Summary 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 aberrations may interact with each other, as it provides insight into the process of the disease development. In this article, we propose a novel method, LogitNet, to infer such interactions among these 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.