# An error bound for Lasso and Group Lasso in high dimensions

arXiv: https://arxiv.org/abs/1912.11398 · HTML: https://mlsanity.com/paper/1912.11398/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2019.

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

- [Directional FDR Control for Sub-Gaussian Sparse GLMs](https://mlsanity.com/paper/2105.00393/) (2021)
- [The non-overlapping statistical approximation to overlapping group lasso](https://mlsanity.com/paper/2211.09221/) (2022)

## Abstract (arXiv)

We leverage recent advances in high-dimensional statistics to derive new L2 estimation upper bounds for Lasso and Group Lasso in high-dimensions. For Lasso, our bounds scale as (k^*/n) log(p/k^*)---n× p is the size of the design matrix and k^* the dimension of the ground truth boldsymbolβ^*---and match the optimal minimax rate. For Group Lasso, our bounds scale as (s^*/n) logleft( G / s^* right) + m^* / n---G is the total number of groups and m^* the number of coefficients in the s^* groups which contain boldsymbolβ^*---and improve over existing results. We additionally show that when the signal is strongly group-sparse, Group Lasso is superior to Lasso.