Recent research has demonstrated that information learned from building a graphical model on the predictor set of a regularized linear regression model can be leveraged to improve prediction of a continuous outcome. In this article, we present a new model that encourages sparsity at both the level of the regression coefficients and the level of individual contributions in a decomposed representation. This model provides parameter estimates with a finite sample error bound and exhibits robustness to errors in the input graph structure. Through a simulation study and the analysis of two real data sets, we demonstrate that our model provides a predictive benefit when compared to previously proposed models. Furthermore, it is a highly flexible model that provides a unified framework for the fitting of many commonly used regularized regression models. The Canadian Journal of Statistics 47: 729–747; 2019 © 2019 Statistical Society of Canada

中文翻译：

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在预测变量中纳入图形结构的双稀疏回归

最近的研究表明，可以利用在正则化线性回归模型的预测变量集上建立图形模型所学到的信息来改善对连续结果的预测。在本文中，我们提出了一个新模型，该模型鼓励在分解系数的水平和分解表示形式的个人贡献水平上都保持稀疏性。该模型为参数估计提供了有限的样本误差范围，并显示了对输入图形结构中误差的鲁棒性。通过仿真研究和对两个真实数据集的分析，我们证明了与以前提出的模型相比，我们的模型可提供预测利益。此外，它是一个高度灵活的模型，为许多常用的正则化回归模型的拟合提供了统一的框架。《加拿大统计杂志》 47：729–747；2019©2019加拿大统计学会