  Genomic instability, the propensity of aberrations in chromosomes, plays a
critical role in the development of many diseases. High throughput genotyping
experiments have been performed to study genomic instability in diseases. The
output of such experiments can be summarized as high dimensional binary
vectors, where each binary variable records aberration status at one marker
locus. It is of keen interest to understand how these aberrations interact with
each other. In this paper, we propose a novel method, \texttt{LogitNet}, to
infer the interactions among aberration events. The method is based on
penalized logistic regression with an extension to account for spatial
correlation in the genomic instability data. We conduct extensive simulation
studies and show that the proposed method performs well in the situations
considered. Finally, we illustrate the method using genomic instability data
from breast cancer samples.
