  Sparsity learning with known grouping structure has received considerable
attention due to wide modern applications in high-dimensional data analysis.
Although advantages of using group information have been well-studied by
shrinkage-based approaches, benefits of group sparsity have not been
well-documented for greedy-type methods, which much limits our understanding
and use of this important class of methods. In this paper, generalizing from a
popular forward-backward greedy approach, we propose a new interactive greedy
algorithm for group sparsity learning and prove that the proposed greedy-type
algorithm attains the desired benefits of group sparsity under high dimensional
settings. An estimation error bound refining other existing methods and a
guarantee for group support recovery are also established simultaneously. In
addition, we incorporate a general M-estimation framework and introduce an
interactive feature to allow extra algorithm flexibility without compromise in
theoretical properties. The promising use of our proposal is demonstrated
through numerical evaluations including a real industrial application in human
activity recognition at home. Supplementary materials for this article are
available online.
