论文标题
广播的非参数张量回归
Broadcasted Nonparametric Tensor Regression
论文作者
论文摘要
我们提出了对广播操作的新颖使用，该操作将单变量函数分布到张量协变量的所有条目中，以非张量回归中的非线性对非线性进行建模。提出了惩罚估计和相应的算法。我们的理论研究允许张量协变量的尺寸发散，表明所提出的估计得出的收敛速率。我们还提供了一个Minimax下限，该界限表征了所提出的估计器在各种场景中的最佳性。进行数值实验以确认理论发现，它们表明所提出的模型比其现有线性对应物具有优势。
We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation yields a desirable convergence rate. We also provide a minimax lower bound, which characterizes the optimality of the proposed estimator for a wide range of scenarios. Numerical experiments are conducted to confirm the theoretical findings, and they show that the proposed model has advantages over its existing linear counterparts.
