# Asymptotic Confidence Regions for High-dimensional Structured Sparsity

arXiv: https://arxiv.org/abs/1706.09231 · HTML: https://mlsanity.com/paper/1706.09231/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2017.

## Built on by (most cited first, 2 of 2)

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

## Abstract (arXiv)

In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero coefficients. This is done by desparsifying the estimator as in van de Geer et al. [18] and van de Geer and Stucky [17], then using an appropriate estimator for the precision matrix Theta. In order to estimate the precision matrix a corresponding structured matrix norm penalty has to be introduced. After normalization the result is an asymptotic pivot. The asymptotic behavior is studied and simulations are added to study the differences between the two schemes.