Abstract: High-dimensional matrix data are common in modern data analysis. Simply applying Lasso after vectorizing the observations ignores essential row and column information inherent in such data, rendering variable selection results less useful. In this paper, we propose a new approach that takes advantage of the structural information. The estimate is easy to compute and possesses favorable theoretical properties. Compared with Lasso, the new estimate can recover the sparse structure in both rows and columns under weaker assumptions. Simulations demonstrate its better performance in variable selection and convergence rate, compared to methods that ignore such information. An application to a dataset in medical science shows the usefulness of the proposal.

Key words and phrases: High-dimensional data, Lasso, model selection, non-asymptotic bounds, restricted eigenvalues, structured Lasso.