An Explicit Mean-Covariance Parameterization for Multivariate Response Linear Regression
An Explicit Mean-Covariance Parameterization for Multivariate Response Linear Regression
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DOI：
10.1080/10618600.2020.1853551
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发表时间：
2018-08
影响因子：
2.4
通讯作者：
Aaron J. Molstad;Guangwei Weng;Charles R. Doss;Adam J. Rothman
中科院分区：
文献类型：
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作者：
Aaron J. Molstad;Guangwei Weng;Charles R. Doss;Adam J. Rothman
摘要利用回归系数矩阵与误差协方差矩阵之间的参数联系，提出了一种拟合多元响应线性回归模型的新方法。具体地，我们假设多变量误差随机向量中的条目之间的相关性与其对应的回归系数矩阵列之间的角度的余弦成比例，因此随着两个回归系数矩阵列之间的角度减小，对应误差之间的相关性增大。我们强调两种模型下，这种参数化出现：潜变量降秩回归模型和误差变量回归模型。我们提出了一种新的非凸加权残差平方和准则，利用这种参数化，并承认一类新的惩罚估计。该优化算法采用加速近端梯度下降算法求解。我们的方法用于研究在NCI-60细胞系上测量的microRNA表达和癌症药物活性之间的关联。一个实现我们方法的R包MCMVR可以在线获得。
Abstract We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding regression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. We highlight two models under which this parameterization arises: a latent variable reduced-rank regression model and the errors-in-variables regression model. We propose a novel nonconvex weighted residual sum of squares criterion which exploits this parameterization and admits a new class of penalized estimators. The optimization is solved with an accelerated proximal gradient descent algorithm. Our method is used to study the association between microRNA expression and cancer drug activity measured on the NCI-60 cell lines. An R package implementing our method, MCMVR, is available online.