# An Interactive Greedy Approach to Group Sparsity in High Dimensions

arXiv: https://arxiv.org/abs/1707.02963 · HTML: https://mlsanity.com/paper/1707.02963/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2017.

## Built on by (most cited first, 1 of 1)

- [A Splicing Approach to Best Subset of Groups Selection](https://mlsanity.com/paper/2104.12576/) (2021)

## Abstract (arXiv)

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.