Identification of supervised and sparse functional genomic pathways.

Functional pathways involve a series of biological alterations that may result in the occurrence of many diseases including cancer. With the availability of various "omics" technologies it becomes feasible to integrate information from a hierarchy of biological layers to provide a more comprehensive understanding to the disease. In many diseases, it is believed that only a small number of networks, each relatively small in size, drive the disease. Our goal in this study is to develop methods to discover these functional networks across biological layers correlated with the phenotype. We derive a novel Network Summary Matrix (NSM) that highlights potential pathways conforming to least squares regression relationships. An algorithm called Decomposition of Network Summary Matrix via Instability (DNSMI) involving decomposition of NSM using instability regularization is proposed. Simulations and real data analysis from The Cancer Genome Atlas (TCGA) program will be shown to demonstrate the performance of the algorithm.