Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with unknown shapes and discontinuous jumps on the boundaries. Moreover, the relationship between the response and the tensor covariates can be nonlinear. In this article, we develop a nonlinear Bayesian tensor additive regression model to accommodate such spatial structure. A functional fused elastic net prior is proposed over the additive component functions to comprehensively model the nonlinearity and spatial smoothness, detect the discontinuous jumps, and simultaneously identify the active regions. The great flexibility and interpretability of the proposed method against the alternatives are demonstrated by a simulation study and an analysis on facial feature data.
翻译:在许多应用中,用于预测的振动共变区往往与未知形状和边界上不连续跳跃在空间上相连;此外,响应和振动共变之间的关系可以是非线性关系;在本篇文章中,我们开发了一个非线性巴雅斯山高频叠加回归模型,以适应这种空间结构;提议在添加成分功能上先设置一个功能引信弹性网,以全面模拟非线性和空间平稳性,探测不连续跳动,并同时识别活动区域;模拟研究和分析面部特征数据,显示拟议方法相对于替代方法的巨大灵活性和可解释性。