# A Short Note of Comparison between Convex and Non-convex Penalized Likelihood

arXiv: https://arxiv.org/abs/2502.07655 · HTML: https://mlsanity.com/paper/2502.07655/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2025.

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

- [Review on Determining the Number of Communities in Network Data](https://mlsanity.com/paper/2503.00352/) (2025)

## Abstract (arXiv)

This paper compares convex and non-convex penalized likelihood methods in high-dimensional statistical modeling, focusing on their strengths and limitations. Convex penalties, like LASSO, offer computational efficiency and strong theoretical guarantees but often introduce bias in parameter estimation. Non-convex penalties, such as SCAD and MCP, reduce bias and achieve oracle properties but pose optimization challenges due to non-convexity. The paper highlights key differences in bias-variance trade-offs, computational complexity, and robustness, offering practical guidance for method selection. It concludes that the choice depends on the problem context, balancing accuracy