# Random weighting in LASSO regression

arXiv: https://arxiv.org/abs/2002.02629 · HTML: https://mlsanity.com/paper/2002.02629/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

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

- [Nonparametric posterior learning for emission tomography with multimodal data](https://mlsanity.com/paper/2108.00866/) (2021)
- [Error Controlled Feature Selection for Ultrahigh Dimensional and Highly Correlated Feature Space Using Deep Learning](https://mlsanity.com/paper/2209.07011/) (2022)

## Abstract (arXiv)

We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters λn and suitable regularity conditions. The random-weighting methods in view concern repeated optimization of a randomized objective function, motivated by the need for computational approximations to Bayesian posterior sampling. In the context of LASSO regression, we repeatedly assign analyst-drawn random weights to terms in the objective function (including the penalty terms), and optimize to obtain a sample of random-weighting estimators. We show that existing approaches have conditional model selection consistency and conditional asymptotic normality at different growth rates of λn as n → ∞. We propose an extension to the available random-weighting methods and establish that the resulting samples attain conditional sparse normality and conditional consistency in a growing-dimension setting. We find that random-weighting has both approximate-Bayesian and sampling-theory interpretations. Finally, we illustrate the proposed methodology via extensive simulation studies and a benchmark data example.