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Sparse Regression Incorporating Graphical Structure Among Predictors

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  • Guan Yu
  • Yufeng Liu

Abstract

With the abundance of high-dimensional data in various disciplines, sparse regularized techniques are very popular these days. In this article, we make use of the structure information among predictors to improve sparse regression models. Typically, such structure information can be modeled by the connectivity of an undirected graph using all predictors as nodes of the graph. Most existing methods use this undirected graph edge-by-edge to encourage the regression coefficients of corresponding connected predictors to be similar. However, such methods do not directly use the neighborhood information of the graph. Furthermore, if there are more edges in the predictor graph, the corresponding regularization term will be more complicated. In this article, we incorporate the graph information node-by-node, instead of edge-by-edge as used in most existing methods. Our proposed method is very general and it includes adaptive Lasso, group Lasso, and ridge regression as special cases. Both theoretical and numerical studies demonstrate the effectiveness of the proposed method for simultaneous estimation, prediction, and model selection. Supplementary materials for this article are available online.

Suggested Citation

  • Guan Yu & Yufeng Liu, 2016. "Sparse Regression Incorporating Graphical Structure Among Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 707-720, April.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:514:p:707-720
    DOI: 10.1080/01621459.2015.1034319
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    References listed on IDEAS

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    Cited by:

    1. Mengyun Wu & Fan Wang & Yeheng Ge & Shuangge Ma & Yang Li, 2023. "Bi‐level structured functional analysis for genome‐wide association studies," Biometrics, The International Biometric Society, vol. 79(4), pages 3359-3373, December.
    2. Qihuang Zhang & Grace Y. Yi, 2023. "Generalized network structured models with mixed responses subject to measurement error and misclassification," Biometrics, The International Biometric Society, vol. 79(2), pages 1073-1088, June.
    3. Rafael Blanquero & Emilio Carrizosa & Pepa Ramírez-Cobo & M. Remedios Sillero-Denamiel, 2021. "A cost-sensitive constrained Lasso," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 121-158, March.
    4. Liu, Jianyu & Yu, Guan & Liu, Yufeng, 2019. "Graph-based sparse linear discriminant analysis for high-dimensional classification," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 250-269.
    5. Linh H. Nghiem & Francis K. C. Hui & Samuel Müller & Alan H. Welsh, 2022. "Estimation of graphical models for skew continuous data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1811-1841, December.

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