# Support recovery and sup-norm convergence rates for sparse pivotal estimation

arXiv: https://arxiv.org/abs/2001.05401 · HTML: https://mlsanity.com/paper/2001.05401/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2020.

## 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)
- [Pivotal Auto-Encoder via Self-Normalizing ReLU](https://mlsanity.com/paper/2406.16052/) (2024)

## Abstract (arXiv)

In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its derivatives as a "non-smooth + non-smooth" optimization problem. Modern techniques to solve these include smoothing the datafitting term, to benefit from fast efficient proximal algorithms. In this work we show minimax sup-norm convergence rates for non smoothed and smoothed, single task and multitask square-root Lasso-type estimators. Thanks to our theoretical analysis, we provide some guidelines on how to set the smoothing hyperparameter, and illustrate on synthetic data the interest of such guidelines.