# On Regularized Sparse Logistic Regression

arXiv: https://arxiv.org/abs/2309.05925 · HTML: https://mlsanity.com/paper/2309.05925/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 12 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [A Survey on Nonconvex Regularization Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning](https://mlsanity.com/paper/1808.05403/) (2018)
- [High-dimensional classification by sparse logistic regression](https://mlsanity.com/paper/1706.08344/) (2017)
- [Efficient DC Algorithm for Constrained Sparse Optimization](https://mlsanity.com/paper/1701.08498/) (2017)
- [Rethinking Symmetric Matrix Factorization: A More General and Better Clustering Perspective](https://mlsanity.com/paper/2209.02528/) (2022)
- [MIST: L0 Sparse Linear Regression with Momentum](https://mlsanity.com/paper/1409.7193/) (2014)
- [Nonconvex Sparse Logistic Regression with Weakly Convex Regularization](https://mlsanity.com/paper/1708.02059/) (2017)
- [Graph-Sparse Logistic Regression](https://mlsanity.com/paper/1712.05510/) (2017)
- [Enriched Robust Multi-View Kernel Subspace Clustering](https://mlsanity.com/paper/2205.10495/) (2022)
- [Multi-Task Learning with Prior Information](https://mlsanity.com/paper/2301.01572/) (2023)

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

- [Accelerated Neural Network Training with Rooted Logistic Objectives](https://mlsanity.com/paper/2310.03890/) (2023)

## Abstract (arXiv)

Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve ℓ1-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic regression with nonconvex regularization term. In this paper, we propose a unified framework to solve ℓ1-regularized logistic regression, which can be naturally extended to nonconvex regularization term, as long as certain requirement is satisfied. In addition, we also utilize a different line search criteria to guarantee monotone convergence for various regularization terms. Empirical experiments on binary classification tasks with real-world datasets demonstrate our proposed algorithms are capable of performing classification and feature selection effectively at a lower computational cost.