Sparse-Group Lasso for Graph Learning From Multi-Attribute Data

We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar random variable with each node. In multi-attribute graphical models, each node represents a random vector. In this paper, we present a sparse-group lasso based penalized log-likelihood approach for graph learning from multi-attribute data. Existing works on multi-attribute graphical modeling have considered only group lasso penalty. The main objective of this paper is to explore the use of sparse-group lasso for multi-attribute graph estimation. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function to estimate the inverse covariance matrix. Sufficient conditions for consistency and sparsistency of the estimator are provided. Numerical results based on synthetic as well as real data are presented.