Efficient Dimensionality Reduction for High-Dimensional Network Estimation

We propose module graphical lasso (MGL), an aggressive dimensionality reduction and network estimation technique for a highdimensional Gaussian graphical model (GGM). MGL achieves scalability, interpretability and robustness by exploiting the modularity property of many real-world networks. Variables are organized into tightly coupled modules and a graph structure is estimated to determine the conditional independencies among modules. MGL iteratively learns the module assignment of variables, the latent variables, each corresponding to a module, and the parameters of the GGM of the latent variables. In synthetic data experiments, MGL outperforms the standard graphical lasso and three other methods that incorporate latent variables into GGMs. When applied to gene expression data from ovarian cancer, MGL outperforms standard clustering algorithms in identifying functionally coherent gene sets and predicting survival time of patients. The learned modules and their dependencies provide novel insights into cancer biology as well as identifying possible novel drug targets.