# A novel nonconvex, smooth-at-origin penalty for statistical learning

arXiv: https://arxiv.org/abs/2204.03123 · HTML: https://mlsanity.com/paper/2204.03123/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 42 references that are in the map.
- First posted on arXiv 6 Apr 2022.

## Builds on (most cited first, 3 of 3)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Regularized deep learning with nonconvex penalties](https://mlsanity.com/paper/1909.05142/) (2019)

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

- [Deep learning from strongly mixing observations: Sparse-penalized regularization and minimax optimality](https://mlsanity.com/paper/2406.08321/) (2024)

## Abstract (arXiv)

Nonconvex penalties are utilized for regularization in high-dimensional statistical learning algorithms primarily because they yield unbiased or nearly unbiased estimators for the parameters in the model. Nonconvex penalties existing in the literature such as SCAD, MCP, Laplace and arctan have a singularity at origin which makes them useful also for variable selection. However, in several high-dimensional frameworks such as deep learning, variable selection is less of a concern. In this paper, we present a nonconvex penalty which is smooth at origin. The paper includes asymptotic results for ordinary least squares estimators regularized with the new penalty function, showing asymptotic bias that vanishes exponentially fast. We also conducted an empirical study employing deep neural network architecture on three datasets and convolutional neural network on four datasets. The empirical study showed better performance for the new regularization approach in five out of the seven datasets.