A method is introduced to perform simultaneous sparse dimension reduction on two blocks of variables. Beyond dimension reduction, it also yields an estimator for multivariate regression with the capability to intrinsically deselect uninformative variables in both independent and dependent blocks. An algorithm is provided that leads to a straightforward implementation of the method. The benefits of simultaneous sparse dimension reduction are shown to carry through to enhanced capability to predict a set of multivariate dependent variables jointly. Both in a simulation study and in two chemometric applications, the new method outperforms its dense counterpart, as well as multivariate partial least squares.

翻译：本文提出了一种对双变量块进行同时稀疏降维的方法。该方法不仅实现降维，还能作为多元回归的估计器，具备从自变量块和因变量块中自动剔除无关变量的能力。文中提供了实现该方法的简明算法。研究表明，同时稀疏降维的优势体现在能显著提升对多元因变量集的联合预测能力。在模拟研究和两个化学计量学应用中，新方法均优于其稠密对应方法以及多元偏最小二乘法。