There has been a lot of work fitting Ising models to multivariate binary data in
order to understand the conditional dependency relationships between the
variables. However, additional covariates are frequently recorded together with
the binary data, and may influence the dependence relationships.  
Motivated by such a data set on genomic instability collected from tumor
samples, we propose a covariate dependent Ising model to study both the
conditional dependency within the binary data and its relationship with the
additional covariates. We use L1 penalties to induce sparsity in the fitted
graphs and in the number of selected covariates and propose two algorithms to
fit the model. Asymptotic results are established and promising interpretations
are discovered on the data analysis.