Estimation of Simultaneously Sparse and Low Rank Matrices

Understand

The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time.

• Such structures arise in the context of social networks or protein interactions where underlying graphs have adjacency matrices which are block-diagonal in the appropriate basis.
• We introduce a convex mixed penalty which involves $\ell_1$-norm and trace norm simultaneously.
• We obtain an oracle inequality which indicates how the two effects interact according to the nature of the target matrix.