Summary of Iterative Reweighted Framework Based Algorithms For Sparse Linear Regression with Generalized Elastic Net Penalty, by Yanyun Ding et al.
Iterative Reweighted Framework Based Algorithms for Sparse Linear Regression with Generalized Elastic Net Penalty
by Yanyun Ding, Zhenghua Yao, Peili Li, Yunhai Xiao
First submitted to arxiv on: 22 Nov 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores a generalized elastic net model that incorporates various types of noise using a _r-norm in the loss function and replaces the _1-norm with a _q-norm for enhanced robustness. The proposed model has computable lower bounds for nonzero entries at first-order stationary points, ensuring better regression performance compared to traditional elastic net methods. To solve this problem efficiently, two algorithms are developed: alternating direction method of multipliers (ADMM) and proximal majorization-minimization method (PMM), utilizing semismooth Newton method (SNN) for subproblem solutions. Experimental results with simulated and real data demonstrate the effectiveness of both algorithms, with PMM-SSN showing superior performance despite its more complex implementation. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper develops a new type of elastic net model that is better at handling noisy data. It uses a special kind of penalty to make the model more robust and then creates two ways to solve this problem: one called ADMM and another called PMM-SSN. Both methods are tested on real and made-up data, and they work well. |
Keywords
* Artificial intelligence * Loss function * Regression
