Spline-Lasso in High-Dimensional Linear Regression

Guo, Jianhua; Hu, Jiun-Ruey; Jing, Bing-Yi; Zhang, Zhen

doi:10.1080/01621459.2015.1005839

Cited by 30 publications

(31 citation statements)

References 22 publications

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“…Guo et al . () shows that the spline type penalty can outperform these alternatives. Another advantage of the spline type penalty is that the quadratic form is computationally more manageable than, for example, the absolute‐value‐based.…”

Section: Methodsmentioning

confidence: 99%

“…With main G effects, some alternatives, such as the fused lasso and smooth lasso, promote first-order smoothness, while this penalty promotes second-order smoothness. Guo et al (2016) shows that the spline type penalty can outperform these alternatives. Another advantage of the spline type penalty is that the quadratic form is computationally more manageable than, for example, the absolute-value-based.…”

Section: Methodsmentioning

confidence: 99%

“…Consider the adjacency structure of SNPs (and other densely measured G factors). The available penalization approaches include the fused lasso (Tibshirani et al, 2005), smooth lasso (Hebiri and van de Geer, 2011), smoothed group lasso (Liu et al, 2012), spline lasso (Guo et al, 2016), and others. When gene expressions (and other G measurements) are described using network structures, network-constrained regularized estimation is proposed.…”

Section: Introductionmentioning

confidence: 99%

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Structured gene‐environment interaction analysis

Zhang

2019

Biometrics

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For the etiology, progression, and treatment of complex diseases, gene‐environment (G‐E) interactions have important implications beyond the main G and E effects. G‐E interaction analysis can be more challenging with higher dimensionality and need for accommodating the “main effects, interactions” hierarchy. In recent literature, an array of novel methods, many of which are based on the penalization technique, have been developed. In most of these studies, however, the structures of G measurements, for example, the adjacency structure of single nucleotide polymorphisms (SNPs; attributable to their physical adjacency on the chromosomes) and the network structure of gene expressions (attributable to their coordinated biological functions and correlated measurements) have not been well accommodated. In this study, we develop structured G‐E interaction analysis, where such structures are accommodated using penalization for both the main G effects and interactions. Penalization is also applied for regularized estimation and selection. The proposed structured interaction analysis can be effectively realized. It is shown to have consistency properties under high‐dimensional settings. Simulations and analysis of GENEVA diabetes data with SNP measurements and TCGA melanoma data with gene expression measurements demonstrate its competitive practical performance.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Structured gene‐environment interaction analysis

Zhang

2019

Biometrics

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“…Hebiri and Van introduced “smooth‐lasso,” where the smoothness between

(β_{j, 1}, \dots, β_{j, q_{j}})

were encouraged by L 2 ‐penalty

\sum_{m = 2}^{q_{j}} {(β_{j, m + 1} - β_{j, m})}^{2}

. Guo et al suggested

\sum_{m = 2}^{q_{j} - 1} {(Δ_{m}^{(2)} β_{j})}^{2}

, where Δ m β j =:(β j , m +1 −β j , m ), and

Δ_{m}^{(2)} β_{j} = : (Δ_{m} β_{j} - Δ_{m - 1} β_{j}) = β_{j, m + 1} - 2 β_{j, m} + β_{j, m - 1}

. Motivating from the ideas of these two methods to capture the smooth features in a group, we propose two types of penalties to capture smoothing changes in each group, which are named the group spline‐penalty and group smooth‐penalty , respectively.…”

Section: Methodsmentioning

confidence: 99%

“…Hebiri and Van 11 introduced "smooth-lasso," where the smoothness between ( j,1 , … , j,q j ) were encouraged by L 2 -penalty ∑q j m=2 ( j,m+1 − j,m ) 2 . Guo et al 13 suggested…”

Section: The Model Setting and Methodologymentioning

confidence: 99%

Structured sparse logistic regression with application to lung cancer prediction using breath volatile biomarkers

Zhang

et al. 2019

Statistics in Medicine

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This article is motivated by a study of lung cancer prediction using breath volatile organic compound (VOC) biomarkers, where the challenge is that the predictors include not only high‐dimensional time‐dependent or functional VOC features but also the time‐independent clinical variables. We consider a high‐dimensional logistic regression and propose two different penalties: group spline‐penalty or group smooth‐penalty to handle the group structures of the time‐dependent variables in the model. The new methods have the advantage for the situation where the model coefficients are sparse but change smoothly within the group, compared with other existing methods such as the group lasso and the group bridge approaches. Our methods are easy to implement since they can be turned into a group minimax concave penalty problem after certain transformations. We show that our fitting algorithm possesses the descent property and leads to attractive convergence properties. The simulation studies and the lung cancer application are performed to demonstrate the accuracy and stability of the proposed approaches.

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Revealing genomic heterogeneity and commonality: A penalized integrative analysis approach accounting for the adjacency structure of measurements

Wang,

Jiang,

Sun

2024

Genetic Epidemiology

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Advancements in high‐throughput genomic technologies have revolutionized the field of disease biomarker identification by providing large‐scale genomic data. There is an increasing focus on understanding the relationships among diverse patient groups with distinct disease subtypes and characteristics. Complex diseases exhibit both heterogeneity and shared genomic factors, making it essential to investigate these patterns to accurately detect markers and comprehensively understand the diseases. Integrative analysis has emerged as a promising approach to address this challenge. However, existing studies have been limited by ignoring the adjacency structure of genomic measurements, such as single nucleotide polymorphisms (SNPs) and DNA methylations. In this study, we propose a structured integrative analysis method that incorporates a spline type penalty to accommodate this adjacency structure. We utilize a fused lasso type penalty to identify both heterogeneity and commonality across the groups. Extensive simulations demonstrate its superiority compared to several direct competing methods. The analysis of The Cancer Genome Atlas melanoma data with DNA methylation measurements and GENEVA diabetes data with SNP measurements exhibit that the proposed analysis lead to meaningful findings with better prediction performance and higher selection stability.

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Spline-Lasso in High-Dimensional Linear Regression

Cited by 30 publications

References 22 publications

Structured gene‐environment interaction analysis

Structured gene‐environment interaction analysis

Structured sparse logistic regression with application to lung cancer prediction using breath volatile biomarkers

Revealing genomic heterogeneity and commonality: A penalized integrative analysis approach accounting for the adjacency structure of measurements

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