# Network-regularized Sparse Logistic Regression Models for Clinical Risk Prediction and Biomarker Discovery

arXiv: https://arxiv.org/abs/1609.06480 · HTML: https://mlsanity.com/paper/1609.06480/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2016.

## Built on by (most cited first, 2 of 2)

- [An Accelerated Block Proximal Framework with Adaptive Momentum for Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2308.12126/) (2023)
- [Globally Convergent Accelerated Algorithms for Multilinear Sparse Logistic Regression with ℓ0-constraints](https://mlsanity.com/paper/2309.09239/) (2023)

## Abstract (arXiv)

Molecular profiling data (e.g., gene expression) has been used for clinical risk prediction and biomarker discovery. However, it is necessary to integrate other prior knowledge like biological pathways or gene interaction networks to improve the predictive ability and biological interpretability of biomarkers. Here, we first introduce a general regularized Logistic Regression (LR) framework with regularized term λ |bmw|1 + ηbmwTbmMbmw, which can reduce to different penalties, including Lasso, elastic net, and network-regularized terms with different bmM. This framework can be easily solved in a unified manner by a cyclic coordinate descent algorithm which can avoid inverse matrix operation and accelerate the computing speed. However, if those estimated bmwi and bmwj have opposite signs, then the traditional network-regularized penalty may not perform well. To address it, we introduce a novel network-regularized sparse LR model with a new penalty λ |bmw|1 + η|bmw|TbmM|bmw| to consider the difference between the absolute values of the coefficients. And we develop two efficient algorithms to solve it. Finally, we test our methods and compare them with the related ones using simulated and real data to show their efficiency.