# Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties

arXiv: https://arxiv.org/abs/1901.04469 · HTML: https://mlsanity.com/paper/1901.04469/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2019.

## Built on by (most cited first, 1 of 1)

- [Asymptotic Behavior of Multi--Task Learning: Implicit Regularization and Double Descent Effects](https://mlsanity.com/paper/2603.05060/) (2026)

## Abstract (arXiv)

In this letter, we consider the problem of recovering an unknown sparse signal from noisy linear measurements, using an enhanced version of the popular Elastic-Net (EN) method. We modify the EN by adding a box-constraint, and we call it the Box-Elastic Net (Box-EN). We assume independent identically distributed (iid) real Gaussian measurement matrix with additive Gaussian noise. In many practical situations, the measurement matrix is not perfectly known, and so we only have a noisy estimate of it. In this work, we precisely characterize the mean squared error and the probability of support recovery of the Box-Elastic Net in the high-dimensional asymptotic regime. Numerical simulations validate the theoretical predictions derived in the paper and also show that the boxed variant outperforms the standard EN.