We focus on regression problems in which the predictors are naturally in the form of matrices. Reduced rank regression and related regularized method have been adapted to matrix regression. However, linear methods are restrictive in their expressive power. In this work, we consider a class of semiparametric additive models based on series estimation of nonlinear functions which interestingly induces a problem of 3rd order tensor regression with transformed predictors. Risk bounds for the estimator are derived and some simulation results are presented to illustrate the performances of the proposed method.

中文翻译：

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矩阵回归的半参数模型

我们专注于预测变量自然是矩阵形式的回归问题。降秩回归和相关的正则化方法已适用于矩阵回归。然而，线性方法的表达能力有限。在这项工作中，我们考虑了一类基于非线性函数序列估计的半参数加法模型，它有趣地引发了带有变换预测变量的三阶张量回归问题。推导了估计器的风险界限，并给出了一些模拟结果来说明所提出方法的性能。