.