Sparse Ising Models with Covariates
This work addresses the need to incorporate covariates into Ising models for exploratory data analysis in domains like genomics, but it is incremental as it extends existing sparse Ising methods with covariate integration.
The authors tackled the problem of modeling conditional dependencies in multivariate binary data with covariates, proposing a sparse covariate-dependent Ising model that results in subject-specific graphs, and they applied it to a tumor dataset to discuss biological significance.
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 dataset on genomic instability collected from tumor samples of several types, we propose a sparse covariate dependent Ising model to study both the conditional dependency within the binary data and its relationship with the additional covariates. This results in subject-specific Ising models, where the subject's covariates influence the strength of association between the genes. As in all exploratory data analysis, interpretability of results is important, and we use L1 penalties to induce sparsity in the fitted graphs and in the number of selected covariates. Two algorithms to fit the model are proposed and compared on a set of simulated data, and asymptotic results are established. The results on the tumor dataset and their biological significance are discussed in detail.