# Sparse Group Lasso: Optimal Sample Complexity, Convergence Rate, and Statistical Inference

arXiv: https://arxiv.org/abs/1909.09851 · HTML: https://mlsanity.com/paper/1909.09851/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2019.

## Built on by (most cited first, 5 of 5)

- [Multi-task Learning for Gaussian Graphical Regressions with High Dimensional Covariates](https://mlsanity.com/paper/2205.10672/) (2022)
- [DDAC-SpAM: A Distributed Algorithm for Fitting High-dimensional Sparse Additive Models with Feature Division and Decorrelation](https://mlsanity.com/paper/2205.07932/) (2022)
- [Anisotropic View Distance Metric for High-Dimensional Data: Theory, Geometry, and Fast Computation](https://mlsanity.com/paper/2206.05215/) (2022)
- [The non-overlapping statistical approximation to overlapping group lasso](https://mlsanity.com/paper/2211.09221/) (2022)
- [Factor-Augmented Machine Learning Panel Regressions](https://mlsanity.com/paper/2607.06368/) (2026)

## Abstract (arXiv)

We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured model -- an actively studied topic in statistics and machine learning. In the noiseless case, matching upper and lower bounds on sample complexity are established for the exact recovery of sparse vectors and for stable estimation of approximately sparse vectors, respectively. In the noisy case, upper and matching minimax lower bounds for estimation error are obtained. We also consider the debiased sparse group Lasso and investigate its asymptotic property for the purpose of statistical inference. Finally, numerical studies are provided to support the theoretical results.