# The Benefit of Group Sparsity in Group Inference with De-biased Scaled Group Lasso

arXiv: https://arxiv.org/abs/1412.4170 · HTML: https://mlsanity.com/paper/1412.4170/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2014.

## Built on by (most cited first, 3 of 3)

- [Chi-square and normal inference in high-dimensional multi-task regression](https://mlsanity.com/paper/2107.07828/) (2021)
- [Spatially relaxed inference on high-dimensional linear models](https://mlsanity.com/paper/2106.02590/) (2021)
- [Generalized Linear Models with Structured Sparsity Estimators](https://mlsanity.com/paper/2104.14371/) (2021)

## Abstract (arXiv)

We study confidence regions and approximate chi-squared tests for variable groups in high-dimensional linear regression. When the size of the group is small, low-dimensional projection estimators for individual coefficients can be directly used to construct efficient confidence regions and p-values for the group. However, the existing analyses of low-dimensional projection estimators do not directly carry through for chi-squared-based inference of a large group of variables without inflating the sample size by a factor of the group size. We propose to de-bias a scaled group Lasso for chi-squared-based statistical inference for potentially very large groups of variables. We prove that the proposed methods capture the benefit of group sparsity under proper conditions, for statistical inference of the noise level and variable groups, large and small. Such benefit is especially strong when the group size is large.