Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection
Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection
复制标题
DOI：
10.1080/01621459.2012.734178
复制
发表时间：
2012-12-01
影响因子：
3.7
通讯作者：
Huang, Jianhua Z.
中科院分区：
文献类型：
--
作者：
Chen, Lisha;Huang, Jianhua Z.
降秩回归是从同一组预测变量预测多个响应变量的有效方法。它减少了模型参数的哑度，并利用了模型参数之间的相互关系。响应变量，从而提高预测精度。我们建议通过使用稀疏诱导惩罚来选择降秩回归的相关变量。我们应用一个组套索类型的惩罚，将回归系数矩阵的每一行作为一个组，并表明这种惩罚满足某些理想的不变性。我们开发了两种数值算法来解决惩罚回归问题，并建立了所提出方法的渐进一致性。特别地，在我们的理论分析中，考虑和研究了降秩回归系数矩阵的流形结构。在我们的模拟研究和真实的数据分析中，新方法与现有的几种多元回归变量选择方法进行了比较，并显示出具有竞争力的性能，在预测和变量选择。
The reduced-rank regression is an effective method in predicting multiple response variables from the same set of predictor variables. It reduces the dumber of model parameters and takes advantage of interrelations between. the response variables and hence improves predictive accuracy. We propose to select relevant variables for reduced-rank regression by using a sparsity-inducing penalty. We apply a group-lasso type penalty that treats each row of the matrix of the regression coefficients as a group and show that this penalty satisfies certain desirable invariance properties. We develop two numerical algorithms to solve the penalized regression problem and establish the asymptotic consistency of the proposed method. In particular, the manifold structure of the reduced-rank regression coefficient matrix is considered and studied in our theoretical analysis. In our simulation study and real data analysis, the new method is compared with several existing variable selection methods for multivariate regression and exhibits competitive performance in prediction and variable selection.