# Likelihood Adaptively Modified Penalties

arXiv: https://arxiv.org/abs/1308.5036 · HTML: https://mlsanity.com/paper/1308.5036/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2013.

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

- [Pre-processing with Orthogonal Decompositions for High-dimensional Explanatory Variables](https://mlsanity.com/paper/2106.09071/) (2021)

## Abstract (arXiv)

A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study stability properties of the penalized maximum likelihood estimator, two types of asymptotic stability are defined. Theoretical properties, including the parameter estimation consistency, model selection consistency, and asymptotic stability, are established under suitable regularity conditions. An efficient coordinate-descent algorithm is proposed. Simulation results and real data analysis show that the proposed method has competitive performance in comparison with existing ones.